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Generalization of some Problems with <i>s</i>-separation

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Applied Mathematics 2015年第1期6卷 1-6页

作者： beih el-sayed el-desouky Mohamed Moustafa Gad shimaa el-Eraqy Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

In this article we apply and discuss el-desouky technique to derive a generalization of the problem of selecting k balls from an n-line with no two adjacent balls being s-separation. We solve the problem in which the separation of the adjacent elements is not having odd and even separation. Also we enumerate the number of ways of selecting k objects from n-line objects with no two adjacent being of separations m, m + 1, …, pm, where p is positive integer. Moreover we discuss some applications on these problems.

关键词： Probability Function ss-separation s-successions n-Line n-Circle

Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

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Open Journal of Modelling and simulation 2021年第4期9卷 351-369页

作者： Mohamed M. Buzaridah Dina A. Ramadan beih.s. el-desouky Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

In this paper, a new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to the inverse Lomax distribution (IFD). This method is known by the flexible reduced logarithmic-X family of distribution (FRL-X). The proposed distribution can be called a flexible reduced logarithmic-inverse Lomax distribution (FRL-IL). The statistical and reliability properties of the proposed models are studied including moments, order statistics, moment generating function, and quantile function. The estimation of the model parameters by maximum likelihood and the observed information matrix are also discussed. In order to assess the potential of the newly created distribution. The extended model is applied to real data and the results are given and compared to other models.

关键词： Lomax Distribution Inverse Lomax Distribution Hazard Rate Function Maximum Likelihood Estimators skewness and Kurtosis Moment Generating Function

some New Results on the Number of Paths

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Open Journal of Modelling and simulation 2015年第3期3卷 63-69页

作者： beih.s. el-desouky Abdelfattah Mustafa E. M. Mahmoud Mathematics Department Faculty of Science Mansoura University Mansoura Egypt Mathematics Department Faculty of Science Aswan University Aswan Egypt

Khidr and el-desouky [1] derived a symmetric sum involving the stirling numbers of the first kind through the process of counting the number of paths along a rectangular array n*m denoted by ?Anm. We investigate the generating function for the general case and hence some special cases as well. The probability function of the number of paths along is obtained. Moreover, the moment generating function of the random variable X and hence the mean and variance are obtained. Finally, some applications are introduced.

关键词： stirling Numbers Generating Function Moment Generating Function Comtet Numbers Maple Program

Multiparameter Higher Order Daehee and Bernoulli Numbers and Polynomials

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Applied Mathematics 2017年第6期8卷 775-785页

作者： beih.s. el-desouky Abdelfattah Mustafa Fatma M. Abdel-Moneim Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

This paper gives a new generalization of higher order Daehee and Bernoulli numbers and polynomials. We define the multiparameter higher order Daehee numbers and polynomials of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. The relations between these numbers and stirling and Bernoulli numbers are obtained. Furthermore, some interesting special cases of the generalized higher order Daehee and Bernoulli numbers and polynomials are deduced.

关键词： Daehee Numbers Daehee Polynomials Higher-Order Daehee Numbers Higher-Order Daehee Polynomials Higher-Order Bernoulli Polynomials Multiparities Daehee Polynomials

Generalized Power Akshaya Distribution and Its Applications

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Open Journal of Modelling and simulation 2021年第4期9卷 323-338页

作者： Ahmed T. Ramadan Ahlam H. Tolba beih.s. el-desouky Department of Basic sciences High Raya Institute New Damietta Egypt Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

In this paper, a new two-parameter distribution called generalized power Akshaya distribution extended from Akshaya distribution is introduced. This distribution is proposed to model lifetime data. Statistical properties like density, hazard, survival and moments are derived. Two parameters estimation is introduced using maximum likelihood and Bayesian techniques. Finally, an application of real data and a simulation study are introduced to illustrate the usefulness of the proposed distribution.

关键词： Akshaya Distribution Generalized Distributions Moments Estimation

solution of Nonlinear stochastic Langevin’s Equation Using WHEP, Pickard and HPM Methods

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Applied Mathematics 2014年第3期5卷 398-412页

作者： Maha Hamed Magdy A. el-Twail beih el-desouky Mohamed A. el-Beltagy Department of electrical & Computer Engineering Engineering Faculty Effat University Jeddah KSA Department of Engineering Mathematics & Physics Engineering Faculty Cairo University Giza Egypt Department of Mathematics Faculty of Science & Mansoura University Mansoura Egypt

This paper introduces analytical and numerical solutions of the nonlinear Langevin’s equation under square nonlinearity with stochastic non-homogeneity. The solution is obtained by using the Wiener-Hermite expansion with perturbation (WHEP) technique, and the results are compared with those of Picard iterations and the homotopy perturbation method (HPM). The WHEP technique is used to obtain up to fourth order approximation for different number of corrections. The mean and variance of the solution are obtained and compared among the different methods, and some parametric studies are done by using Matlab.

关键词： Nonlinear stochastic D.E Langevin’s Equation WHEP Technique Picard Approximation HPM Technique

solution of stochastic Van der Pol Equation Using spectral Decomposition Techniques

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Applied Mathematics 2020年第3期11卷 184-202页

作者： Maha Hamed Ibrahim L. el-Kalla Mohamed A. el-Beltagy beih.s. el-desouky Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt Department of Engineering Mathematics & Physics Faculty of Engineering Mansoura University Egypt Department of Engineering Mathematics & Physics Faculty of Engineering Cairo University Giza Egypt

In this paper, we introduce the study of the general form of stochastic Van der Pol equation (sVDP) under an external excitation described by Gaussian white noise. The study involves the use of Wiener-Chaos expansion technique (WCE) and Wiener-Hermite expansion (WHE) technique. The application of these techniques results in a system of deterministic differential equations (DDEs). The resulting DDEs are solved by the numerical techniques and compared with the results of Monte Carlo (MC) simulations. Also, we introduce a new formula that facilitates handling the cubic nonlinear term of van der Pol equations. The main results of this study are: 1) WCE technique is more accurate, programmable compared with WHE and for the same order, WCE consumes less time. 2) The number of Gaussian random variables (GRVs) is more effective than the order of expansion. 3) The agreement of the results with the MC simulations reflects the validity of the forms obtained through theorem 3.1.

关键词： Van der Pol Oscillator Wiener-Chaos Expansion Wiener-Hermite Expansion Limit Cycle White Noise Damping Force

A Family of Generalized stirling Numbers of the First Kind

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Applied Mathematics 2014年第10期5卷 1573-1585页

作者： beih.s. el-desouky Nabela A. el-Bedwehy Abdelfattah Mustafa Fatma M. Abdel Menem Mathematics Department Faculty of Science Damietta University Damietta Egypt Mathematics Department Faculty of Science Mansoura University Mansoura Egypt

A modified approach via differential operator is given to derive a new family of generalized stirling numbers of the first kind. This approach gives us an extension of the techniques given by el-desouky?[1]?and Gould?[2]. some new combinatorial identities and many relations between different types of stirling numbers are found. Furthermore, some interesting special cases of the generalized stirling numbers of the first kind are deduced. Also, a connection between these numbers and the generalized harmonic numbers is derived. Finally, some applications in coherent states and matrix representation of some results obtained are given.

关键词： stirling Numbers Comtet Numbers Creation Annihilation Differential Operator Maple Program