Scientific Research Publishing

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53182#.VLcX2MnQrzE Author(s)     B. S. El-Desouky , F. A. Shiha , A. M. Magar Affiliation(s) Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt . ABSTRACT In this article, we study the generalized Bernoulli learning model based on the probability of success p i = a i /n where i = 1,2,...n 0< a 1 < a 2 <...< a n < n 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 p i = i / n p i = i 2 / n 2 and p i = i p / n p respectively. The probability function P(W n = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.   KEYWORDS Stirling Numbers , Bernoulli Learning Models , Comtet Numbers , Inclusion-Exclusion Prin...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50593#.VEX4z1fHRK0 Author(s) K. C. Garrett 1 , Kendra Killpatrick 2* Affiliation(s) 1 Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN, USA . 2 Natural Science Division, Pepperdine University, Malibu, CA, USA . ABSTRACT The Legendre-Stirling numbers were discovered by Everitt, Littlejohn and Wellman in 2002 in a study of the spectral theory of powers of the classical second-order Legendre differential operator. In 2008, Andrews and Littlejohn gave a combinatorial interpretation of these numbers in terms of set partitions. In 2012, Mongelli noticed that both the Jacobi-Stirling and the L...