We study compositions of the integer n in which the first part, successive differences, and the last part are constrained to lie in prescribed sets L,D,R, respectively. A simple condition on D guarantees that the generating function f(x,L,D,R) has only a simple pole on its circle of convergence and this at r(D), a function independent of L and R. Thus the number of compositions is asymptotic to...

background: a high-fat diet (hfd) and fat accumulation promote the oxidative stress formation, which in turn has hazardous effects on reproductive system and fertility. therefore, the present study examines the potential positive effects of a restricted high-fat diet (rhfd) and antioxidants consumption on sperm parameters in rats. methods: 48 male albino wistar rats divided to four groups (n=12...

in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.