Ebimene James Mamadu   Jude Chukwuyem Nwankwo   Ebikonbo-Owei Anthony Mamadu   Irerhievwie Oghenetega Stephen   Henrietta Ify Ojarikre   Ignatius Nkonyeasua Njoseh   and Jonathan Tsetimi   

The description of memory effects in wave propagation and anomalous diffusion is best analyzed using the time-fractional telegraph equation (TFTE), widely applicable in fluid flow, signal transmission, and biological systems. In this paper, the analytic solution of TFTE in the whole space-domain and in a half-domain is investigated using the Mamadu integral transform. For a reliable and accurate representation of hereditary and nonlocal properties in TFTE, the fractional derivatives are defined in the Caputo sense. The Mamadu Transform converts the problem into an algebraic equation to ease the solution process. The contour integration is then employed to compute the inverse Mamadu Transform, where the solution structure is determined at the poles of the transformed function via the residue theorem. Additionally, the spatial characteristics of the solution are reconstructed through the inverse Fourier transform, ensuring an adequate representation in the transformed domain. Using specific values for the parameters α,ÎČ,a,b and c, we analyze the system response by evaluating the resulting characteristic equation. The results depict the effectiveness of the Mamadu Transform, in conjunction with the inverse Fourier transform for solving the TFTE, offering systematic and flexible techniques to handle diverse problems in a complex domain.

Ebimene James Mamadu   

Integral transforms such as the Elzaki, Aboodh, Sumudu, Natural, Sawi, and Shehu transforms have been developed to tackle some complex differential equations through the substantial advancements in the application of integral transforms. To seek the improvement of convergence, stability, and accuracy when solving differential equations, the Mamadu transform is developed and implemented. The Mamadu transform is an essential analytical tool built using a well-known kernel function that incorporates a polynomial and exponential-based terms. A major advantage of the Mamadu transform is the inclusion of a weight function to improve long-term behavior and singularities in differential equations. The method involves reducing a complex differential equation to an algebraic expression, making solution derivation and manipulation simpler. Also, the method offers a well-structured and efficient problem solving. Three examples are considered to illustrate the effectiveness and effectiveness of the Mamadu transform in the solution of different differential equations. Comparing with other traditional methods shows increased accuracy, faster convergence, and higher stability. The method is equally helpful in terms of computational efficiency and accuracy for the solution of fractional calculus, where other methods fail. Furthermore, the study reflects the relevance of Mamadu transform as a renowned analytical technique in applied sciences, particularly in fields such as mathematical modeling and engineering.

Sujit K. Bose   

Transmission of data by fiber-0ptic cables over long distances in particular, is a preferred channel of communication. However, it is known that bends in such cables lead to loss of power of the carrier light wave traveling towards the desired destination, thus deteriorating the delivery process of the data packets. An analytical theory of this power loss due to the geometric macrobending only, ignoring altogether the microbending processes of microcracking and thermal heating, was presented by this author in a recent paper, in which a simplifying approximation was assumed. A simple, yet important in practice, step-index fiber with a homogeneous core and a cladding of slightly less refractive index was considered. The bend in question was ideally configured as a circular tore, and simple toroidal coordinates were employed to formulate the governing Maxwell equations for the propagating light wave. Moreover, the solution of the Maxwell equations was expressed in terms of the single Hertz vector , and as the propagation takes place in the axial direction, that equation reduces to a single toroidal wave equation for the axial component . Because of the fact that optical fibers are very thin, the toroidal equation was then approximated by a cylindrical wave equation. This lacuna is removed in this paper, and the full toroidal wave equation is treated strictly to the first order in the radial coordinate , superseding the earlier approximate theory. The present extended first order theory however yields exactly the results reported in the earlier approximate theory, in as much as the additional terms in the electric and magnetic intensities of the field, obtained from the solution for do not unexpectedly contribute to the bendloss formulae. Accordingly, as was found in the earlier approximate theory, it means that when the radius of curvature of the bend exceeds a certain critical value , the bendloss of power varies linearly with practically independent of , while if , it varies as , depending on as a factor of the form . In practice therefore, bends in a fiber-optic cable, particularly formation of unnecessary small coils, is best avoided to the extent permitted by the architecture of a given application.

Ebimene James Mamadu   Henrietta Ify Ojarikre   Jude Chukwuyem Nwankwo   Daniel Chinedu Iweobodo   Ebikonbo-Owei Anthony Mamadu   Jonathan Tsetimi   and Ignatius Nkonyeasua Njoseh   

The motivation behind this work is the recent advances in literature for seeking numerical techniques for time fractional telegraph equations. A coupled technique combining the finite difference method, -weighted method and cubic B-splines is underexplored in literature specific for time fractional telegraph equations. Also, there are limited comparative studies between cubic B-splines-based numerical schemes and other hybrid numerical methods for time fractional telegraph equation. Most studies focus on deploying standard cubic B-splines as basis functions and not orthogonal polynomials. This paper aims to find an approximate solution to the time fractional telegraph equation using discretized explicit and implicit forward difference schemes combined with the -weighted method. To achieve this, we employed cubic B-splines as basis functions to enhance the efficiency and accuracy of the solutions. The orthogonal collocation method is then employed to generate a linear system of equations, which are solved using numerical methods for the approximate solution. Two numerical examples illustrate the efficiency of this method, showing how the schemes rapidly converge when the step size is reduced. Interestingly, the results show that the implicit system outperforms the explicit design. Furthermore, the paper advances the area by proposing a new framework for solving time fractional telegraph equations that involves the application of orthogonal polynomials as basis functions, providing better accuracy and convergence.

Sujit K. Bose   

An optical fiber essentially consists of a transparent core medium with a thin cladding of a slightly less refractive index for total internal reflection of a passing signal of light. The material is usually homogeneous, but lately graded-index fiber cables are gaining increased application for greater efficiency in the propagation characteristics. Technology has evolved to furnish grading of the refractive index of the core to have different profiles. A parabolic profile of some degree is often mentioned in texts (Keiser [7], p .63), but lately profiles of various other shapes, including nonsmooth steps (Cvijetic [1], p.35) have come in to usage for better wave guide action. A theoretical study of light waves propagating through such fibers is presented in this article, based strictly on the Maxwell equations of electromagnetism solved in terms of the single Hertz vector . The dispersion equation for the guided wave propagation is obtained in general terms from the theory. The method is first developed for the case of the parabolic profile and then extended to any general form of the refractive index. Numerical computation of the dispersion equation, for the first three modes in the parabolic case, with , show interestingly enough that the dispersion curves are pairs of segmented curves having opposite curvatures. A study of a non-smooth index fiber, like that of NZDSF, is also carried out from the general method developed, for which the dispersion equation does not show any dispersion whatsoever for the fundamental mode - the purpose for which it is designed for practical use.

Anis Nelissa Abdul Hamid   Shahirulliza Shamsul Ambia   Sumarni Abu Baka   and Noratika Nordin   

This manuscript introduces a novel enhancement to the Fuzzy C-Least Median (FCLM) model by incorporating Canberra distance into Multiple Linear Regression (MLR) frameworks, aiming to address the intricate challenge of predicting ambiguity in data clustering. The study examines household income and demographic data in Malaysia and systematically assesses the performance of the MLR model alongside the proposed FCLM-CD MLR model. The evaluation includes comparisons with MLR, FCM MLR (Fuzzy C-Means Multiple Linear Regression), and FCLM MLR (Fuzzy C-Least Median Multiple Linear Regression) models. The FCLM-CD MLR model incorporates the Fuzzy C-Least Median (FCLM) algorithm, enriched with Canberra distance, to address clustering ambiguity. Key evaluation metrics such as Root Mean Square Error (RMSE) and R-Squared values are employed to assess predictive accuracy and explanatory power. Results reveal that the FCLM-CD MLR model outperforms the standard MLR model, FCM-MLR and FCLM-MLR, demonstrating superior predictive accuracy and enhanced explanatory power. The integration of FCLM with Canberra distance represents a significant methodological advancement, offering a promising approach to addressing clustering challenges and capturing variations in household income effectively. Notably, the incorporation of Canberra distance into FCLM emerges as a pivotal element in bolstering the effectiveness of predictive modelling. This study contributes to the field by overcoming clustering challenges and providing nuanced insights into the complexities of household income and demographic data. The amalgamation of FCLM and Canberra distance presents a methodological innovation with broad implications for predictive modelling across diverse domains, enriching the landscape of data analysis methodologies.

Araceli GimĂ©nez Lorente   

The application of graph theory in ethology is a relevant field, where the background of this study is focused only from the points of view of biology and chemistry. Our study is to find patterns in a specific behavior of bees, their dance. The purpose is to present the dance of bees as graphs, finding a mathematical character to animal ethology and a pattern that allows us to communicate with them. The methodology used is the observation of the dances of the hymenoptera through the viewing of videos, and bibliographic material. It is intended to analyze the communication of bees, translating their trajectory to the digraphs associated with the three different dances that we know, and through the associated matrix algebra, determine their homeomorphisms and main characteristics. The main result will be to extrapolate the schemes of the dances of the bees to directed graphs and their respective associated matrices to carry out a mathematical study. The dance of the bees is a very complex language that is analyzed with the digraphs in the sections that bear the name of the different dances, previously an introduction to these dances is made. Bees are capable of creating what we understand as a symbolic mathematical language to communicate. This is a point of connection with another intelligent species, and with the help of discrete mathematics, we can communicate; these results are partial since this study is preliminary, but necessary as a first phase. In the "discussion" section, some observations are made about this research and its possible implementation. Although this study of ethology from the mathematical point of view by approximation of graph theory is unprecedented, it is necessary for its possible future applications. For all these reasons, we see the need for this study.

Ana Vivas   Anne Fernando   and Evelyn Thomas   

The increasing importance of media's role in the transmission of diseases presents a novel dimension to be considered in disease modeling. In our study, we introduce a comprehensive model based on a system of ordinary differential equations to elucidate the dynamics of COVID-19's spread, with a particular focus on the influence of media. Utilizing established compartmental modeling approaches, our model categorizes individuals into six distinct groups: Asymptomatic, Clinically Ill, Quarantined, Hospitalized, Recovered, and Vaccinated. This classification enables a nuanced analysis of the interactions that significantly impact disease propagation. Furthermore, our model innovatively incorporates parameters specifically designed to evaluate media exposure's effect on disease transmission dynamics. Employing the Next-Generation Method, we derive an explicit formula for the Basic Reproduction Number, a critical metric in epidemiology. Our findings include the conditions necessary for achieving a Disease-Free Equilibrium, highlighting the potential for disease eradication or persistence within a population. Through stability analysis, we identify specific conditions under which COVID-19 can be either eliminated or become endemic, offering insights into effective disease management strategies. Our analysis is enriched with numerical simulations, utilizing data from the Virginia Department of Health among other sources, to validate our model's predictions. This study not only sheds light on the pivotal role of media in disease spread but also provides a foundational framework for predicting and managing the dynamics of COVID-19 transmission.

Agnella N. Mandia   Joseph K. Mung’atu   and Patrick G.O Weke   

Determination of aggregate risk as a function of dependence amongst random variables is a vital step in modelling any insurance or financial portfolio. The standard independence assumption simplifies calculations but has the downside of overstating or understating aggregate risk. Compared to comonotonicity, negative dependence has received little attention due to difficulty in extending its bivariate results into multivariate cases despite its natural risk minimization properties and potential to create internal hedging. In this paper, we investigate properties of counter-monotonicity (FrĂ©chet-Hoeffding lower bound) in higher dimensions (d ≄ 3) by restricting characteristics of individual random variables . Using Archimedean copulas, we introduce a measure of multivariate negative dependence derived from d-dimensional hypervolumes of independent and counter-monotonic distribution functions. The choice of integrals facilitates natural boundaries of the measure within (0, 1), enabling smooth derivation of its properties. In addition, we establish a moment-based version for raw statistics and a numerical example illustrating an application using an arbitrary seven-dimensional portfolio of health insurance risks. Analysts can apply the findings of this study within decentralized insurance or finance characterized by fewer risks that do not obey the Central Limit Theorem. The measure facilitates accurate measurement of portfolio countermovements and selects appropriate hedging strategies for dependent portfolios.

Kenya SuĂĄrez-DomĂ­nguez   Rocio R. Gallegos Villela   Ruth del C. Galindo-LĂłpez   Alejandra NĂșñez-Ramos   Yoana PĂ©rez-Badell   and Elena Izquierdo Kulich   

Mathematical models are essential for understanding and predicting physical phenomena in both scientific and industrial contexts. While conventional differential and integral calculus is often sufficient for describing most phenomena, there are instances where systems exhibit irregular and unpredictable behaviors over time or space, making ordinary calculus tools inadequate. In such cases, stochastic formalism, which relies on probability functions, becomes a valuable alternative for modeling these complex systems. This paper aims to provide a more comprehensive exploration of the fundamental properties and concepts of stochastic processes. It highlights the importance of the master equation, a key tool for understanding how microscopic processes impact the macroscopic behavior observed. Additionally, the article outlines the methodology for deriving stochastic differential equations, which take into account the stochastic nature of external variables that interact with the system and its environment. To illustrate the practical applications of these methods, the article presents several examples of how stochastic modeling is used to describe natural and industrial processes. These examples showcase the versatility and effectiveness of stochastic formalism in addressing real-world challenges and predicting the behavior of complex systems. This paper emphasizes the significance of stochastic modeling in bridging the gap between the microscopic and macroscopic aspects of physical phenomena, providing a deeper understanding of complex systems and their behavior. Stochastic formalism has become an indispensable tool for researchers and engineers working in various fields, enabling them to tackle the challenges posed by irregular and unpredictable systems.

Rasaki Olawale Olanrewaju   Sodiq Adejare Olanrewaju   and Wasiu Adesoji Adepoju   

In this article, we proposed and thoroughly described Bayesian bifurcated autoregressive process with student-t pairwise auto-correlated random noises for degenerated, lineage, or segmentation characterization process that usually lead to bifurcated autoregressive process. An informative prior of the Beta distributional form, that is, , for bifurcated autoregressive coefficients that ranges from [0,1], that is, , was proposed in conjunction with an Inverted-Gamma () distribution for the student-t distributed likelihood. The derived posterior distribution for the emerged priors and likelihood yielded a conjugated multivariate student-t like-distribution. Markov Chain Monte Carlo (MCMC) based approach in an embedded Metropolis-within-Gibbs algorithm was used to estimate the Bayesian bifurcated autoregressive coefficients, and it was ascertained that the derived posterior distribution takes a quadratic form of the multivariate student-t density. The posterior solutions of the Bayesian bifurcated autoregressive process were applied to eight imbalanced classes of a strain bacterial infection called Escherichia coli sequence and simulation studies, such that the obtained results were compared with the classical bifurcated autoregressive and ordinary autoregressive results. The merit of the Bayesian bifurcated autoregressive process over the classical bifurcated autoregressive process and autoregressive process was that the estimated bifurcated autoregressive coefficients via posterior solutions were stable across the application of the Escherichia coli sequence and simulation studies with a reduced bias-corrected method of Boot and LBC.

G. C. Abanum   I. C. Eli   and D. C. Iweobodo   

In this paper, an ordinary differential equation of order forty-five (ODE45) was considered for the prediction of the decreased and increased sample of normal agricultural assets over the biodiversity scenario, which is driven by growth rate coefficients of normal and auxiliary agriculture due to normal and auxiliary agricultural activities. We considered the effects of decreasing and increasing two parameter values that enhance normal agriculture growth due to normal agricultural activities. The main aim was to evaluate the effects of decreasing (increasing) the values on the pattern of growth of biodiversity of normal agricultural assets. It was discovered that decreasing the parameter values of the coefficient of the growth rate of normal and auxiliary agriculture together from 5% to 90% generally resulted in biodiversity losses. In contrast, when the parameter values were increased together from 105% to 120%, the result changed from biodiversity loss to biodiversity gain. When all the model parameter values were held constant, the yield of normal agricultural variable changes deterministically together with the length of the growing season. However, when the growth rate coefficients were varied and other parameter values were kept constant, the normal agricultural variables also changed. The study discovered that increasing the growth rate coefficients leads to the production of more food that meets the needs of society today and in the future.

Tania S. Khaleque   and Sumaiya B. Islam   

The relation between heat transfer coefficient, Nusselt number and the Rayleigh number has a significant role in mantle convection. By boundary layer theory, it is found that for constant viscosity case, and for temperature-dependent viscosity case, , where is the viscous temperature parameter in the variable viscosity function defined in Arrhenius form and the coefficient depends on cell-width. The values of Nusselt number are obtained for unit aspect ratio cell for Rayleigh-BÂŽenard convection model where the cases like constant viscosity and temperature dependent viscosity are considered with high Rayleigh Number (). The convection model is solved numerically by the finite element method based PDE solver for different Rayleigh numbers and viscosity contrast. The values of found numerically are used to obtain theoretically the proportionality constant by using the Shanks transformation which is one of the best all-purpose methods for accelerating convergence of sequences. The results are presented by several tables and figures. It is found that Shanks transformation successfully predicts the value of for constant viscosity convection case, but failed to predict a constant value for the temperature-dependent viscosity case.

Albert H. Lee III   Edward L. Boone   Roy T. Sabo   and Ryad Ghanam   

Random allocation models used in clinical trials can help reduce the between group bias which may occur when comparing multiple treatment groups to determine the preferred treatment method. Often however, this determination leaves researchers battling ethical issues of providing patients with unfavorable treatments. Many methods such as Play the Winner and Randomized Play the Winner Rule have historically been utilized to determine patient allocation, yet, these methods are prone to increased unfavorable assignments. Recently a new Bayesian Method using Decreasingly Informative Priors has been proposed but, this method can be time consuming when multiple individual Markov Chain Monte Carlo (MCMC) updating methods are required. We present an experimental design study via simulation using Dynamic Linear Models as an alternative method to increase allocation speed while also decreasing patient allocation samples necessary to identify the more favorable outcome and we illustrate the effectiveness of this new method. Furthermore, a sensitivity analysis is conducted on multiple parameters to demonstrate the method is robust. Finally, a Bayes Factor criterion is used to determine termination through decisive evidence in favor of the better treatment assignment.

Patrick Chidzalo   John Abonongo   Agnella Nemuo Mandia   and Marcelin Romeo Noumegni Kenmoe   

The precise calculation of risk-neutral probability density plays a pivotal role in modeling and forecasting European put and call options, holding significant importance. The Burr-XII distribution, which effectively captures the right-skewed characteristics of financial data, has seldom been introduced in the derivatives market and remains infrequently used in risk-neutral density valuation. In this study, we propose a methodology to obtain the risk-neutral density function specifically tailored for Burr-XII European options. By deriving closed-form expressions for call and put options and conducting simulations of derivative premiums, we demonstrate the model's flexibility and its ability to accurately represent option prices. The derived closed-form expressions further facilitated the identification of key smoothness properties, providing insights into the underlying behavior of the pricing function. Additionally, we establish a set of smoothness properties based on the derived closed forms, enabling us to develop a numerical iterative algorithm utilizing the bivariate Newton-Raphson method. Through this algorithm, we successfully capture the risk-neutral probability density with high precision, ensuring compatibility with the call-put parity constraint. The findings of this research have wide-ranging consequences. Professionals in the finance sector can gain advantages from a more precise and flexible European option pricing model, which can enhance risk evaluation and support well-informed decision-making.

V.James   and B.Sivakumar   

The past decade has witnessed enormous advances in the applications of matrix algebra in the life sciences. These advances have significant implications for the future practice of economics, Network analysis, Data analysis, Image processing, Optimization problems, and Quantum mechanics. The main objective of matrix algebra is to solve a system of equations using classical algorithm methods like Gauss elimination or matrix inversion. In recent years, handling a large number of data or finding the solutions to a large number of systems of equations is one of the problems in matrix algebra techniques. One of the effective methods to solve system of polynomial is Grobner basis techniques. It is a powerful tool in matrix algebra and in this method the leading terms of the polynomials are eliminated until no further reductions are possible. The objective of this paper is to solve Input-Output economic problems using the Grobner basis method which is one of the matrix algebra techniques. In real world, many decisions are taken based on the output of Input-Output table or Leontief models problems which have a large number of data or industries. There are two types of Leontief models, namely closed and open models. In this article, we consider the closed Leontief model. Also, we present one simple algorithm based on Grobner basis techniques to find the solution of a system of equations that occur on the Markov model.

Kago Kebotsamang   Thabiso Malomo   and Oarabile Lekhane   

Botswana has not updated its life tables since 2011. This implies that the current life tables may not reflect the current mortality trends, which could have a negative impact on end users such as insurance and pension fund companies. This study aims to estimate mortality rates and construct new life tables for Botswana. We used the Heligman-Pollard and Lee-Carter models to estimate mortality rates in Botswana for the years 2016-2019. The Heligman-Pollard model parameters were estimated through a Bayesian melding approach with incremental mixture importance sampling. The Lee-Carter model was estimated using a maximum likelihood approach and residual bootstrapping to construct confidence intervals of the estimated mortality rates. The Lee-Carter model was found to produce similar results to the Heligman-Pollard model. The results of the two models estimated life expectancy for males and females in Botswana to be about 68 and 74 years, respectively. The results of this study can be used to update the life tables for Botswana and improve the accuracy of mortality estimates for end users such as insurance and pension fund companies.

MĂĄrio Basto   Teresa Abreu   Ricardo Gonçalves   and JosĂ© M. Pereira   

Understanding concepts like confounding and effect modification is essential to biostatistics due to their potential influence on the interpretation of statistical results. The ability to appropriately identify and comprehend the links between research variables relies on having a firm grasp of these ideas. Statistical methods, such as stratification-related procedures and logistic regression, can be used to account for potential confounding factors. This helps to determine the real link between two variables of interest by controlling for the potentially skewing effects of the confounding variables. The ability to identify subsets of the population that may be more or less receptive to an intervention necessitates an understanding of effect modification. If, for instance, one learns that regular exercise is particularly useful in warding off heart disease in younger people, one could direct preventative efforts toward them. This paper aims to highlight the existence of associations between two binary variables that may be misleading or distorted due to the existence of confounding or effect modifier variables, that must be accounted for. The Mantel-Haenszel analysis and logistic regression are two techniques addressed in this study that help to statistically adjust the association between variables. Typically, only one of these methods is used in a study. This paper contrasts and illustrates the application of both techniques. To do this, four hypothetical situations are examined in order to provide the researcher with a comparative analysis of the two procedures and how to interpret the outcomes from each. Although the data may need to be adapted for each of the analyses, the outcomes are usually the same. The results indicate that both approaches are useful as long as they are used correctly. Nevertheless, depending on the situation, one or the other may be advisable.

Nuri Celik   

As the number of observation points examined in studies increases, it is assumed that these points come from an underlying real function. Statistical methods that have been developed for this type of data are called functional data analysis. Therefore, there has been a great interest in adapting some traditional statistical methods into the functional data sets like hypothesis testing, regression or analysis of variance (ANOVA). The analysis of variance (ANOVA) is used for comparing the means of more than three groups. Therefore, if the data comes as a functional data form, the functional ANOVA methodologies must be used to compare the mean function of the groups. In literature, one-way ANOVA and two-way ANOVA methodologies have been developed for functional data set. In this paper, we expand the functional one-way and two-way analysis of variance methodologies to three-way analysis of variance methodology or so-called factorial experimental design. We obtain the parameter estimations of the cell mean function and common variance-covariance function. We also propose sum of squares and test statistics by using these estimations. The test statistics and sum of squares are obtained via pointwise test methodology which has been used for ANOVA for functional data sets. A real data set about the measure of depression levels of health employees of Turkey during the Covid-19 pandemic is conducted for the illustration. The data set is collected between January 2021 and December 2021 for monthly and we have three factors that affect the depression levels of health workers as gender, profession and age. Therefore, in order to test the effects of the treatments, we use the proposed methodology for three-way ANOVA.

Hai Phan   and Seonguk Kim   

The Cox-Ross-Rubinstein (CRR) market model is one of the simplest and easiest ways to analyze the option pricing model. CRR has been employed to evaluate a European Option Pricing (call options) model without complex elements, including dividends, stocks, and stock indexes. Instead, it considers only a continuous dividend yield, futures, and currency options. The CRR model is simple but strong enough to describe the general economic intuition behind option pricing and its principal techniques. Also, it gives us basic ideas on how to develop financial products based on current deviations and volatilities. The paper investigates the CRR model using numerical approaches with python code. It provides a practical event using the mathematical model to demonstrate the application of the model in the financial market. First, the paper provides a simple example to figure out the basic concept of the model. Only a two-period binomial model based on the introductory definitions of the call options makes us understand the concept more easily and quickly. Next, we used actual data on Tesla stock fluctuations from the Nasdaq website (See section 3). We developed the python code to make it easier to understand figures, including tables and graphs. The code allows us to visualize and simplify the model and output data. The code analyzes the stock data to evaluate the probability of the stock’s price increasing or decreasing. Then, it used the CRR model to estimate all possible cases for the stock’s prices and investigate the call and put option pricing. The code was based on the introductory code of binomial option pricing, but we improved it to get more information and provide more detailed results from the data. The detailed codes are provided in section 3 of the paper. As a result, we believe the CRR model is a fundamental formula, but the improved python code can suggest a new direction for evaluating the probability and investigating the value of the stocks. Also, we expect to develop the code to extend the Black Scholes Pricing model, increasing the number of periods.

Madhusudan V Atre   and Hrvoje Volarević   

In this paper, a mathematical formalism for defining the J-Curve phenomenon is set up in the form of a corresponding differential equation with practical application. An explicit form of the differential equation to describe the J-Curve, as well as the solution of the differential equations in terms of polynomials with coefficients satisfying a particular property was presented for the first time. The J-Curve and S-Curve are modelled as Riccati's nonlinear differential equation of the 1^st order. A mathematical form of the differential equation is proposed that corresponds in structure to the Laguerre Polynomials (linear differential equation of the 2^nd order), resulting in J-Curve as a solution. To confirm this, it is necessary to fulfil two main criteria for the mathematical validation of the J-Curve - confirmation of the structure of Laguerre polynomials (a polynomial equation with coefficients of alternating sign) and an R-squared score greater than 0.6. Two case studies are presented to validate the theoretical concepts and demonstrate the application of J-Curve mathematical modelling - Returns on Venture Investments (where returns from start-up investments are analysed over a 12-year period) and Returns on Long-Term Stock Investments (based on actual financial data for the period from 2016 to 2020 for the NIFTY 500 Index of the National Stock Exchange of India). A direct connection between the mathematical formulation and the graphs obtained is shown, which corresponds to the mathematical validation of the J-Curve phenomenon. It is mathematically shown how the financial data manifest the J-Curve behaviour, satisfying the initial assumptions of such a model. The mathematical model set up in this way can be verified in practice on different other types of data, which could create interest in an interdisciplinary approach in such research. This could include studies particularly from other economic fields such as micro- or macroeconomics.

Md. Tohidul Islam   Md. Anwarul Islam Bhuiyan   and Sohana Jahan   

Supervised Regularized Multidimensional Scaling (SRMDS), a non-linear variant of classical Multi-Dimensional Scaling (cMDS) is proposed recently which involves Radial basis function. The method is focused on the effective selection of centers of the radial basis functions in transforming data from a higher dimensional space to a lower dimension. The transformation matrix is determined by minimizing stress. Weights of components of the stress that are of great importance for classification of data got less focus in Supervised Regularized Multidimensional Scaling. In this article, we have investigated several forms of non-linear functions which may be used as weights of the stress measure. A new form of Z-shape weight function dependent on intraclass information of the dataset is introduced which prefers to preserve global structure of the dataset. The efficiency of the proposed approach is illustrated on several benchmarking datasets which shows that the weighted Supervised Regularized Multidimensional Scaling (WSRMDS) outperforms the base method and some other state of the art approaches such as Linear Discriminant Analysis (LDA), and Supervised Principal Component Analysis (SPCA). Observing the finding of this research, among different weight functions, Z-shape weight function is recommended to use since it works better then any other weight functions for most of the data sets.

Aydin Teymourifar   Jie Li   Dan Li   and Taicheng Zheng   

In this study, an open-source simulation model is presented for solving scheduling problems. The model is capable of solving different benchmarks. The methods involved in the simulation are mainly based on generating dispatching rules or using them to solve problems, but there are other heuristics as well. Dispatching rules in an evolutionary process are generated using Gene Expression Programming. For this aim, a coding method, which has not been described in the literature before, is explained. Along with the explanation of the properties of the source code, information about deterministic, dynamic models, buffer states, machine breakdown states, and the methods used to deal with them is presented. Concepts are explained with visual examples. In addition, a subject that has not been investigated in the literature before is analyzed by using the simulation model. This topic is to examine the results of solving machine assignment and operation sequencing sub-problems in flexible job shop scheduling problems with different rules. Moreover, objective functions that the source code can handle are discussed. Unlike many studies in the literature, the codes are presented to the readers as open source. Also, it is open to development and can be easily modified by users to solve other types of problems. Finally, in the study, experimental results are presented on the basis of some benchmarks available in the literature, and the limits of the study and source code are explained.

Marlina Setia Sinaga   Hanna D. M. Hutabarat   and Yulita Molliq Rangkuti   

The tourism sector is significantly and directly affected economically, due to the Covid-19 pandemic. This is a serious problem that requires immediate treatment. It is feared that the tourism industry will weaken further, as it is one of the foreign exchange earners with a large enough influence. The development of the tourism sector with the parameters of the current needs of the tourism society is, namely 4A, Amenity, Attractions, Accessibility, and Ancillary. The concept of the new normal destination to become a safe tourist destination during the Covid-19 pandemic was built by simulating a genetic algorithm that imitates the theory of evolution to get a solution that is close to optimal. Parameter 4A is achieved by adding 3M (Wearing masks, washing hands, and maintaining distance), and 3T (Testing, Tracing, and Treatment) as control of the spread of Covid-19. The main contribution of this research is to find a solution that is close to optimal with the parameters of the tourism society's needs through simulations of new normal destinations with 3M and 3T constraints to control the spread of Covid-19.

Aydin TEYMOURIFAR   

Artificial neural networks (ANNs) have been used for estimation in numerous areas. Raising the accuracy of ANNs is always one of the important challenges, which is generally defined as a non-linear optimization problem. The aim of this optimization is to find better values for the weights of the connections and biases in ANN because they seriously affect the efficiency. This study uses two approaches to do such optimization in an ANN. For this aim, we create a feed-forward backpropagation ANN using the functions of MATLAB's deep learning toolbox. To improve its accuracy, in the first approach, we use the Levenberg - Marquardt algorithm (LMA) for training, which is available in MATLAB's deep learning toolbox. In the second approach, we optimize the values of weights and biases of ANN with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), available in MATLAB's global optimization toolbox. Then, we assess the accuracy of estimation for the trained ANNs. In this way, for the first time in the literature, we compare these methods for the optimization of an ANN. The used data sets are also available in MATLAB. Based on the acquired results, in some data sets, training with LMA, and for some others training with PSO cause the best results, however, training with LMA is faster, significantly. Although the used approaches and the obtained conclusions are beneficial for researchers that work in this field, they have some limitations. For instance, since only the functions and data sets from MATLAB are used, it can only serve as an example for researchers.

Ashiribo S. Wusu   Olusola A. Olabanjo   and Benjamin S. Aribisala   

The first case of the novel coronavirus (COVID–19) in sub–Saharan Africa was confirmed by Nigeria and the figure has since then been on the rise. Current global efforts are geared towards getting effective vaccine for the cure of the disease. The hope of accessing the relieve offered by the arrival of such vaccine will obviously take significant amount of time. In the face of the resurgence of the disease, the need to slow the spread and flatten the curves is currently a priority of both governmental and non–governmental organisations in Nigeria. If the dynamics of the disease can be determined, then it becomes easier to strategize and make suitable preventive policies that will slow the spread and ultimately flatten the curves. Here, the goal is to develop a compartmental–based model for analysing the dynamics of the pandemic in Nigeria. Considering the control policies currently in place - social distancing, mask usage, personal hygiene and quarantine, and using data provided by Nigeria Centre for Disease Control (NCDC), World Health Organization (WHO) and Wolfram Data Repository on COVID–19, the proposed model is fitted to the available data using the Quasi-Newton algorithm. The infection rate, average latent time, average infective time and average mortality rate are estimated. Also, the overall effectiveness of the current control policies is measured. Predictions on the turning points and possible vanishing time of the virus in Nigeria are made. Recommendations on how to manage the resurgence of the disease in Nigeria are also suggested.

Mulyono   Abil Mansyur   and Faridawaty Marpaung   

Population problems can cause problems, both in terms of political, economic, socio-cultural life, defense and security, as well as other aspects of life concerning the use of natural resources and the environment. By knowing the population growth rate, the Medan city government can implement a policy to anticipate social problems that may arise. This study aims to determine the number and rate of female population growth in the city of Medan in 2025. The Leslie matrix model is a model that can be used to predict the number and rate of female population growth. The step taken to predict the number of population p in the following year is to form a column vector whose entry is the initial number of population for each age class. Next look for n (t + p) which is the total population for the following year using the formula n(t+p)=A^pn(t) where A is the Leslie matrix. Furthermore, to predict the population growth rate using the Leslie matrix is to find the positive eigenvalues λ of the matrix A. Based on positive eigenvalues λ, three cases occur, namely: 1) the population will tend to increase if λ>1; 2) the population will tend to decline if λ<1 ; 3) the population will tend to be stable if λ=1. Based on data analysis, the total female population in the city of Medan in 2025 is 1,576,294. Furthermore, the eigenvalues of λ=1,3673 which mean that the number of female populations in the city of Medan tends to increase.

Seiji Tomita   and Oliver Couto   

Consider the below mentioned Equation: ax⁴+by⁴+cz⁴+dw⁴=0---[1]. In section (1) we consider solution's with the condition on the coefficient's of equation[1]. Namely the product (abcd)=square. In section [2] we consider the coefficients of Equation [1], with the product of coefficient's (abcd) not equal to a square. Historically Equation [1] has been studied by Ajai Choudhry, A. Bremner, M.Ulas [ref. 5] in 2014. Also Richmond [ref. 1 & 2] has done some ground work in 1944 & 1948. This paper has gone a step further, by finding many parametric solutions & new small numerical solutions by the use of unique Identities. The identities are unique, because they are of mixed powers (combination of quartic & quadratic variables) which are then converted to only degree four identities. As an added bonus in section [B], we came up with a few quartic (4-1-n ) numerical solutions for (n < 50) by elliptical mean's. A table of numerical solutions for the (4-1-n) Equation arrived at by brute force computer search is also given [ref # 7].

Duygu Dönmez Demir   and GĂŒlsĂŒm ƞanal   

The aim of this study is to present some inequalities for n-times differentiable functions. These inequalities are associated with the perturbed trapezoid inequality. n th derivatives of absolute values of the considered functions are s-convex and tgs-convex. In previous studies, some inequalities for the classes of twice differentiable functions which are convex, s-convex and tgs-convex have been introduced. We expand twice differentiable functions to n-times differentiable functions. Finally, some applications are given to verify new inequalities proposed in this study.

M. Ahmadi. Baseri   and H. Mazaheri   

In this paper, we give sufficient conditions for the existence of remotest points with recurrence relations. Then, we apply these relations to generalize recent best proximity point theorems. The findings of the present research contribute and enrich previous results reviewed in the literature.

Laxmi P. Paudel   

Overweight and obesity has been a major health problem in the United States. The severity is highest in the southeastern region. Social contagion is a significant factor for the progression of the obesity and its identification and control may lead to effective planning in the intervention of the obesity epidemic. In this paper, we devise a SIR model that capture the current dynamics of obesity in the southeastern region of the United States. We discuss the spread of obesity among friends and relatives through social network. With the help of the mathematical model, we discuss the effectiveness of the current intervention programs to control the obesity. We also purpose some affirmative actions to the public health policy makers, the city planning authority, and the community itself that could minimize and even reverse the pattern of obesity.

E. L. Pankratov   

In this paper, we introduce an approach to decrease dimensions of bipolar heterotransistors framework a circuit of a voltage divider biasing common emitter amplifier. Framework of the approach, we consider manufacturing of the divider in heterostructure with specific configuration. Several specific areas of the heterostructure should be doped by diffusion or by ion implantation. After this doping, dopant and/or radiation defects should be annealed by using optimized scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. To make prognosis of technological process and obtain recommendations to optimize the process, we introduce an analytical approach to analyze mass and heat transport in heterostructures with account mismatch-induced stress.

Reza Ahangar   

An introduction to nonlinear operator dynamical systems with a brief technical notation will be presented. The operator is designed to include all nonanticipating (causal) delay and functional dierential equations. Condi- tions for the existence and uniqueness of these noanticipating operator dierential equations (NODE) will be investigated. At last the perturbed solutions of these type nonlinear systems and some properties will be presented.

Bishnu Hari Subedi   and Ajaya Singh   

In this paper, we study fast escaping sets of transcendental semigroups. In particular, we discuss some fundamental structure and properties of fast escaping sets. We also show how far the classical dynamical theory of fast escaping sets of transcendental entire functions applies to general settings of transcendental semigroups and what new phenomena can occur.

Onur Kaya   and Mehmet Önder   

In this study, first we investigate the Fibonacci vectors, Lucas vectors and their vector products considering two Fibonacci vectors, two Lucas vectors and one of each vector. We give some theorems for the mentioned vector products and then we give the conditions for such vectors to be perpendicular or parallel. We also introduce the area formulas for the parallelograms constructed by Fibonacci and Lucas vectors with respect to Fibonacci and Lucas numbers. Moreover, we determine some formulas for the cosine and sine functions of the angles between two Fibonacci vectors, two Lucas vectors and lastly a Fibonacci vector and a Lucas vector. Finally, we investigate the Fibonacci quaternions and Lucas quaternions. We give some corollaries regarding the quaternion products of two Fibonacci quaternions, two Lucas quaternions and one of each quaternion. We conclude with the result that the quaternion product of such quaternions is neither a Fibonacci quaternion nor a Lucas quaternion.

Stephen Taiwo Salako   

We discuss the orthogonality problem of moving grids, where we minimize a cost function with a regularization term and improve the orthogonality of grids by making the angle between grids close to .The initial grid used is obtained by a well-established method known as the grid deformation method. We will then replace the cost function in the orthogonality problem with sum of squared differences (SSD) to discuss the image registration problem. We will discuss the non-uniqueness of solutions, existence of optimal solutions and prove the existence of Lagrange multipliers of the image registration problem using the Direct Method in Calculus of Variation and then derive an optimality system based on the construction of a Lagrangian functional from which optimal transformations can be calculated.

Oğuzhan Bahadr   

The object of the present paper is to study on a P-Sasakian manifold with quarter symmetric non-metric connection. In this paper, we consider some properties of the curvature tensor, projective curvature tensor, concircular curvature tensor, conformal curvature tensor with respect to quarter symmetric non-metric connection in a P-Sasakian manifolds. Finally, we give an example.

ALUKO O.   and MWAMBI H.   

We analyzed repeated measurement of continuous responses with monotone dropout. We are interested in reducing the bias associated with treatment effects, but the results' credibility relies on the validity of the techniques applied to analyze the data, and under the conditions where the techniques gives reliable answers. Furthermore, the robustness of the trial findings are determined through the application of sensitivity analysis which verifies to which extent the results are affected by changes in techniques, values of unmeasured variables and model assumptions. Moreover, the results obtain from the missing not at random (MNAR) is the same as their counterpart in missing at random (MAR). In addition, using multiple imputation (MI) in the analysis also improves the accuracy of results.

S. Jahan   

Personal identification or verification is a very common requirement in modern society specially to access restricted area or resources. Biometric identification specially faces identification or recognition in a controlled or an uncontrolled scenario has become one of the most important and challenging area of research. Images often are represented as high-dimensional vectors or arrays. Operating directly on these vectors would lead to high computational costs and storage demands. Also working directly with raw data is difficult, challenging or even impossible sometimes. Dimensionality reduction has become a necessity for pre-processing data, representation and classification. It aims to represent data in a low-dimensional space that captures the intrinsic nature of the data. In this article we have applied a Supervised distance preserving projection (SDPP) technique, Semidefinite Least Square SDPP (SLS-SDPP), we have proposed recently to reduce the dimension of face image data. Numerical experiments conducted on very well-known face image data sets both on gallery images and blurred images of various level demonstrate that the performance of SLS-SDPP is promising in comparison to two leading approach Eigenface and Fisherface.

Aydin Teymourifar   Gurkan Ozturk   and Ozan Bahadir   

Many evolutionary algorithms have been used to solve multi-objective scheduling problems. NSGA-II is one of them that is based on the Pareto optimality concept and generally obtains good results. However, it is possible to improve its performance with some modifications. In this paper, two modified NSGA-II algorithms have been suggested for solving the multi-objective flexible job shop scheduling problem. The neighborhood structures defined for the problem are integrated into the algorithms to create better generations during the iterations. Also, their initial populations are created with an effective heuristic. In the first modified NSGA-II, after the creation of the offspring population, a neighbor of each individual in the parent population is constructed, and then one of them is selected according to the domination state of the solutions. Then the populations are merged to create a new population. In the second modified NSGA-II, only the solutions on the first and second fronts of the parent population and also their neighbors are merged with the offspring population. Other operators of the algorithms like the non-dominated sorting and calculating the crowding distances are as the classic NSGA-II. A comparison is done with a classic NSGA-II based on two metrics. The results show that as it is in the first modified NSGA-II, including neighbors of more individuals of the population provides better results because it increases diversity and intensity of the search. The performance of the second modified NSGA-II is almost similar to the NSGA-II. So, it can be concluded that although integrating the neighborhood structures can improve the performance of search, it is better to define that the structures should be applied to how many and which solutions, in otherwise the quality of search may not increase.

ƞule Ă‡ĂŒrĂŒk   and Serpil Halici   

In this study, we investigate Fibonacci quaternions and their some important properties. Then, we define a special sequence using the elements of the Fibonacci quaternion sequence. Furthermore, we calculate the autocorrelation, right and left periodic autocorrelation values by using the elements of the newly defined sequence.

Mehmet Alegoz   and Zehra Kamisli Ozturk   

In this study, we focus on designing the supply chain network of a company that sells households goods to its customers located in various cities of Turkey. Since the production plant of the company is fixed and cannot be changed, we divide the supply chain network design problem into two separate problems. In first problem, we focus on the network between the supplier and the production plant. This problem can be thought as a supplier selection problem and there are many qualitative and quantitative criteria, which affect this process. Therefore, we use Buckley's Fuzzy AHP algorithm, which enables us to evaluate the suppliers according to all types of criteria. In second phase of the study, we focus on the supply chain network between the production plant, warehouses and customers and develop a multi objective mathematical model. Although, the proposed mathematical model gives optimal solution for our company data within a reasonable time, large size instances cannot be solved by using this model due to the complexity of problem. For this reason, we propose various metaheuristic approaches based on tabu search and compare the results with optimal solution. Computational results show that one of our approaches gives high quality results within a reasonable time. We conclude the study by discussing the numerical results and giving some future work suggestions to interested readers.

Abir Kessebi   and Bahri Rezig   

Current researches on wireless sensor networks (WSN) are focusing on reducing the total amount of energy consumption and extending the network lifetime. WSN have many application fields like industry, health care, commercial and residential applications. The main goal of this paper is to evaluate, using MATLAB/Simulink simulations, the average amount of energy consumed in a WSN based on a clustering topology; to predict the optimal number of clusters in order to optimize the energy and also to study the cloud integration effects on lifetime and energy time dependency. The clustering topology is based on defining K clusters with N/k nodes, each node transmits data to the cluster head which will collect data from all of its own nodes, compute it and send it to the base station (BS). In our simulation, we have focused on many principal metrics in WSN such as optimal number of clusters, duty cycle, lifetime and distance to BS. Finally we have studied the effect of integrating cloud into classic WSN, the effect in terms of energy consumption and sensor node lifetime.

David Blackman Hon.   

In aerodynamics, there are two types of surfaces: stiff and flexible. Stiff surfaces may gain energy from differential wind velocity on opposite sides of the particle. Flexible surfaces dissipate such energy through flutter i.e. like the tail of a kite. Kites have two components, the airfoil and the tail. Airfoils provide lift for the kite through the differential air currents. In such a dichotomous world the Ebola virus resembles the tail of the kite as opposed to the airfoil. One would expect the Ebola virus to flutter and fall. Through mathematical analysis of the electron micrograph it is concluded that the virus is not airborne, but it is probably waterborne.

HĂŒseyin Oğuz   and Elçin Yusufoğlu   

In this study, a numerical solution of elasticity problem is examined. This problem is a plane contact problem. The frictional contact problem for an elastic strip under a rigid punch system is considered. The frictional contact problem is related to infinite length elastic strip in contact with N punches under the influence of horizontal and vertical forces. The lower boundary of the strip is hinged. The solution of contact problems is often reduced to the solution of an integral equation. This integral equation system can be derived from contact problem by using the basic equations of elasticity theory and the given boundary conditions. The singular integral equation system is solved with the help of Gauss Jacobi Quadrature Collocation Method. The frictional contact problem for a homogenous and orthotropic elastic layer are investigated numerically the pressure distribution under the punch system due to the geometrical and mechanical properties of elastic layer are examined and the results are shown in the graphics and tabular form.

G.P. Vinogradov   

The problem of constructing a choice model of an agent endogenously shaping purposes of his evolution is under debate. It is demonstrated that its solution requires the development of well-known methods of decision-making while taking into account the relation of action mode motivation to an agent's ambition to implement subjectively understood interests and the environment state. The latter is submitted for consideration as a purposeful state situation model that exists only in the mind of an agent. It is the situation that is a basis for getting an insight into the agent's ideas on the possible selected action mode results. The agent's ambition to build his confidence in the feasibility of the action mode and the possibility of achieving the desired state requires him to use the procedures of forming a model-representation based on the measured values of the environment state. This leads to the gaming approach for the choice problem and its solution can be obtained on a set of trade-off alternatives.

Cansel Yormaz   Serife Naz Elmas   and Simge Simsek   

In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics. This study leads to the possibility of employing algebraic techniques of quaternions and coquaternions to absorbing in quantum mechanics. The founded equations are compared with the Hamiltonian energy equations generally are known and the Hamilton energy equations are obtained in Minkowski space.

Aydin Teymourifar   and Gurkan Ozturk   

In this paper, a hybrid method is proposed to generate feasible neighbors for the flexible job shop scheduling problem. Many of the optimization and artificial intelligence methods have been used to solve this important and NP-hard combinatorial problem which provides the basis for solving real-life problems. It is well-known that for such problems the hybrid methods obtain better results than the other approaches. For instance, the applied non-hybrid neural networks for the combinatorial problems, as the Hopfield neural network, usually converge early. Also, their results almost always contain large gaps. These shortcomings prevent them to find good results. Another necessity for a quality search is to find suitable neighbors of the obtained solutions; however, it is possible to create infeasible neighbors during the optimization process. The aim of this study is to overcome these deficiencies. In the suggested approach, at first, an initial solution is generated and then using the left shift heuristics, its gaps are removed. Based on the critical path and critical block concepts, 6 neighbors are constructed for the obtained solution. After the generation of each neighbor, a neural network runs and controls the constraints of the problem. If the achieved neighbor is feasible it is saved. Else if it is infeasible, the neural network tries to transform it into a feasible solution. This is done by applying penalties to the start time of the operations on the violated constraints, which shifts them to the right or the left. During this process, if there are not any violated constraints, the neural network reaches the stable condition so it stops and the obtained solution is saved as a feasible neighbor. Otherwise, after a certain number of the iterations, it stops without any feasible neighbors. Then these steps are repeated for the other created neighbors. This constraint-based process provides an effective and diverse search. Finally, the obtained neighbors, are improved using the left shift heuristics. Also to demonstrate the importance of the initial solutions, they are generated randomly and also using the Giffler and Thompson's heuristic. The comparison between the proposed approach and the methods from the literature shows that it constructs better neighbors. However, using the Giffler and Thompson heuristic to create the initial solution improves the results significantly.

Simge Simsek   and Cansel Yormaz   

The aim of this paper is to apply the necessary and sufficient conditions of well-known Lagrangian equations with time dependent case for Minkowski 4-space. Many fundamental geometrical properties for time dependent Minkowski 4-space have been obtained in this paper. The energy equations have been applied to the numerical example in order to test its performance. In the numerical examples, we have studied with two time parameters (earth and space time) for accordance to Minkowski 4-space coordinates. This idea is an interesting approach to energy function with Earth-time and Space-time in physical comment. Moreover, velocity and two time dimensions for energy movement equations have been presented a new concept. This study show some physical application of those equations and interpretations are made in Minkowski space too. Results showed that Lagrangian functions for any surface are same type and depend on time coordinates.

Mihail Cocos   and Kent Kidman   

A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of 2 forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used to decide when a matrix of 2 forms is equivalent to a skew symmetric matrix. We apply this algorithm to verify whether a full rank curvature connection is locally metric.

Naeem Salem   and Said Beloul   

The aim of this paper is to establish some common fixed point results for two weakly subsequentially continuous and compatible of type (E) pairs of self mappings via implicit relation in modified intuitionistic fuzzy metric spaces, also we give an example to illustrate our results.

R. Marta GarcĂ­a FernĂĄndez   and Miguel V. Carriegos   

Linear systems with constant real coefficients are completely described in terms of feedback actions. In this paper the problem is studied in the framework of linear systems where coefficients depending continuously on a set of parameters. Some invariants are given as well as criteria to find a complete classification in low dimension.

M. Z. I. Bangalee   Roushanara Begum   M. Ferdows   Md. Matiar Rahman   and Mir Shariful Islam   

The buoyancy driven natural convection flow in an open cavity has become an important issue to study. In this study, the difficulties of computing natural convection flow in open cavity with an extended computational domain around the cavity are reported. The Îș-Δ turbulence model is used for the computation to capture the turbulence nature of the air flow inside the cavity. ANSYS CFX software is used to solve the governing equations in this study. Effects of different aspect ratio and different temperature at the left wall and thus the temperature difference between the left and the right walls are analyzed numerically as well. Average mass flow, temperature, velocity etc. at different location in the cavity for different boundary conditions are studied and reported. A comparison between the present work and a previous work is also reported here to validate the methodology. Finally, relations among non-dimensional parameters (e.g. Ra, Re, Pr, Nu numbers) are also presented.

Souida Boukrioua   Adel Aissaoui   and Nacerdine Hemici   

We consider a quasistatic contact problem between two viscoelastic bodies with long-term memory and damage. The contact is bilateral and the tangential shear due to the bonding field is included. The adhesion of the contact surfaces is taken into account and modelled by a surface variable, the bonding field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, differential equations and fixed point.

V. A. Meshkoff   

On the ground of Prime Numbers Classification it is generalized approach to Composite Numbers Factorization presented. The resulting task goes to the different Diophantine equations reducing. Some methods of reducing and its practical application, in particular for Fermat numbers, are demonstrated.

Said Elkassimi   Said Safi   and B. Manaut   

This paper proposes an algorithm based on ZF and MMSE methods for blind channel equalization, which is compared with adaptive filter algorithms which are Constant Modulus Algorithm (CMA), Fractional Space CMA (FSCMA) and Sign Kurtosis Maximization Adaptive Algorithm (SKMAA). The simulations show that the proposed algorithm gives satisfied result versus CMA, FSCMA and SKMAA algorithms. The study is done under certain conditions, it is implemented in noisy environment, for different number of symbols and different SNR values with QPSK modulation. Equalization of channel is more performing if we use the proposed algorithms.

AndrĂĄs Simonovits   

In van Groezen, Leers and Meijdam (2003) (for short, GLM), the government pays child support and pensions to raise fertility and replace the insufficient old-age saving of myopic workers, respectively. Concentrating on the equilibrium core of GLM, we analyze its simplest possible versions. We impose credit constraint on workers, and extend GLM's analysis to heterogeneous rearing costs and preferences for enjoying children. Two major results: (i) the infusion of public transfers only raises social welfare when the bulk of private savings has been crowded out; (ii) the introduction of fertility-dependent pensions raises average fertility but diminishes welfare.

Michael Scarinci   Katherine Encarnacion   Angel R. Pineda   and Lance S. Evans   

Plants of the many subspecies of Artemisia tridentata are dominant shrubs of the Great Basin Desert of the United States. Many subspecies of Artemisia tridentata show extensive eccentric growth in which vascular cambium dies and no longer produces secondary xylem in stems. The purpose of this study was to create three-dimensional images of xylary rings from stem segments so that characteristics of individual xylary rings among successive segments could be accurately represented. Four stem segments from a branch were sized and aligned in MATLAB. Three xylary rings were given a unique color for visualization. All portions of images were removed so only the xylary rings were visible. Rings of the four segments were aligned to make a three-dimensional visualization. The images were analyzed to determine the locations of complete rings, locations of partial rings, percentages of arcs of rings of individual rings, and calculations of ring areas. Eccentric growth is localized. For example, on one stem segment all three rings were complete while the next segment 20 mm along the stem had two incomplete rings. The visualization and resulting data generated provide information about eccentric growth which, in turn, reflects the overall health and mechanical stability of stems.

Andrei Zelenyy   and Alexey Bunyakin   

This article presents numerical simulation of planar potential flow around an airfoil with possibility of changing its shape. Two-dimensional unsteady flow model with scalar velocity potential, which allows us to calculate pressure distribution along an airfoil from Cauchy-Lagrange integral, is used. For this purpose, an airfoil contour is approximated by a complex cubic spline with possibility of displacement its vertices. This algorithm has been used in the context of fluid-structure interaction and has been applied successfully to determination of stability of an elastic airfoil segment interacting with a flow stream, so-called panel flutter problem. Calculation of external flow is carried out by vortex panel method with Kutta-Joukowski trailing edge condition, which makes mathematical solution unique. Using this method of approximation of an airfoil in combination with the method of discrete vortices provides a semi-analytical solution for complex potential for whole computational domain of air flow. This solution significantly accelerates process of numerical computation of time-averaged aerodynamic force as well as the dynamic stability problem for aeroelastic wing design and temporal evolution of its natural disturbances.

Yasar Pala   and Mutlu Ozgur Ertas   

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method doesn't require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at a first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Seiji Tomita   and Oliver Couto   

Historically equation ( paⁿ+qbⁿ+rcⁿ=puⁿ+qvⁿ+rwⁿ ) has been studied for degree 2, 3, 4 etc., and equation (paⁿ+qbⁿ=pcⁿ+qdⁿ ) herein called equation (1) has been published for n=4 ,p=1,q=4 (Ref.no. 1) by Ajai Choudhry. Also Tito Piezas & others has discussed about equation (1) (Ref. no. 3 & 2). While Ref. no. (1, 2 & 3) deals with equation no. (1) for degree n=4 this paper has provided parametric solutions for degree n=2, 3, 4, 5, 6, 7, 8 & 9. Also there are instances in this paper where parametric solutions have been arrived at using different methods.

Igor Ya. Subbotin   and Michael Gr. Voskoglou   

The Generalized Rectangular Fuzzy Assessment Model (GRFAM) is applied for the evaluation of student group acquisition of the van Hiele levels of geometric reasoning and an example is presented illustrating our results. The GRFAM is a variation of the Center of Gravity defuzzification technique created in an effort to treat better the ambiguous assessment cases being at the boundaries between any two successive assessment grades.

Ali Molkhasi   

We investigate WB-height-unmixed of tensor product of distributive lattices: Cohen-Macaulay rings related to tensor products of distributive lattices are constructed using the method of Stanly and Reisner.

Victor Chulaevsky   

We present the adaptive feedback scaling method for the Anderson localization analysis of several large classes of random Hamiltonians in discrete and continuous disordered media. We also give a constructive scale-free criterion of localization with asymptotically exponential decay of eigenfunction correlators, which can be verified in applications with the help of numerical methods.

Seiji Tomita   and Oliver Couto   

Consider the below mentioned equation: [aⁿ+bⁿ+cⁿ+dⁿ+eⁿ+fⁿ] = [pⁿ+qⁿ+rⁿ+sⁿ+tⁿ+uⁿ]-----(A) Historically in math literature there are instances where solutions have been arrived at by different authors for equation (A) above. Ref. no. (1) by A. Bremner & J. Delorme and Ref. no. (10) by Tito Piezas. The difference is that this article has done systematic analysis of equation (A) for n=2,3,4,5,6,7,8 & 9. While numerical solutions for equation (A) is available on "Wolfram math" website, search for parametric solutions to equation (A) in various publications for all n=2,3,4,5,6,7,8 & 9 did not yield much success. The authors of this paper have selected six terms on each side of equation (A) since the difficulty of the problem increases every time a term is deleted on each side of equation (A). The authors have provided parametric solutions for equation (A) for n=2, 3, 4, 5 & 6 and for n=7, 8 & 9 solutions using elliptical curve theory has been provided. Also we would like to mention that solutions for n=7, 8 & 9 have infinite numerical solutions.

Khaled Jaber   and Shadi Al-Tarawneh   

New exact solutions of the Fractional Riccati Differential equation y^(α) = a ( x) y² + b ( x ) y + c ( x ) are presented. Exact solutions are obtained using several methods, firstly by reducing it to second order linear ordinary differential equation, secondly by transforming it to the Bernoulli equation, finally the solution is obtained by assuming an integral condition on c (x) involves an arbitrary function. Using the conditions imposed on Riccati equation's coefficients we choose the form of the coefficients of the Riccati equation. For this case the general solution of the Riccati equation is also presented.

A. M. Abouammoh   and Arwa M. Alshangiti   

This paper introduces a new probability model that is the modified generalized inverted exponential distribution. This new probability model is a generalization of the well-known inverted exponential distribution as a special case. Statistical and reliability properties of the modified version are derived. Shapes for the probability density function, reliability function and failure rate function are shown with graphical illustration. The truncated distribution is studied in details. Further, estimation by the method of maximum likelihood is discussed through numerical simulation. Finally, a real data set is used where the proposed model fits better than the generalized inverted exponential distribution and the asymptotic confidence interval is given.

Ibrahim A.A   Chun P.B   Abubakar S.I   Garba A.I   and Mustafa.A   

In this paper, we aim at utilizing the Cayley tables demonstrated by the Authors[1] in the construction of a Generator/Parity check Matrix in standard form for a Code say C Our goal is achieved first by converting the Cayley tables in [1] using Mod2 arithmetic into a Matrix with entries from the binary field. Echelon Row operations are then performed (carried out) on the matrix in line with existing algorithms and propositions to obtain a matrix say G whose rows spans C and a matrix say H whose rows spans C^⊄, the dual code of C, where G and H are given as, G = (I_k | X ) and H= ( -X^T | I_n-k ). The report by Williem (2011) that the adjacency Matrix of a graph can be interpreted as the generator matrix of a Code [3] is in this context extended to the Cayley table which generates matrices from the permutations of points of the AUNU numbers of prime cardinality.

Seiji Tomita   and Oliver Couto   

Different authors have done analysis regarding sums of powers (Ref. no. 1,2 & 3), but systematic approach for solving Diophantine equations having sums of many bi-quadratics equal to a quartic has not been done before. In this paper we give methods for finding numerical solutions to equation (A) given above in section one. Next in section two, we give methods for finding numerical solutions for equation (B) given above. It is known that finding parametric solutions to biquadratic equations is not easy by conventional method. So the authors have found numerical solutions to equation (A) & (B) using elliptic curve theory.

Seiji Tomita   and Oliver Couto   

Consider the below mentioned equation: x⁴+y⁴+z⁴=·É∗tⁿ----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x⁴+y⁴+z⁴=·É∗tⁿ--- (A)

Giuseppe Bruno   

This paper shows the implementation of some pricing techniques for multiname credit derivatives. Among these financial instruments we consider Basket Default Swaps (BDS) and Collateralised Debt Obligations (CDO). The pricing methodologies put forward are based on Monte Carlo simulations. These techniques are written in the R programming language. This software framework provides an ample set of functions for credit risk modelling. Two main issues are put forward in this paper: the first one is the employment of Quasi Random Number (QRN) for reducing the variance of price estimate in the Monte Carlo experiment; the second one is the code parallelization of some pricing techniques using R end-user techniques.

Nyamugure Philimon   MaphosaMuchaona   and Maseka Lesaoana   

This paper analysed activities undertaken in optimizing locomotive utilisation at National Railways of Zimbabwe (NRZ). Failure to attain breakeven and meet set targets is associated with underutilising resource capacity. The identified locomotive constraints in this paper do not have a linear relationship hence the application of nonlinear programming in formulating the Locomotive Optimization Model (LOM). The objective function in the model is to maximize the quantity of traffic moved by a given number of locomotives available for use which consequently converts to revenue generated. The model results show a failure by NRZ to meet breakeven targets in the year 2013. Different model scenarios are formulated using attainable locomotive figures and it is observed in the model scenario B where a 15% increase in speed, trailing load and availability of locomotives will results in attainment of breakeven targets.

Oliver Couto   and Seiji Tomita   

The work on equation (B) below has been studied by others for different degree ‘n' and equation (A) below for degree five, has been previously published by Mr. Ajai Choudhry (Ref. no. 1). But combined systematic analysis for degrees 2,3,4,5,6,7,8 & 9 etc. has not been done before, as is done in this paper. Consider the below mentioned equations: as ⁿ + bt ⁿ + cu ⁿ = aw ⁿ + bx ⁿ + cy ⁿ---(A) and as ⁿ + bt ⁿ + cu ⁿ + dv ⁿ = aw ⁿ + bx ⁿ + cy ⁿ + dz ⁿ ---(B).

Xinying Pai   

In this paper, we investigate how the Laplacian coefficients changed after some graph transformations. So, I express some results about Laplacian coefficients ordering of graphs, focusing our attention to the bicyclic graphs. Finally, as an application of these results, we discuss the ordering of graphs based on their Laplacian like energy.

Alongkot Suvarnamani   and Sakunna Koyram   

In this paper, we consider the multiplicative pulsated Fibonacci sequences. First, we show the new proof of the explicit formulas of multiplicative pulsated Fibonacci sequences of second order. Then the second type of multiplicative pulsated Fibonacci sequences is introduced and explicit formulas for the form of its members are formulated and proved.

Xiao Liu   

Logistic mixtures, unlike normal mixtures, have not been studied for their topography. In this paper we discuss analogs of some of the multivariate normal mixture results for the multivariate logistic distribution. We focus on graphical techniques that are based on displaying the elevation of the density on the ridgeline. These techniques are quite elementary, and carry full information about the location and relative heights of the modes and saddle points. Moreover, we turn to a technique that names II-Plot which denotes that the first differentiation of the second component density ratios the difference between the first differentiations of the second component density and the first component density.

Victor Chulaevsky   

We extend the techniques and results of the multi-particle variant of the Fractional Moment Method, developed by Aizenman and Warzel, to disordered quantum systems in general finite or countable graphs with polynomial growth of balls, in presence of an exponentially decaying interaction. In the strong disorder regime, we prove complete exponential multi-particle strong localization. Prior results, obtained with the help of the multi-scale analysis, proved only a sub-exponential decay of eigenfunction correlators.

M. Kamrul Hasan   M. Ashraful Huq   M. Habibur Rahaman   and B. M. Ikramul Haque   

Recently, a straightforward formula has been presented for evaluating singular integrals. Earlier extrapolation technique was used to guess the functional values at the singular points since most of the classical formulae contain both ends points. In this article a more accurate straightforward formula is presented for evaluating singular integrals. The new formula converges faster than others existing formulae. The Romberg integration scheme of this method also converges faster.

V. Amarendra Babu   K.V.Ramarao   and T.Anitha   

We introduce the concept of vague additive groups (VAG) by linking the vague set and group theory. Also we define the concept of vague normal additive group (VNAG) and vague ring (VR). The properties of VAG are investigated.

M. Sarboland   and A. Aminataei   

This paper's purpose is to provide a numerical scheme to approximate solutions of the nonlinear Klein-Gordon equation by applying the multiquadric quasi-interpolation scheme and the integrated radial basis function network scheme. Our scheme uses Ξ-weighted scheme for discretization of the temporal derivative and the integrated form of the multiquadric quasi-interpolation scheme for approximation of the unknown function and its spatial derivative. To confirm the accuracy and ability of the presented scheme, this scheme is applied on some test experiments and the numerical results have been compared with the exact solutions. Furthermore, it should be emphasized that with the presently available computing power, it has become possible to develop realistic mathematical models for the complicated problems in science and engineering. The mathematical description of various processes such as the nonlinear Klein-Gordon equation occurring in mathematical physics leads to a nonlinear partial differential equation. However, the mathematical model is only the first step towards the solution of the problem under consideration. The development of the well-documented, robust and reliable numerical technique for handing the mathematical model under consideration is the next step in the solution of the problem. This second step is at least as important as the first one. Therefore, the robustness, the efficiency and the reliability of the numerical technique have to be checked carefully.

Valeryi Meshkoff   

It is known, that any prime number has presentation in linear and quadratic forms. These properties may be used for finding class subsets of prime numbers. For that it is showed, that all prime numbers simple quadratic forms consist of a²+mb², m=1,±2,3 . On these grounds it is examination for variants of prime numbers classification. It is discovered eight non-intersecting subsets of prime numbers, in conformity with equivalence classes modulo 24. The proposed classification is used for analyses Mersenne and Fermat numbers and composite numbers.

I. A. Al-Subaihi   

In this paper, a published algorithm is investigated that proposes a three-step iterative method for solving nonlinear equations. This method is considered to be efficient with third order of convergence and an improvement to previous methods. This paper proves that the order of convergence of the previous scheme is two, and the efficiency index is less than the corresponding Newton's method. In addition, the three-step iterative method of the scheme is implemented, and the previously published numerical results are found to be incorrect. Furthermore, this paper presents a new three-step iterative method with third order of convergence for solving nonlinear equations. The same numerical examples previously presented in literature are used in this study to correct those results and to illustrate the efficiency and performance of the new method.

Alexandr Kozachok   

The additional equalities (additional differential equations) for the Navier – Stokes and other vector PDE are established in this paper. These equations are obligatory requirements (properties) of three functions forming a vector field on Euclidean space. Therefore all solutions of the vector PDE should satisfy these requirements. Without these equalities the Navier–Stokes equations with so called a continuity equation are underdetermined as vector system and any “exact solution” is not solution of the true Navier – Stokes vector equation.

K. P. Samanta   and B. Samanta   

In this article, we have obtained some novel results on bilateral generating functions of the polynomials, , a modified form of Konhauser biorthogonal polynomials, by group-theoretic method. As special cases, we obtain the corresponding results on Laguerre polynomials, . Some applications of our results are also discussed.

Gagik Aghekyan   and Karen Sahakyan   

In this paper, we investigate the behavior of critical points of some polynomials whose roots are the vertices of some parallelogram, in case of rotation two of them on a given circle. In this case, the trajectory is the Cassini ovals.

B. O. zaltın   and I. Dag˘adur   

The idea of difference sequence spaces was introduced by Kızmaz [14] and this concept was generalized by Et and Çolak [6] . Recently the difference sequence spaces have been studied in (see, [3] , [7] , [17] , [18]). The purpose of this article is to introduce the sequence spaces using a modulus function f and more general C_λ− method in viev of Armitage and Maddox [2]. Several properties of these spaces, and some inclusion relations have been examined.

Mohammad Shafique   and Fatima Abbas   

The problem of Magneto Hydrodynamic viscous flow due to a shrinking sheet of Newtonian fluids has been solved numerically by using SOR Iterative Procedure. The similarity transformations have been used to reduce the highly nonlinear partial differential equations of motion to ordinary differential equations. The results have been calculated on three different grid sizes to check the accuracy of the results. The numerical results for Newtonian fluids are found in good agreement with those obtained by the previous results.

Igor Ya. Subbotin   and Michael Gr. Voskoglou   

Fuzzy logic due to its nature of characterizing each case with multiple values offers is a rich field of resources covering the assessment of situations characterized by a degree of fuzziness and/or uncertainty. In this paper, we present two different fuzzy assessment models: The Centre of Gravity (COG) model and Trapezoidal Fuzzy Assessment Model (TRFAM). The last one is a new model covering the ambiguous cases being at the boundaries between two successive assessment intervals. An application (students' assessment) is also presented, through which the above methods are compared to each other and also with two traditional assessment methods based on principles of bivalent logic (the calculation of means and of the GPA index). Some useful conclusions are drawn about the characteristics of the above fuzzy assessment models.

Karen Sahakyan   

In this article a new quadrature and cubature formulas are obtained. These formulas are formulas of Hermitian type, which exactly on some trigonometric polynomials. The question of the convergence of the quadrature process associated with these formulas is investigated. Numerical analysis of these formulas is holds. The obtained formulas may have an advantage in integrating strongly oscillating functions.

Michael J. Dinneen   Nan Rosemary Ke   and Masoud Khosravani   

In this paper we study the problem of labeling the edges of a graph with positive integers such that the sequence of the sums of incident edges of each vertex makes a finite arithmetic progression. We give conditions for paths, cycles, and bipartite graphs to have such a labeling. We then address the opposite problem of finding an edge labeled graph for a given finite arithmetic progression. We use a constructive procedure to fully characterize those finite arithmetic progressions that have representations as edge labeled graphs. Then by presenting a pseudo polynomial-time algorithm, we address a more general problem of finding edge labels for a graph when the vertex labels are given. Finally, we count the connected graphs, up to eight vertices, that accept such a labeling by using a simple algorithm that detects a valid edge labeling.

J. P. Jaiswal   

In this paper we construct a new third-order iterative method for solving nonlinear equations for simple roots by using inverse function theorem. After that a class of optimal fourth-order methods by using one function and two first derivative evaluations per full cycle is given which is obtained by improving the existing third-order method with help of weight function. Some physical examples are given to illustrate the efficiency and performance of our methods.

Zahid Khan   Radzuan B.Razali   and Sarfaraz Ahmed   

The Reliability Prediction is an important tool for designing, decision making and estimating future system success. Design engineers are often required to develop and estimate Reliability before the product is produced. Inaccurate predictions can lead to over design and/or excessive spare parts procurement. This work is based on the study of Reliability Analysis carried out on Electronic Communication Systems used in the aircraft avionics. This system was applied in the beginning for the Secure Speech Equipment designed specifically to encrypt voices as well as for fax and computer data. The Part Stress Analysis modeling is used in this study which is a worldwide standard for performing reliability predictions. The Reliability Block diagram is also developed as a tool for reliability prediction.

Pawan Kumar Sharma   and Mukesh Dutt   

This communication investigates the effect of magnetic field on unsteady free convection oscillatory flow through vertical parallel porous flat plates, when free stream velocity, temperature and concentration oscillates in time about a non zero constant mean. The governing equations are solved by adopting complex variable notations. The analytical expression for velocity, temperature and concentration fields have been obtained using perturbation technique. The effect of various parameters on mean flow velocity, transient velocity, transient temperature, transient concentration, mean skin frication, amplitude and phase of skin-friction and heat transfer have been discussed and shown graphically.

Arzu Denk   and S. Gulsan Topal   

In this paper, we consider the existence of triple positive solutions for the second order semipositone m-point boundary value problem on time scales. We emphasize that the nonlinear term f may take a negative value.

Mulyono   and Saib Suwilo   

A digraph is primitive provided there is a positive integer k such that for each pair of vertices u and v there exist walks of length k from u to v and from v to u. The scrambling index of a primitive digraph D is the smallest positive integer k such that for each pair of vertices u and v in D there is a vertex w such that there exist walks of length k from u to w and from v to w . A two-colored digraph is a digraph each of whose arc is colored by red or blue. In this paper we generalize the notion of scrambling index of a primitive digraph to that of two-colored digraph. We define the scrambling index of a two-colored digraph D⁽²⁾ to be the smallest positive integer h + ℓ over all pairs of nonnegative integers (h, ℓ) such that for each pair of distinct vertices u and v there is a vertex w with the property that there are walks form u to w and from v to w consisting of h red arcs and ℓ blue arcs. For two-colored Wielandt digraph on n ≄ 4 vertices we show the scrambling index lies on the interval [n²ïŒ3n + 3, n²ïŒ2ČÔ+2±Ő.

M. Iqbal Jeelani   and S.A.Mir, M.S.Pukhta   

In this paper we suggest a new modified ratio estimator of population mean of the study variable using the linear combination of known values of Quartile deviation and Median of the auxiliary variable under Rank set sampling. Mean squared error up to the first degree of approximation are derived and compared with modified ratio estimators given by Kadilar and Chingi [1] based on simple random sampling. The proposed modified ratio estimators under rank set sampling perform better than the ratio estimators given by Kadilar. The simulated study has been carried out in support of the results.

Grozio Stanilov   

We establish that a subset of symmetric no degenerated 4- order Toeplitz matrices is a group and introduce the corresponding geometry called Toeplitz geometry. We introduce also the notion of induced Toeplitz geometry. Essentially we show that in these geometries any two vectors have some absolute invariants and defining the notion of plane we find also some absolute invariants of pairs consisting from vectors and planes. For all investigations we apply only the computer system Maple.

Gbolahan Bolarin   and O.M Bamigbola   

Finding the best way to vaccinate people against infectious disease is an important issue for health workers. In this study a compartmental two-time delay SVEIRS mathematical model with pulse vaccination and saturated incidence was formulated to examine the dynamics of infectious disease in a population. The existence of the disease free periodic solution was established and the compact form was derived. From our study, it was discovered that short pulse vaccination or long latent period or long immune period will guarantee eradication of the disease in the population. Lastly, the conditions for the incurability of the disease were examined.

Z. Yucedag   and R. Ayazoglu (Mashiyev)   

This paper is concerned with the existence of solutions to a class p(x) -Kirchhoff type problem with Dirichlet boundary data. Using a direct variational approach and the theory of the variable exponent Lebesque-Sobolev spaces, we establish some conditions that ensure the existence of nontrivial weak solutions.

Sidnyaev N.I.   Razgulyaev S.V.   and Shafikova S.E.   

This paper considers algorithms of search of an extremum, to solve the problem of planning the experiment using the gradient method. A feature of the algorithm is that when searching for the motion (when the maximum) does not occur in the direction of the gradient, which is unknown to us, but its estimate. Estimate of the gradient at the point when this factor space is based on the results of measurements carried out in the neighborhood. Researcher's task is to build a sensible plan with center to determine the estimate of the gradient in it.

Chii-Huei Yu   

The multiple integral problem is closely related with probability theory and quantum field theory. This paper uses the mathematical software Maple for the auxiliary tool to study two types of multiple integrals. We can obtain the infinite series forms of these two types of multiple integrals by using integration term by term theorem. In addition, we provide some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

Azhikhanov Nurlan   Zhunisov Nurseit   and Marasulov Usen   

In this work we defined the stress-strain state of anisotropic (transversely-isotropic) formation at a liquid filtration in it. There were established connection between voltage of formation and pressure of are filtrated. Numerical solution of the problem was received based on the finite element method with application of an isoparametric element of the first order.

Enfer Diez   

In this paper I present a polynomial different from of Euler, Genochi, Bernoulli and Bernstein. Ere different because each of them has a specific purpose is to say that each of these polynomials corresponds to a power of an integer and therefore exist as many polynomials as powers of integers. These polynomialsa are characterized by the same source (generatriz) and for this reason it is shown that: the sum of two such polynomials never is a third polynomial root corresponding to a power of an integer. This shows absolutely, Beal’s conjecture and again on T. Fermat. I think both Pierre Fermat and Andrew Beal were aware of these polynomials before stating his conjecture.

Hong Zhou   

We study a Gaussian beam propagation through a metamaterial lens by direct numerical simulations using COMSOL. We find that a metamaterial lens can deflect the beam significantly by either adjusting the shape of the lens or increasing the dielectric permittivity of the metamaterials.

R. Subba Rao   A. Naga Durgamamba   and R.R.L. Kantam   

A new probability model size biased Lomax is considered for a life time random variable. The problem of acceptance sampling when the life test is truncated at a pre-assigned time is discussed with a known shape parameter. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure the specified mean life time is evaluated. The operating characteristic functions of the sampling plans are derived. Producer’s risk is also discussed. A table for the ratio of true mean life to a specified mean life that ensure acceptance with a pre-assigned probability is provided. The results are given by an example.

M. Yamuna   and K. Karthika   

A domatic partition of a graph G = ( V, E ) is a partition of V into disjoint sets V₁, V₂, ..., V_K such that each Vi is a dominating set for G. A subdivision of a graph G is a graph resulting from the subdivision of edges in G. In this paper we discuss about the minimal properties of domatic subdivision stable graph and we show that every graph is an induced subgraph of a domatic subdivision stable graph. We discuss methods of generating new domatic subdivision stable graphs from existing domatic subdivision stable graphs using graph operations.

D.Ravi kiran   B.Rami reddy   and N.Ch.Pattabhiramacharyulu   

In this paper, a three species eco system, involving three pairs is considered to examine the local asymptotic stability: A Prey-Predator, a Commensal-Host and an Ammensal-Enemy. Among the three species, one plays a dual role: A host and an enemy. Time is considered as a discrete unit and the system is modeled as a set of three difference equations. All the equilibrium states are identified and the local asymptotic stability of some of the equilibrium states is examined by considering the perturbation equations. It is observed that among the states, the state in which the Prey and its Host species are washed out(extinct), is spectrally stable and the state where the Predator/Ammensal species is washed out, is asymptotically stable. The results are illustrated with two dimensional plots as well as surface plots.

Mustafa Avci  

The present paper deals with a nonlocal problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^N. The problem studied is a stationary version of the original Kirchhoff equation involving the p-Laplace operator. The question of the existence of weak solutions is treated. Using variational approach and applying the Mountain Pass Theorem together with Fountain theorem, the existence and multiplicity of solutions is obtained in the Sobolev space W^1,p(Ω).

Andrey Pavlov V.  

We prove a new inversion formula for Laplace transform in form SiCoLL(S(x))=c S(x),c=const., where Si is the sine-transform , Co is the cosine-transform of Fourier for not negative x , and L is the Laplace transform on real axis for not negative x .

Oleksandr Mokliachuk   

In this paper, models that approximate stochastic processes from the space Sub_φ(Ω) with given reliability and accuracy in L_p(T) are considered for some specific functions φ(t). For processes that are decomposited in series using orthonormal bases, such models are constructed in the case where elements of such decomposition cannot be found explicitly.

Alexandr Kozachok   

In this article second Navier – Stokes (NSE) exact transformation to the simpler equations is covered. This transformation is executed by classical methods of Mathematical Analysis. It is shown that 3-D NSE can be conversed to a traditional vector form which looks like 2-D Vorticity Transport Equations. Second result, as well as first one, is very important for the solution of Navier–Stokes existence and smoothness one of seven Millennium Prize Problems that were stated by the Clay Mathematics Institute. The proof of solution’ existence of such equations is simpler than traditional NSE. New equations will simplify the solutions of many other problems of Applied Mathematics in engineering, aeronautics, etc.

Ngutor Nyor   Omolehin J.O.   and Rauf K.   

The objective of the study was to allocate the available buses of the transport authority to the authority’s service intra and inter states routes in a manner that will yield optimum profit, taking all the constraints into consideration. The problem was modeled using Linear Programming (LP) and the TORA - computer software result yielded a maximum objective value of N897, 214 per day after 20 iterations, which is a better result compared to the current intuitive schedule by the authority that yields N766, 046 per day.

Keldibay Alymkulov   

The solution of the boundary value problem is constructed singularly perturbed differential equation of the order two with the turning point by method of boundary layer function.

Tiberiu Harko   Francisco S. N. Lobo   and M. K. Mak   

Ten new exact solutions of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y² are presented. The solutions are obtained by assuming certain relations among the coefficients a(x), b(x) and c(x) of the Riccati equation, in the form of some integral or differential expressions, also involving some arbitrary functions. By appropriately choosing the form of the coefficients of the Riccati equation, with the help of the conditions imposed on the coefficients, we obtain ten new integrability cases for the Riccati equation. For each case the general solution of the Riccati equation is also presented. The possibility of the application of the obtained mathematical results for the study of anisotropic general relativistic stellar models is also briefly considered.

Byung-Soo Lee   

In 2011, Gabeleh and Akhar [3] introduced semi-cyclic-contraction and considered the existence and convergence results of best proximity points in Banach spaces. In this paper, the author introduces a cone semi-cyclic φ-contraction pair in cone metric spaces and considers best proximity points for the pair in cone metric spaces. His results generalize the corresponding results in [1-5].

Victor Shchigolev   

In the present paper, we study a homogeneous cosmological model in Friedmann-Robertson- Walker (FRW) space-time by means of the so-called Homotopy Perturbation Method (HPM). First, we briefly recall the main equations of the cosmological model and the basic idea of HPM. Next we consider the test example when the exact solution of the model is known, in order to approbate the HPM in cosmology and present the main steps in solving by this method. Finally, we obtain a solution for the spatially flat FRW model of the universe filled with the dust and quintessence when the exact solution cannot be found. A comparison of our solution with the corresponding numerical solution shows that it is of a high degree of accuracy.

Pawan Kumar Sharma   and Sushil Kumar Saini   

This communication investigates the effect of magnetic field and radiating heat transfer on unsteady free convection viscous incompressible electric conducting fluid past a vertical surface in a rotating porous medium. It is assumed that surface is rotating with angular velocity W and the porous vertical surface is subjected to constant suction velocity. The variable heat flux is also assumed on the vertical surface varies with time; the governing equations are solved by adopting complex variable notations. The analytical expressions for velocity and temperature fields are obtained. The effects of various parameters on mean velocity, mean temperature, transient velocity and transient temperature have been discussed and shown graphically.

M.Mourabet   A. El Rhilassi   M.Bennani-Ziatni   and A. Taitai   

In this study, Response Surface Methodology (RSM) and Artificial Neural Network (ANN) were employed to develop an approach for the evaluation of fluoride adsorption process. A batch adsorption process was performed using apatitic tricalcium phosphate an adsorbent, to remove fluoride ions from aqueous solutions. The effects of process variables which are pH, adsorbent mass, initial concentration, and temperature, on the adsorption capacity (q_e (mg/g)) of fluoride were investigated through three-levels, four-factors Box-Behnken (BBD) designs. Same design was also utilized to obtain a training set for ANN. The results of two methodologies were compared for their predictive capabilities in terms of the coefficient of determination(R²), root mean square error (RMSE), and the absolute average deviation (AAD) based on the experimental data set. The results showed that the ANN model is much more accurate in prediction as compared to BBD.

M. Haythorpe   

It is well known that 3regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3-regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1-, 2- or 3-edge-connected depending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3-regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.

Hariwan Zikri Ibrahim   

In this paper we introduce and study the notion of (i, j)-ÎČ-I-i-open sets in ideal bitopological spaces and investigate some of their properties. Also we present and study (i, j)-ÎČ-I-i-continuous and (i, j)-ÎČ-Ii- almost continuous functions. Furthermore, we obtain basic properties and preservation theorems of (i, j)-ÎČ-I-i-continuous and (i, j)-ÎČ-I-i-almost continuous.

B. Achchab   A. Agouzal   N. Debit   and K. Bouihat   

In this paper, we derive an a posteriori error estimator, for nonconform- ing _nite element approximation of convection-diffusion equation. The a posteriori error estimator is based on the local problems on stars. Finally, we prove the reliability and the efficiency of the estimator without saturation assumption nor comparison with residual estimator

Abedlkader GASMI   and Afaf SALHI   

This paper concern with the two dimensional, steady flow problem of viscous incompressible fluid through an orifice. A problem of such type has been solved by applying Laplacian-Driver Method or LAD method given by Roache [1]. The resulting system of linear equations is solved by He’s homotopy perturbation method (HPM). The obtained results give a good agreement with the previous numerical solutions which reveals the effectiveness and convenience of the homotopy perturbation method (HPM).

R. Ponraj   S. Sathish Narayanan   and R. Kala   

Let G be a (p; q) graph. Let f : V (G) → {1; 2 ...,p} be a function. For each edge uv, assign the label |f (u) − f (v)|. f is called a difference cordial labeling if f is a one to one map and |e_f (0) − e_f (1)| ≀ 1 where e_f (1) and e_f (0) denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordial labeling behavior of subdivision of some snake graphs.

A. Lesfari   

In this paper we will give a proof of the classical Moser's lemma. Using it, we give a proof of the main Darboux theorem, which states that every point in a symplectic manifold has a neighborhood with Darboux coordinates.

Lev Kh. Ingel   

Previous investigations using the numerical modeling of moist convection in the atmosphere found an interesting effect: clouds arising through the water vapor condensation shield partially the underlying surface and change its radiation balance. The vertical heat fluxes on the surface become horizontally inhomogeneous, that can exert a back profound effect on the convection and dynamics of clouds, in particular, resulting in their horizontal transference (a cloud "runs away from its own shadow"). This paper is dedicated to the corresponding generalization of the classical Rayleigh problem on the convective instability of horizontal layer of a fluid. This generalization has as its object to describe the effect mentioned above – the influence of partial surface shielding on convection. The results show that the given relatively small modification of the Rayleigh problem, taking into account the possibility of the horizontally shifted thermal response to the vertical motions, leads to qualitatively new results. There appears a new, easily realizable type of instability, for which the strengthening of disturbances moving horizontally is typical.

Yu. A. Chirkunov   and E. O. Pikmullina   

Within one-dimensional model of shallow water it is investigated a one-parameter family of equations describes the propagation of surface waves above a straight bottom. The parameter of the family is the slope of the bottom. This family is generated by the equations of one-dimensional model of shallow water with a horizontal bottom. By means of the method of A- operators it is found that this system has an infinite aggregate of non-trivial zero-order conservation laws generated by the system of linear differential equations. As a result of special choice of the hodograph transformation, the system of equations of one-dimensional model of shallow water with a horizontal bottom is generated by the same system of linear differential equations. The group analysis of the systems is carried out. An infinite aggregate of non-degenerate solutions of the equations of one-dimensional model of shallow water with a straight bottom is received. All of the degenerate solutions of these equations are found. Thus, the data base of exact solutions of the equations of one-dimensional model of shallow water with a straight bottom is created. The solutions obtained in this paper may be used in the study of tsunami waves and fluid distribution in channels.

B.Satyanarayana   N. Srimannarayana   and Y. Pragathi Kumar   

In [10] we defined and studied a class of generalized hypergeometric functions . In this paper an attempt has been made to obtain some bilateral generating relations with . Each result is followed by its applications to the classical orthogonal polynomials.

Subhoshmita Mondal   and Sarangam Majumdar   

The isolate of white muscardine, Beauveria bassiana was isolated from soil using SDAY media. The experiment was studied under submerged culture in selective broth at varied interval of days, in view of dry weight of hyphal biomass. In this presentation we want to introduce a mathematical growth model of Beauveria bassiana and the perspective of stochastic analysis of this fungus and compare with experimental data.

S. N. Matia   and S. Alam   

In prey-predator system prey populations take various defensive mechanism to save themselves from predator and/or to get advantage in inter-species competition. In this work, we analyzed the dynamics of preypredator system with two prey species and single predator population in which two prey populations are fighting for the same resources. Here, it is assumed that one prey population exhibits herd behavior as their own defense mechanism and second prey population releases toxin elements which give them advantage of inter-species competition. From the analysis of our model we observed that the strategy of herd behavior as self defense mechanism is stronger than the toxin producing strategy. Also due to herd behavior of prey the model shows ecologically meaningful dynamics near origin.

B. S. Lee   and Arif Rafiq   

The purpose of this paper is to prove that the modified Mann iteration process can be applied to approximate the common fixed point of three strictly hemicontractive mappings in smooth Banach spaces.

R.K.Mishra   and Simaranjeet Kaur   

As we know that the sporting achievement is always interesting fascinating to human. The major of performance to improve the record and broken as with time, keeping the importance of the subject we have decided to study the problem as suggested by D.Edward & M.Hamson [1]. In this communication we have collected the data for 200m men/ women race athlete time for all three medalists (Gold, silver & bronze) in Olympics from last 60 years i. e. from 1948 to 2008. All the data have been presented in tabular form. It have been observed that the steady fall in winning times for the men’s race indicates that no limiting time for runner at all, which seems unreasonable. We may conclude that the linear model is only valid for a limited range of the years (It may be less than 60 years of the span). Obviously a different model would seem more suitable as T= a exp(-b). Another important conclusion is that, the more rapid improvement shown in women’s performance could indicates a closing up winning times with the men so that there would be equality between men’s and women’s time near about the year 2090 if performance improvement continued at the same rate.

Sirajo Abdulrahman   Niniuola Ifeoluwa Akinwande   Omotayo Bamidele Awojoyogbe   and Usman Yusuf Abubakar   

In this paper, we developed a new mathematical model for the dynamics of hepatitis B virus (HBV) transmission in a population with vital dynamics, incorporating vertical transmission and sexual maturity. We obtained the basic reproduction number R₀ , proof the local and global stability of the disease-free equilibrium of the model. Sensitivity analysis of R₀ with respect to the model parameters were carried out. Our result shows that birth rate, death removal rate, HBV sexual transmission probability per contact rate, and the average total sexual contacts rate are highly sensitive parameters that affect the transmission dynamics of HBV in any population. Thus, vaccination, condom usage and reduced-average sexual partner(s) are good strategies that can lead to controlling HBV transmission.

V. R. Lakshmi Gorty   

In this paper, the generalized Hankel-type wavelet transformation is developed. Using the developed theory of generalized Hankel-type convolution, the generalized Hankel-type translation is introduced. Properties of the kernel are developed in the study. Using the properties of kernel the generalized Hankel-type wavelet transformation is defined. The existence of the generalized Hankel-type wavelet transformation is given by a theorem. The boundedness and inversion formula for the generalized Hankel-type wavelet transformation is obtained. A basic wavelet which defines continuous generalized Hankel-type wavelet transformation, its admissibility conditions and the wavelet to the function is proved. Examples have been shown to explain the studied continuous generalized Hankel-type wavelet transformation.

D.V. Solomatin   

We study the proposed L.M. Martynov, the rank of a planarity for varieties of commutative semigroups.

Samuel Abubakar   Ninuola Ifeoluwa Akinwande.   and Sirajo Abdulrahman . Festus Abiodun Oguntolu   

In this paper we proposed a Mathematical model of Measles disease dynamics. The Disease Free Equilibrium (DFE) state, Endemic Equilibrium (EE) states and the characteristic equation of the model were obtained. The condition for the stability of the Disease Free equilibrium state was obtained. We analyze the bifurcation of the Disease Free Equilibrium (DFE) and the result of the analysis was presented in a tabular form.

Gagik Aghekyan   and Karen Sahakyan   

In the paper we consider the dynamic behavior of the critical points of some cubic polynomials, with the motion of one of the roots of the polynomial along a given trajectory. Some dynamic property of polynomials is investigated. The statements about traces of critical points of some polynomials are proved. The equations of curves, on which critical points move, are obtained.

Alexandru Lazari   

In this paper the zero-order Markov processes with final sequence of states X and unit transition time are analyzed. The evolution time T(p) of these systems is studied, where p represents the distribution of the states of the system. The problem of minimization the expectation E(T(p)) is considered. This problem is reduced to a geometric program, which is efficiently solved using convex optimization based on interior-point methods. The main idea of the proof is to show that the expression E(T(p))+1 is a posynomial function in variables which represent the components of distribution of the states that participate in final sequence of states. For some particular cases the explicit solution is obtained.

Mustafa Avci   

This paper deals with the existence of weak solutions for some nonlocal problem involving the p (x)- Laplace operator. Using a direct variational method and the theory of the variable exponent Sobolev spaces, we set some conditions that ensures the existence of nontrivial weak solutions.

Hassan Laarabi   Mostafa Rachik   Ouafa El Kahlaoui   and El Houssine Labriji   

In the present work, we consider a mathematical model of an SIR epidemic model with saturated incidence rate and saturated treatment function. We use an optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. Some results concerning the existence and the characterization of the optimal control will be given. Numerical simulations are also presented.

Byung-Soo Lee   

A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in [1].

Aiyesimi Y.M   Abah S.O.   and Okedayo G.T.   

The effects of mass and radiative heat transfer on free convective flow of a viscous incompressible optically thick fluid towards a vertical surface have been investigated. The nonlinear non-dimensional, similarity-transformed boundary-layer equations governing the problem are solved using an efficient numerical method based on the Runge-Kutta integration scheme and shooting iteration technique. Numerical calculations were carried out for different values of the various non-dimensional quantities governing the flow regime. The analysis shows that the temperature decreases with increasing radiation parameter, N while an increase in the Prandtl number leads to a corresponding decrease in the temperature profile; a rise in the thermal Grasshof and the mass transfer number leads to increase in the velocity profile and a rise in the Schmidt number Sc leads to a decrease in the concentration profile.

Alexandr Kozachok   

In this article the Navier – Stokes (NSE) exact transformations to the simpler equations is covered. This transformation is executed by classical methods of Mathematical Analysis. The solution of such equations is simpler than solution of the well known NSE. These new equations essentially facilitate the solutions of the Navier – Stokes Millennium Problem and different problems of numerous applications of Applied Mathematics in engineering.

Z. Kalateh Bojdi S. Ahmadi-Asl and A. Aminataei 

In this paper, a new and efficient approach for numerical approximation of second order linear partial differential-difference equations (PDDEs) with variable coefficients is introduced. Explicit formulae which express the two dimensional Jacobi expansion coefficients for the derivatives and moments of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. The main importance of this scheme is that using this approach reduces solving the general linear PDDEs to solve a system of linear algebraic equations, wherein greatly simplify the problem. In addition, some experiments are given to demonstrate the validity and applicability of the method.

Yomi Monday Aiyesimi Abdulhakeem Yusuf and Jiya Mohammed 

Hydromagnetic boundary layer micropolar fluid flow over a stretching surface embedded in a non-Dacian medium with variable permeability was considered in this work. The governing partial differential equations were transformed into their equivalent cylindrical coordinate system from its original form (rectangular form). A set of similarity parameters are employed to convert the governing partial differential equations to ordinary differential equations. The obtained self-similar equations are solved using the Adomian Decomposition Method. The effect of various physical parameters on the velocity profile, microrotation and temperature distribution were investigated. The obtained results shows that as the magnetic parameter and the inverse Darcy number D^-1 increase the velocity profile and the microrotation reduce while the temperature profile increases.

J. P. Jaiswal 

In the present paper, by approximating the derivatives in the Newton-Steffensen third-order method by central difference quotient, we obtain a new modification of this method free from derivatives. We prove that the method obtained preserves their order of convergence, without calculating any derivative. Finally, numerical tests confirm that our method give the better performance as compare to the other well known derivative free Steffensen type methods.

Utkin A.I. and Yushkanov A.A. 

Local electrical conductivity of a thin metal film, with the different coefficients of the reflection surfaces, is calculated in this article. The dependence of conductive function on the dimensionless frequency of volume electrons collisions, the dimensionless frequency of the external field and the dimensionless distance to the upper surface layer is analyzed. The case of thin film, when the thickness a lot more than average free path length of electrons, which led to the classic results for the electrical conductivity, is considered. The kinetic equation of Boltzmann in approximation of electrons relaxation time is used.

Yury I. Volkov 

In this paper we define and study the hybrids of exponential families and linear positive operators corresponding to them. These operators include some well-known operators as special cases.

Rasaq O. Olayiwola Razaq O. Jimoh Abdulhakeem Yusuf and Samuel Abubakar 

A mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.

Albana Diez 

Riemann’s hypothesis affirms that the existence of zeros for zed function have as the royal part as the only solution. In this article I analyzed and in turn demonstrates the existence of infinitys royal numbers for his royal part. To define all zeros, we will apply the method of progressive substitution.

Enfer Diez 

In this work I present the method to divide with rule and the compass any segment given in three parts and also, the polynomials of degree one for the construction of the angle with rule and the compass: b²x – 2xa² + 2a² = 0 (1) for any angle that belongs to an isosceles triangle. (b’)²x – 2xa² + 2(a+n)² = 0 (2) for any triangle which sum of two of his angles is minor to 90Âș, always (2a > b) ; (x > 1); x =(2; 3;4 ; 5; 6). (bx)²p₁ – 2a²p₁ + 2a²p = 0 (3) (p) prime number fixed, and x = (p₁; p₂; p₃;
.......±è_k) ; always (p < p₁ < p₂<

).

Tiberiu Harko Francisco S. N. Lobo and M. K. Mak 

The Chiellini integrability condition of the first order first kind Abel equation is extended to the case of the general Abel equation of the form where In the case α= 2 the generalized Abel equations reduces to a Riccati type equation, for which a Chiellini type integrability condition is obtained.

A. K. PAL and G. P. Samanta   

The present paper deals with the problem of a ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, local and global stability are addressed. We have also studied the effect of discrete time delay on the model. Computer simulations are carried out to illustrate our analytical findings.

Leonardo Acho 

A class of RC-OTA hysteretic-chaotic oscillators has been previously reported using electronics; therefore, hysteresis is realized by an electronic circuit. To obtain a mathematical model of this RC-OTA chaotic-electronic device, hysteresis modeling turns an important issue. Here, we develop a new mathematical hysteretic model proposing a new jounce-chaotic oscillator. Chaosity test is proved using PoincarÂŽe theory. After that, a synchronization scheme is granted to synchronize our new jounce-chaotic oscillator (the transmitter) to a dynamics second-order system (the receiver).

Abdul Majeed Siddiqui Tahira Haroon and Zarqa Bano 

This article examines the slip effect on the creeping flow of an incompressible second grade fluid in an axisymmetric channel having varying width. We have used three different methods depending upon the geometrical configuration to find out the solution. The results obtained are applied to study the flow of a second grade fluid through a smooth stenosis. To understand the flow behavior near stenosis, resistance to the flow and shear stress at the wall are calculated. The results obtained are graphically evaluated for different values of dimensionless non-Newtonian parameters, maximum height of the stenosis and slip parameter. It is observed that the resistance to the flow and wall shear stress increase with increasing value of non-Newtonian parameter and maximum height of the stenosis and decrease as the value of slip parameter increases.

S. Alam and A. K. Chongdar 

In this note, we have obtained some novel results on mixed trilateral generating functions involving , a modification of Jacobi polynomials by group-theoretic method. We have introduced a linear partial differential operator and found the corresponding extended form of the group. Finally, we obtained a novel generating function with the help of which, our desired result has been established.

Andrey Pavlov V. 

We consider K nodes in series in conditions of identical service: the time of service of one customer on one device of nodes is the same for all different nodes (a.s.) . In every node N devices are located, N≄1. Each node contains the infinite set of places for wait. The tonal number of customers, the time of wait in nodes 2,...,K remains limited for all moments of times in heavy traffic conditions on the first node , if ρ>1, ρ= 1, ρ→1 . The fact takes place , if the time of service of one customer by one device of node less than constant. Similar results are got in the general situation and for disciplines of service ”without interruption”.

K. K. Singh and Bineeta Nath 

Similarity solutions are obtained for one-dimensional adiabatic flow behind a gas-ionizing cylindrical shock wave propagating in a rotational axisymetric non-ideal gas with radiation heat flux, in presence of an azimuthal magnetic field. The electrical conductivity in the medium ahead of the shock is assumed to be negligible, which becomes infinitely large after passage of the shock. The ambient medium is considered to have variable axial velocity component in addition to the variable azimuthal velocity. In order to obtain the similarity solutions, the initial density of the medium is assumed to be constant and the initial angular velocity to be obeying a power law and to be decreasing as the distance from the axis increases. Effects of an increase in the value of the parameter of non-idealness of the gas, in the value of radiation parameter and in the value of the index for variation of azimuthal velocity of the ambient medium (or in the value of the index for variation of the ambient magnetic field) on the shock propagation are investigated. It is observed that the non-idealness of the gas or radiation heat-flux has decaying effect on the shock wave.

Andrej V. Plotnikov and Tatyana A. Komleva 

In this article we consider the some properties of the fuzzy R-solution of the controlled linear fuzzy differential inclusions. Also, many engineering systems use piecewise constant controls. However the majority of results of the theory of optimum control are received for measurable controls. In the given paper we introduce the algorithm of replacement of measurable control on piecewise constant control so that the corresponding fuzzy R-solutions of linear fuzzy systems would be close (with necessary accuracy)

K. P. R. Rao G.N.V. Kishore and P.R.Sobhana Babu 

In this paper, we have given a unique common fixed point theorem for four mappings in a cone metric type space which is a slight variant of theorems of [1, 10]. We also gave an example to illustrate our main theorem. Finally we have given an example in which theorem of [10] is not applicable whereas our corollary is applicable.

E.L. Pankratov and E.A. Bulaeva 

It has been recently shown, that manufacturing a diffusion-junction rectifier in a multilayer structure at optimal relation between annealing time, materials and thicknesses of layers of the structure gives us possibility to increase sharpness of p-n-junctions and to increase homogeneity of dopant distribution in enriched area. In this paper we estimate distributions of concentrations of charge carriers in the p-n-junction. At the same time we introduce an analytical approach to estimate the distributions. The approach gives us possibility to take into account spatiotemporal variations of properties of materials and several effects at one tine (diffusion of charge carriers et all), which recently have taken into account independently from each other.

Sarangam Majumdar 

Linear assignment problems are very well known linear programming problems. In a ground reality the entries of the cost matrix is not always crisp. In many application this parameters are uncertain and this uncertain parameters are represented by interval. In this contribution we propose interval Hungarian method and consider interval analysis concept for solving interval linear assignment problems.

D.L. Tsyganov 

The paper discusses possible methods of approximation of the chemical reaction rate constant for the range of values that lie outside of the experimental temperature range: direct approximation of chemical reaction rate constants obtained by processing experimental values; approximation based on an analytical model of dependence of the integrated process cross-section on energy; and approximation based on the direct solution of the chemical reaction rate constant equation with arbitrary dependence of the integrated process cross-section on energy. The second-order reactions CH₄+ČŃ→C±á₃+H+M, CH₃+ČŃ→C±á₂+H+M, CH₃+ČŃ→C±á+H₂+M were explored. To solve the integrated equation, the variational Tikhonov's regularization method was used. It was shown that this method allowed both estimating the threshold energy value and re-establishing the cross-section form. By using the calculated cross-section we can obtain estimated chemical reaction rate constants over a wide temperature range. The data obtained can be used in various calculations in applied fields, in particular, in hypersonic gas dynamics problems, as well as for filling information system databases.

Mujde Yilmazturk Ozgur Mizrak and Mehmet Kucukaslam 

In this paper, the concept of deferred statistical cluster points of real valued sequences is defined and studied by using deferred density of the subset of natural numbers. For p(n) and q(n) satisfying certain conditions, we give some results for the set of deferred statistical cluster points ;q (x). We provide some counter examples regarding ;q (x). Also we obtain some inclusion results for ;q (x). At last we consider the case and where the sequence is strictly increasing sequence of positive natural numbers with