‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

In this paper, control of a non-isothermal continuous stirred tank reactor in which two parallel autocatalytic reactions take place has been addressed. The reactor shows chaotic behavior for a certain set of reactor parameters. In order to control the product concentration, an optimal state feedback controller has been designed. Since concentrations of reactor species are ...

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...

The aim of this paper is to introduce the concept of Λ operator of a fuzzy set in a fuzzy bitopological space.Then we study (i, j)-fuzzy Λγ -set and its properties. Moreover, we define (i, j)-fuzzy Λ-closed set, (i, j)-fuzzy Λγ -closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts of (i, j)-fuzzy Λ-closed set and (i, j)-fuzzy generalized closed set are i...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy weakly generalized closed set and intuitionistic fuzzy weakly generalized open set in intuitionistic fuzzy topological space. We investigate some of their properties. Also we study the application of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy wT1/2 space and intuitionisti...

A method for generating an interpolation closed G arc spline on a given closed point set is presented. For the odd case, i.e. when the number of the given points is odd, this paper disproves the traditional opinion that there is only one closed G arc spline interpolating the given points. In fact, the number of the resultant closed G arc splines fulfilling the interpolation condition for the od...

In this dissertation, we study the following two topics, i.e., the union closed set conjecture and the maximum edges cut in connected digraphs. The union-closed-set-conjecture-topic goes as follows. A finite family of finite sets is union closed if it contains the union of any two sets in it. Let XF = ∪F∈FF . A union closed family of sets is separating if for any two distinct elements in F , th...

In this paper we present a new framework for computing the backward reachability from an upward-closed set in a class of parameterized (i.e. infinite state) systems that includes broadcast protocols and petri nets. In contrast to the standard approach, which performs a single least fixpoint computation, we consecutively compute the finite state least fixpoint for constituents of increasing size...