Zero forcing is a game played on a graph that starts with a coloring of the vertices as white and black and at each step any vertex colored black with a unique neighbor colored white “forces” the color of the white vertex to become black. In this note we look at what happens when we balance the size of the initial set of vertices colored black and the number of steps, called speed of propagaion...

In this paper, we investigate the Zero-Forcing equalizer based on Fast One Sided Jacobi (ZF-FOSJ) algorithm for the Multiple Input Multiple Output Power Line Communication (MIMO PLC) systems. The proposed algorithm determines the pseudo-inverse of estimated channel matrix using only real matrix and operations free from trigonometric functions. The hardware implementation complexity is reduced c...

We propose a modulus based zero-forcing (MZF) detection for multi-input multi-output (MIMO) channels. Traditionally, a ZF detector nulls out all interferences from other layers when detecting a current layer, which can yield suboptimal detection-performance due to the noise-enhancement issue. In many communication systems, finite alphabets such as M quadrature-amplitude-modulation (QAM) are wid...

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 paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

Zero forcing can be described as a graph process that uses color change rule in which vertices white to blue. The throttling number of minimizes the sum initially colored blue and time steps required entire graph. Positive semidefinite (PSD) zero is commonly studied variant standard alters rule. This paper introduces method for extending using PSD process. Using this extension method, graphs wi...

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

in this paper, some fundamental concepts are given relating to fuzzytopological spaces. then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. also the fuzzy topological spaces which are hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

fuzzy rough n-ary subhypergroups are introduced and characterized.