Abstract: Let defined multistep game ΓG on a graph tree Γ. The postman’s problem on a complete graph with finite number of agents which responsible for the postman’s route and with varying weights given to the graph edges is a stage game G in each vertex on graph tree Γ. The problem G will be called a competitive one-period postman problem with varying parameters. In this parer competitive many-period postman problem with with varying papametres is examined. A multistep game with the postman problem realized on each step having a finite number of agents and varying matrix of weights given to the graph edges depending on the step (period), will be called a competitive many-period postman problem with varying parameters. The payoffs of the postman problem participants (players) including the postman himself in the simultaneous games G are their profits minus costs for providing postman’s movement on the routes. The routes are the players’ strategies. An algorithm for finding a compromise situation for solving simultaneous games is proposed. The theory is illustrated by the example of three-step game of three players. 7250 Xeniya Grigorieva and Oleg Malafeev Mathematics Subject Classification: 91 Axx

Abstract: In this work we obtain an exact solution to cubic Duffing oscillator equation with initial conditions and bounded periodic solutions. This solution is expressed in terms of the Jacobi elliptic function cn. In particular, we may apply the exact solution in the study of the cubic nonlinear Schrodinger equation, which is reduced to a cubic Duffing oscillator equation by means of a traveling wave transformation.

Abstract: The inverse Weibull distribution can be readily applied to a wide range of situations including applications in medicine, reliability and ecology. In this article we introduce a new model of generalized inverse Weibull distribution referred to as the Exponentiated generalized inverse distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment thus generalizing some results in the literature. Expressions for the density, moment generating function and rth moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix

Abstract: For the normal cumulative distribution function: Φ(x) we give the new approximation 2**(-22**(1-41**(x/10))) for any x>0, which is very simple (with only integer constants and operations and / and power elevation **) and is very simply explicitly invertible having 1 entry of x. It has 3 decimals of precision having absolute error less than 0.00013. We compute the inverse which approximates the normal quantile function, or probit, and it has the relative precision of 1 percent (from 0.5) till beyond 0.999. We give an open problem and a noticeable bibliography. We report several other approximations. Mathematics Subject Classification: 33B20 , 33F05 , 65D20 , 97N50

Abstract: The paper is devoted to development and numerical implementation for a method for investigation of stress-strain state of the solids with large elastic-plastic deformations. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The arc-length method is used. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar.

Abstract: Abstract Diabetes is a chronic disease with a huge and growing socio-economic burden affecting individuals, families and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment. Our model shows that, using optimal control, the number of diabetics with and without complications can be significantly reduced in a period of 10 years.

Abstract: Conjugate gradient (CG) methods are widely used for solving large scale unconstrained optimization problems. Many studies have been devoted to develop and improve these methods. In this paper, we compare our new CG coefficient

Abstract: Nowadays, Telemarketing is an interactive technique of direct marketing that many banks apply to present a long term deposit to bank customers via the phone. Although the offering like this manner is powerful, it may make the customers annoyed. The data prediction is a popular task in data mining because it can be applied to solve this problem. However, the predictive performance may be decreased in case of the input data have many features like the bank customer information. In this paper, we focus on how to reduce the feature of input data and balance the training set for the predictive model to help the bank to increase the prediction rate. In the system performance evaluation, all accuracy rates of each predictive model based on the proposed approach compared with the original predictive model based on the truth positive and receiver operating characteristic measurement show the high performance in which the smaller number of features.

Abstract: In the present paper, medium and long term yield simulation and energy estimation are carried out for conventional tillage and for no-tillage. Analyses were performed by means of forecasting model SALUS. Such software was fed with several data sets: climatological data summaries (since 1990), climate forecasts (from 2011 to 2025), soil characteristics, crops and management techniques for eight different farms involved in the study. For each farm, simulations provided yield in the case of both conventional and no-tillage. Technical input and yield were converted into energy in order to estimate efficiency. Medium and long term forecasts reveal how no-tillage can provide a better energy efficiency, with enhanced effects in the long term.

Abstract: We have checked the Volterra integral equations of the second kind with an integral of the form of a convolution by using the Elzaki transform. Mathematics Subject Classification: 45B05, 44A05

Abstract: In this paper, we investigate the traveling wave solutions for some new fifth-order partial differential equations introduced by Wazwaz in [1]. We use the G′/G expansion method to determine soliton solutions of these equations. Also, a periodic solutions to these equations are investigated by means of rational sine or cosine ansatze methods. The conditions of existence and uniqueness of such solutions are also presented. Mathematics Subject Classification: 74J35, 35G20.

Abstract: The paper is devoted to development and numerical implementation for a method for investigation of stress-strain state of the solids with large elastic deformations. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The incremental method is used. A spatial discretization is based on the finite element method. The examples of problems and their solutions are given.

Abstract: Nonlinear conjugate gradient (CG) methods are widely used for solving large scale unconstrained optimization problems. Many studies have been devoted to modified and improve this method. In this paper, a new parameter of CG method that possesses global convergence properties using exact line search is proposed. Numerical results show that the new formula is best and more efficient when compared with the other classical CG methods

Abstract: Regression analysis is a method used to determine the relationship between the predictor variables with the response variables. One of the uses of regression analysis is in the analysis of longitudinal data, and using bi-responses. Nonparametric regression approach is used when the shape of the curve regression is unknown, so we called the model of bi-responses nonparametric regression model for longitudinal data. The purposes of this study are to obtain the function form of the nonparametric bi-responses regression on longitudinal data, to obtain the spline estimator in estimating the nonparametric bi-responses regression curve on longitudinal data, and to apply the spline estimator in estimating the curve of nonparametric bi-responses regression on longitudinal data on simulated data. bi-responses nonparametric regression model on longitudinal data on the equation () kit ki it kit y f x 

Abstract: Consider data pairs 1 1 ( ,..., , ,..., , ) i ir i ip i x x t t y involving in a semiparametric regression model ( , ) i i i i y x t      , where 1 ( , ) ( ), p i i i j ji j x t x g t        1, , ; i n  1,..., j p  is the semiparametric regression curve. Response variable i y is assumed to be proportional to predictor variable 1 ( ,..., ) i i ir x x x   , but at the same time, its relationship with other predictor variables 1 ( ,..., ) i i ip t t t  is unidentified. The i x   and ( ) j ji g t are, parametric and nonparametric components respectively. In this study, the nonparametric component is approximated by Fourier series which is expressed by

Abstract: In this work, we investigate the traveling wave solutions for (2+1)dimensional dispersive long water-wave system. We use the G′/G expansion method to determine kink and soliton solutions of this model. Also, a periodic solutions are obtained by using rational cosine and rational sine method. Mathematics Subject Classification: 74J35, 35G20

Abstract: In operation the fundamentals of a technique of numerical research of finite strains of the isotropic hyperelastic bodies, oriented on application FEM are stated. The first section is devoted kinematics of finite strains in the Lagrangian frame, tensors and measures of the strain, defining are entered speeds, various tensors of stress are reduced. In the second section physical parities of the hyperelastic isotropic environment are formulated, using the thermodynamics equations. In the third section it is reduced resolving the equation in a current configuration and the parities defining speed of change of a stress tensor of Cauchy-Euler as linear function from a tensor of a spatial gradient of speed are output.

Abstract: The objective of this work was to investigate the brake specific fuel consumption (BSFC) of the engine, installed in an agricultural tractor, fueled before with diesel oil (B0) and then with biodiesel (B100). This was done both vs. the engine speed, which vs. engine load. To understand the influence of the fuel heating value and the brake thermal efficiency (BTE), a mathematical modeling of the BTE vs. engine speed and engine torque was developed. The bench tests on the engine, fueled with the two fuels (B0 and B100), allowed to point out that on average, the BTE of the engine was unchanged in the comparison between the two fuels, while the average BSFC was 19% higher with the B100, consistent with the lower heating value of B100 (-17.2%). However, the power output of the engine with the B100 was not reduced by the same amount, but with an average value of 11%, as there was a partial recovery due to the slight increase in the fuel consumption rate. The fitting of the mathematical model to the engine, fuelled with the two fuels (B0 and B100), allowed to draw the diagrams of the calculated BTE and BSFC contours for both fuels, with a good accuracy represented by a mean relative error of 2.1±2.2% (B0) and 2.0±1.5% (B100). Finally, the comparison of the previous results, allowed to highlight the points of the engine speed-torque plane where the biodiesel BTE was different than that of diesel oil BTE. It emerged that the engine fuelled with B100 had a higher BTE at low load and speed, but lower than that of B0 at high speed due to reduced inclination to evaporate compared to diesel oil, which is critical when the speed increases and the time available for combustion is reduced.

Abstract: Local numerical methods for scattered data interpolation often require a smart subdivision of the domain in geometrical polyhedral structures. In particular triangulations in the plane (2D) and tetrahedrizations in the space (3D) are widely used to dene interpolation models. In this paper we give a short survey on the main methods for the scattered data problem and we recall preliminaries on triangulations and their related properties. Finally, combining two well-known ideas we present a new triangle-based interpolation method and show its application to a case study.

Abstract: An intuitionistic fuzzy set (IFS), an extended version of a fuzzy set, is more applicable for representing vague information since it provides a way to control a degree of hesitation. One of most prominent research directions on the theory of IFSs is measurement of similarity between IFSs. Even several similarity measures have been proposed, some unreasonable cases can be made by such measures. In this paper, we present two similarity measures: one is a set-theoretic measure, the other combines the former measure and the concept of similarity measures on a concept lattice. In our experimental study, we focus our attention on two basic directions of performance evaluation: one is how much the proposed measures are reasonable and the other is how much accuracy the measures produce when they are applied to pattern recognition. The experimental results show that the both measures are reasonable and achieve satisfactory performances on pattern recognition. Mathematics Subject Classification: 03E72, 68T10

Abstract: The Analytic Hierarchy Process (AHP) is a mathematical technique for multi-criteria decision-making. Complex problems or issues involving value or subjective judgments are suitable applications of the AHP approach. ‘Factors considered for the selection of Undergraduate Engineering Institution by the students’, is the research topic of interest. It involves a number of qualitative judgments based on multi-criteria at multi-levels and can be addressed using AHP. Students’ opinions are collected in AHP using pair wise comparisons. As the number of alternatives increases, the number of comparisons increases enormously. Hence the selection of a proper measuring instrument that will reduce the data collection

Abstract: We considered the local Markov approximation method for the definition of the precision characteristics of statistical analysis algorithms of information processes with unknown discontinuous parameters in the presence of Gaussian distortions 4470 O. V. Chernoyarov et al. and illustrated the use of the stated approach in practical applications for the analysis of operating efficiency of detectors and measurers of the quasi-determined and random signals.

Abstract: Humans need to eat a good and balanced nutritious diet that provides calories for energy requirements and nutrients for proper growth, repair and maintenance of the body tissues. Moreover, it is essential for resisting and preventing diseases and infection that may lead to problems such as anemia, scurvy and rickets. In recent studies, medical researchers have discovered that good nutrition can help to reduce the risks of coronary heart disease and certain types of cancer. Menu and diet planners face tremendous challenges and difficulties in order to improve human health. Serving healthier meals is a major step towards achieving that objective. However, constructing and planning a nutritious and balanced menu manually is complicated, inefficient and time-consuming. The aim of this study is to develop a mathematical model for diet planning that meets the necessary nutrient intake for the secondary school student as well as minimizing a budget. The data were collected from various boarding schools and also from the Ministry of Education. Nutrition planning is a well-known optimization problem and the goal is to find the best possible optimal solution. Therefore the model was solved by using optimization method along with Integer Programming. This model can be adopted to solve other diet planning problems such as for the military, hospitals nursing home and universities.

Abstract: In this paper, we revisited the concept of secure dominating set introduced by Cockayne et al. We characterized secure dominating set in terms of the concept of external private neighborhood of a vertex. Also we give necessary and sufficient conditions for connected graphs to have secure domination number equal to 2. We give some characterizations of the concept of secure domination in the joins K1 + G and G + H, where G and H are connected non-complete graphs and then determine their corresponding secure domination numbers. Mathematics Subject Classification: 05C69

Abstract: Meshless Local Petrov Galerkin (MLPG) techniques are pure meshless methods nowadays used to solve a large class of Partial Differential Equations. Recently, the Direct MLPG (DMLPG) techniques have been proposed. They are based upon the Generalized Least Square Method. DMLPG technique alleviates some difficulties found in MLPG, such as tricky numerical integration. In this article we report our expansion of DMLPG techniques to 3D Poisson problems. We also compare MLPG vs DMLPG performances.

Abstract: Cryptography is an evolving field that research into discreet mathematical equation that is representable by computer algorithm for providing message condentiality. The scheme has been widely used by nation-states, corporates and individual who seeks privacy for data in storage and during transmission. This paper provides a ground up survey on elliptic curve cryptography. It tailors the mathematics behind elliptic curve to the applicability within a cryptosystem. In brief, elliptic curve is a study of points on two-variable polynomials of degree 3. With curve dened over a finite field, this set of points acted by an addition operation forms a finite group structure. Also known as torsion points, they are used to represent the coded messages. Encryption and decryption transform a point into another point in the same set. Besides providing conceptual understanding, discussions are targeting the issues of security and efficiency of elliptic curve cryptosystem. This paper serve as a basis in guiding anyone interested to understand the fundamental concept behind this cryptosystem. Moreover, we also highlight subareas of research within the scope of elliptic curve cryptosystem.

Abstract: This paper considers the solutions of systems of ordinary differential equations via a numeric-analytical method referred to differential Transforms Method (DTM). For numerical interpretation, two illustrative examples are used. The results obtained show a strong agreement with their corresponding exact solutions. The method is therefore proven to be effective and reliable, and as such, can be applied to systems of ODEs involving higher orders.

Abstract: The prices of rice keep changing from time to time. It creates risks to producers, suppliers, consumers, and other parties that involved in marketing and production of rice. Thus, it is important to do forecasting on rice prices data set. This paper tries to apply a hybrid methodology which is an integration of empirical mode decomposition (EMD) and autoregressive integrated moving average (ARIMA). The EMD-ARIMA is applied on the data of the monthly prices of rice in Malaysian Ringgit (MYR) per metric ton. Forecasting result found that EMD can improve the accuracy of the ARIMA forecasting on the prices of rice based on the comparison of root mean squared error (RMSE) and mean absolute error (MAE).