Topological aspects of the Medvedev lattice

We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give a complete picture of the relationships of inclusion holding between these sublattices, these filters, and this ideal. We show that the sublattice of the closed Medvedev degrees is not a Brouwer algebra. We investigate the dense degrees of mass problems that are closed under Turing equivalence, and we prove that the dense degrees form an automorphism base for the Medvedev lattice. The results hold for both the Medvedev lattice on the Baire space and the Medvedev lattice on the Cantor space.     

Filters in (Quasiordered) Semigroups and Lattices of Filters

A filter in a semigroup is a subsemigroup whose complement is an ideal. (Alternatively, in a quasiordered semigroup, a slightly more general definition can be given.) We prove a number of results related to filters in a semigroup and the lattice of filters of a semigroup. For instance, we prove that every complete algebraic lattice can be the lattice of filters of a semigroup. We prove that every finite semigroup is a homomorphic image of a finite semigroup whose lattice of filters is boolean and which belongs to the pseudovariety generated by the original semigroup. We describe filter lattices of some well-known semigroups such as full transformation semigroups of finite sets (which are three-element chains) and free semigroups (which are boolean).     

关于剩余格中滤子的格结构

This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.     

剩余格中的滤子

This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in residuated lattice was proposed with its basic properties being discussed.     

Pretopologies, preuniformities and probabilistic metric spaces

Summary A pretopology on a given set can be generated from a filter of reflexive relations on that set (we call such a structure a preuniformity). We show that the familly of filters inducing a given pretopology on Xform a complete lattice in the lattice of filters on X. The smallest and largest elements of that lattice are explicitly given. The largest element is characterized by a condition which is formally equivalent to a property introduced by Knaster--Kuratowski--Mazurkiewicz in their well known proof of Brouwer's fixed point theorem. Menger spaces and probabilistic metric spaces also generate pretopologies. Semi-uniformities and pretopologies associated to a possibly nonseparated Menger space are completely characterized.     

On fuzzy fantastic filters of lattice implication algebras

Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.     

格蕴涵代数中滤子的逻辑性质(英文)

讨论了当格蕴涵代数L是完全分配格时蕴涵运算的一些性质 ,在格蕴涵代数L上引入了集合的蕴涵传递性概念 ,证明了格蕴涵代数的滤子满足蕴涵传递性和替换定理 ,即格蕴涵代数的滤子满足命题逻辑的三段论推理规则和替换定理     

基于仿酉矩阵的紧支撑二元正交小波滤波器组的构造

高维小波是处理多维信号的有力工具,张量积和栅格结构的小波有其自身的特点,但在实际应用中,我们仍需要构造小波滤波器来满足特定情形下的需要以提高滤波的效果,而构造正交滤波器,在多相域里就等价于构造仿酉阵,在本文中,我们通过对仿酉矩阵的研究,证明二元一次对称的仿酉阵一定能够块对角化,利用这种性质,给出了不可分离的二元正交小波滤波器组及线性相位小波滤波器的构造,并给出了相应的例子．     

On Rough Intuitionistic Fuzzy Ideals（Filters） in Lattices

In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal（filter） which is a generalized intuitionistic fuzzy ideal（filter） of a lattice and study some related properties of such ideals（filters）.     

S-fuzzy Version of Stone's Theorem for Distributive Lattices

In this paper,we initiate a study of S-fuzzy ideal(filter) of a lattice where S stands for a meet semilattice.A S-fuzzy prime ideal(filter) of a lattice is defined and it is proved that a S-fuzzy ideal(filter) of a lattice is S-fuzzy prime ideal(filter) if and only if any non-empty α-cut of it is a prime ideal(filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals(filters).     

条件交半格中的相对极大滤子

引入偏序集的相对极大滤子的概念,证明在任意条件交半格中一个滤子是相对极大滤子当且仅当它是滤子格的完全交不可约元.一个格是分配的当且仅当每一个相对极大滤子都是素滤子.随后研究了Heyting代数中相对极大滤子的刻画,最后定义和研究了完全并既约生成格.     

双重伪补Ockham代数的理想与滤子

描述了双重伪补Ockham代数的理想和滤子的某些性质。我们证明了一个双重伪补Ockham代数的核理想格与其余核滤子格同构。     

Near-unanimity is decomposable

In the interpretability lattice, the varieties possessing a near unaninimity term constitute a filter. It is shown that this filter is the proper intersection of two larger filters. One of these two filters is shown to be modular.     

Filters in the partition lattice

Given a filter \(\Delta \) in the poset of compositions of n, we form the filter \(\Pi ^{*}_{\Delta }\) in the partition lattice. We determine all the reduced homology groups of the order complex of \(\Pi ^{*}_{\Delta }\) as \({\mathfrak S}_{n-1}\)-modules in terms of the reduced homology groups of the simplicial complex \(\Delta \) and in terms of Specht modules of border shapes. We also obtain the homotopy type of this order complex. These results generalize work of Calderbank–Hanlon–Robinson and Wachs on the d-divisible partition lattice. Our main theorem applies to a plethora of examples, including filters associated with integer knapsack partitions and filters generated by all partitions having block sizes a or b. We also obtain the reduced homology groups of the filter generated by all partitions having block sizes belonging to the arithmetic progression \(a, a + d, \ldots , a + (a-1) \cdot d\), extending work of Browdy.     

效应代数的素滤子，同余关系与商

本文通过引入R-滤子,引入了格效应代数中素滤子的概念,并讨论了R-滤子,素滤子,同余关系和商之间的关系.     

关于Scott拓扑存在开滤子拓扑基的分配备格

本文利用引入的ＫＳ性质,刻划了那些其Ｓｃｏｔｔ拓扑可由开滤子生成的分配备格,该结果也是对［１］中一公开问题的一种解答．本文的刻划定理对于判定分配备格的Ｓｃｏｔｔ拓扑是否与Ｓｃｏｔｔ开滤子拓扑一致具有较强的可操作性,应用该刻划定理给出大量非连续格,其Ｓｃｏｔｔ拓扑具有开滤子基．     

Cyrtologies of Convergences,I

We study the complete lattice of convergences, that is, of relations between a set and the set of its filters. Various properties of convergences (like isotonicity, antitonicity, being a pseudotopology, a pretopology, an adherence) determine subsets of the lattice of convergences which possess certain particular features called “cyrtological”. The morphisms associated to these sets, said “cyrtomorphisms”, are basic in the study of convergences. A method of generation of GALOIS connections relative to cyrtomorphisms is proposed. Semigroups generated by some cyrtomorphisms are analyzed.     

蕴涵格的同余关系及熵蕴涵格

在蕴涵格中引入了蕴涵滤子的概念 ,讨论了蕴涵滤子的一些基本性质 ,并由此建立了由素蕴涵滤子决定的同余关系及其商蕴涵格 ,以便为Fuzzy推理建立严格的逻辑基础作些必要的准备 .     

Limiting optimal adaptive filtering with unknown disturbance covariance

The accuracy of estimating the variance of the Kalman-Bucy filter depends essentially on disturbance covariance matrices and measurement noise. The main difficulty in filter design is the lack of necessary statistical information about the useful signal and the disturbance. Filters whose parameters are tuned during active estimation are classified with adaptive filters. The problem of adaptive filtering under parametric uncertainty conditions is studied. A method for designing limiting optimal Kalman-Bucy filters in the case of unknown disturbance covariance is presented. An adaptive algorithm for estimating disturbance covariance matrices based on stochastic approximation is described. Convergence conditions for this algorithm are investigated. The operation of a limiting adaptive filter is exemplified.     

蕴涵格的滤子及同余关系

在蕴涵格中引和了蕴涵滤子的概念，讨论了蕴涵滤子的一些基本性质，并由此建立了由素蕴涵滤子决定的同余关系及其商蕴涵格，以便为Fuzz推理建立了严格的逻辑基础作些必要的准备。