in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions  $ u(x,0) = u_0 (x)$  and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ;  f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

Given a topological space X and a complete lattice L, we study the space of L-predicates F L (X) = X ! L op ] op , continuous maps from X to L op in its Scott-topology. It yields a functor F L () from TOP-L, a full subcategory of TOP subsuming continuous domains, to SUP, the category of complete sup-lattices and maps preserving suprema. Elements of F 2 (X) are continuous predicates (= closed se...

The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...

This paper presents a novel topology of single-phase multilevel inverter for low and high power applications. It consists of polarity (Level) generation circuit and H Bridge. The proposed topology can produce higher output voltage levels by connecting dc voltage sources   in series and parallel. The proposed topology utilizes minimum number of power electronic devices which helps in reduction o...

The authors study the Hodge theory of the exterior differential operator d acting on q-forms on a smoothly bounded domain in R, and on the half space R + . The novelty is that the topology used is not an L 2 topology but a Sobolev topology. This strikingly alters the problem as compared to the classical setup. It gives rise to a boundary value problem belonging to a class of problems first intr...

and Applied Analysis 3 The final solution to problems in 1.3 can yield optimal lower and upper bounds of eigenvalues. Actually, from 1.3 , we have In ∥q ∥ ∥ 1 ) ≤ λn ( q ) ≤ Mn ∥q ∥ ∥ 1 ) ∀q ∈ L1, 1.4 which are optimal. Several extremal problems on Dirichlet, Neumann, and periodic eigenvalues of the Sturm-Liouville operator and the p-Laplace operator have been studied recently, where the potent...

We investigate uniqueness issues that arise in l∞-optimization to linear spaces and Bergman fans of matroids. For linear spaces, we give a polyhedral decomposition of R based on the dimension of the set of l∞-nearest neighbors. This implies that the l∞-nearest neighbor in a linear space is unique if and only if the underlying matroid is uniform. For Bergman fans of matroids, we show that the se...

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...