the concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. in this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. also, we introduce the notion of  -hypergroups and closed  -subhypergroups. finally, we study the concept of  -semihypergroups associated to binary...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

In this note we nd the exact solution for the minimal recurrence S n = min bn=2c k=1 faS n?k + bS k g; where a and b are positive integers and a b. We prove that the solution is the same as that of the recurrence relation S n = aS dn=2e + bS bn=2c. In other words, S n = S 1 +(a+b?1)S 1 P n?1 i=1 a z(i) b blg nc?z(i) , where z(i) is the number of zeros in the binary representation of i. The proo...

We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these fami...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

The complete solution in (n, yx, yj) 6 Z3 of the Diophantine equation b„ = ±2yi yi is given, where (bn)nez is Berstel's recurrence sequence defined by />o = Z>i=0, b2 = l, b„+3 = 2bn+2 4b„+l + 4bn.

Some identities between partitions and compositions were obtained in the literature. As a natural extension, we introduce and study modulo-p partitions, where p is a positive integer. Moreover, several recurrence relations and some sufficient conditions for the existence of modulo-p partitions are given, respectively. In addition, we obtain some identities of modulo-p partitions. In the end, us...

Chebyshev polynomials of the first and the second kind in n variables z. , Zt , ... , z„ are introduced. The variables z, , z-,..... z„ are the characters of the representations of SL(n + 1, C) corresponding to the fundamental weights. The Chebyshev polynomials are eigenpolynomials of a second order linear partial differential operator which is in fact the radial part of the Laplace-Beltrami op...

Abstract. Following Poupard’s study of strictly ordered binary trees with respect to two parameters, namely, “end of minimal chain” and “parent of maximum leaf” a true Tree Calculus is being developed to solve a partial difference equation system and then make a joint study of those two statistics. Their joint distribution is shown to be symmetric and to be expressed in the form of an explicit ...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.