A k-element subset D of a finite multiplicative group G of order v is called a (v, k, λ, μ)partial difference set in G (PDS) provided that the multiset of ‘differences’ {d1d −1 2 | d1, d2 ∈ D, d1 6= d2} contains each nonidentity element of D exactly λ times and each nonidentity element in G\D exactly μ times. See [11] for background on partial difference sets. We will limit our attention to abe...

Given two graphs G = (VG, EG) and H = (VH , EH), a homomorphism from G to H is a function f : VG → VH such that for every uv ∈ EG, f(u)f(v) ∈ EH . A homomorphism from G to H is referred to as an H-colouring of G and the vertices of H are regarded as colours. The graph H is called the target of the homomorphism. These definitions extend to directed graphs by requiring that the mapping must prese...

We construct multiplicative Green?s (or +Green?s) function for *Sturm-Liouville (*SL) equation. The basic properties of *Green?s are given. Then, *SL equation is evaluated by using function. Effectiveness in *case will thus be seen some examples.

There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0, 1}n → Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions ...