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A Family of Generalized Stirling Numbers of the First Kind

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

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Extension of Generalized Bernoulli Learning Models

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Open Journal of Modelling and Simulation 2015年第1期3卷 26-31页

作者： B. S. El-Desouky F. A. Shiha A. M. Magar Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulnasser and Khidr [1], Rashad [2] and EL-Desouky and Mahfouz [3] as special cases, where pi = i/n pi = i2/n2 and pi = ip/np respectively. The probability function P(Wn = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.

关键词： Stirling Numbers Bernoulli Learning Models comtet Numbers Inclusion-Exclusion Principle

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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

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