The set equality problem is to decide whether two sets A and B are equal or disjoint, under the promise that one of these is the case. Some other problems, like the Graph Isomorphism problem, is solvable by reduction to the set equality problem. It was an open problem to find any w(1) query lower bound when sets A and B are given by quantum oracles with functions a and b. We will prove Ω( n 1/3...

......An instruction set architecture (ISA) is one of the most important interfaces in a computer system because it divides software from hardware. Most widely used ISAs were developed decades ago and are proprietary. This may make sense because hardware implementations were and are mostly proprietary and most software was proprietary when these ISAs were developed. Today, however, we appreciat...

The notions of pre-local function, semi-local functions and α-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of P -I-open sets and P -I-closed sets in ideal topological spaces are discussed. Relations between I-open sets and P -I-open sets are provided, and several properties related to P -I-open sets, pre-local...

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

In the present paper, we prove uniqueness of renormalized solution class quasilinear elliptic problems with L1 data given by −div(B(x,u1)∇u1)=finΩ1,−div(B(x,u2)∇u2)=finΩ2,u1=0on∂Ω,(B(x,u1)∇u1)ν1=(B(x,u2)∇u2)ν1onΓ,(B(x,u1)∇u1)ν1=−h(x)(u1−u2)onΓ.The open sets Ω1 and Ω2, Γ as interface between them, are two components domain Ω. The f is in L1(Ω). addition to uniform ellipticity, also prescribe ass...

in this paper, using pre-semi-open l-sets and their inequality, a new notion of ps-compactness is introduced in l-topological spaces, where l is a complete de morgan algebra. this notion does not depend on the structure of the basis lattice l and l does not need any distributivity.

In this state-of-the-art paper, important advances that have been made during the past five years for both general and interval type-2 fuzzy sets and systems are described. Interest in type-2 subjects is worldwide and touches on a broad range of applications and many interesting theoretical topics. The main focus of this paper is on the theoretical topics, with descriptions of what they are, wh...