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...

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.

A Mendelsohn design M(k,v) is a pair (V,B) t where IV\=v and B is a set of cyclically ordered k-tuples of distinct elements of V, called blocks, such that every ordered pair of distinct elements of V belongs to exactly one block of B. A M( k, v) is called cyclic if it has an automorphism consisting of a single cycle of length v. The spectrum of existence of cyclic M(3,v)'s and M(4,v)'s is known...

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...

Schwarz and Weck-Schwarz have shown that a T2-ordered space (X, τ, ) whose underlying topological space (X, τ) is completely regular need not be a completely regularly ordered space (that is, T3.5 + T2-ordered T3.5-ordered). We show that a completely regular T2-ordered space need not be completely regularly ordered even under more stringent assumptions such as convexity of the topology. One exa...

Highly self-ordered alumina nanopore arrays were fabricated using hard anodization technique in different mixtures of oxalic/phosphoric acid. The phosphoric acid concentration was varied from 0.05 to 0.3 M while the oxalic acid concentration was changed between 0.3 and 0.4 M. The self ordered nanoporous arrays were obtained in anodization voltage changing from 130 to 200 V. The interpore distan...