Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L′(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounde...

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...

Given a finite partially ordered set B, it is often of interest to describe the largest possible subsets SC B which consist of mutually incomparable elements of B. Such subsets are usually called maximum antichains or maximum Sperner families of .P after Sperner [I 51, who first characterized these maximum antichains in the case that 9 is a finite Boolean lattice, i.e., the set of all subsets o...

Within the past 20 years or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type A 2 B 4+ 2 O7 where A is a rare-earth ion and B is usually a transition metal. Both the A and B sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to...

Problem of the type −∆pu = f(u) + h(x) in (a, b) with u = 0 on {a, b} is solved under nonresonance conditions stated with respect to the first eigenvalue and the first curve in the Fučik spectrum of (−∆p,W 1,p 0 (a, b)), only on a primitive of f .

We prove that an Alexander quandle of prime order is generated by any pair of distinct elements. Furthermore, we prove for such a quandle that any ordered pair of distinct elements can be sent to any other such pair by an automorphism of the quandle.

Let G be a nite group and let i (G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the i 's are established. In particular it is shown that i = k i jGj=jGj 2 for some non-negative integers k i and that P 1 i=1 i is either 1 or at most 1/2 for solvable groups.

Given three n-tuples {λi}i=1, {μi}i=1, {νi}i=1 of complex numbers, we introduce the problem of when there exists a pair of normal matrices A and B such that σ(A) = {λi}i=1, σ(B) = {μi}i=1, and σ(A+B) = {νi}i=1, where σ(·) denote the spectrum. In the case when λk = 0, k = 2, . . . , n, we provide necessary and sufficient conditions for the existence of A and B. In addition, we show that the solu...

This paper presents a method for assessing skill of performance from video, for a variety of tasks, ranging from drawing to surgery and rolling dough. We formulate the problem as pairwise and overall ranking of video collections, and propose a supervised deep ranking model to learn discriminative features between pairs of videos exhibiting different amounts of skill. We utilise a two-stream Tem...

Given an infinite Boolean algebra B, we find a natural class of ∅-definable equivalence relations EB such that every imaginary element from B is interdefinable with an element from a sort determined by some equivalence relation from EB . It follows that B together with the family of sorts determined by EB admits elimination of imaginaries in a suitable multisorted language. The paper generalize...