粗糙Galois连接

在粗糙集中讨论概念格,定义粗糙形式背景、粗糙概念,给出它们的性质,在粗糙形式背景中借助蕴涵算子研究上、下近似运算,并且定义和讨论了粗糙Galois 连接。     

Non-commutative fuzzy Galois connections

 Fuzzy Galois connections were introduced by Bělohlávek in [4]. The structure considered there for the set of truth values is a complete residuated lattice, which places the discussion in a “commutative fuzzy world”. What we are doing in this paper is dropping down the commutativity, getting the corresponding notion of Galois connection and generalizing some results obtained by Bělohlávek in [4] and [7]. The lack of the commutative law in the structure of truth values makes it appropriate for dealing with a sentences conjunction where the order between the terms of the conjunction counts, gaining thus a temporal dimension for the statements. In this “non-commutative world”, we have not one, but two implications ([15]). As a consequence, a Galois connection will not be a pair, but a quadruple of functions, which is in fact two pairs of functions, each function being in a symmetric situation to his pair. Stating that these two pairs are compatible in some sense, we get the notion of strong L-Galois connection, a more operative and prolific notion, repairing the “damage” done by non-commutativity. Dedicated to Prof. Ján Jakubík on the occasion of his 80th birthday.     

Isotone fuzzy Galois connections with hedges

We study isotone fuzzy Galois connections and concept lattices parameterized by particular unary operators. The operators represent linguistic hedges such as “very”, “rather”, “more or less”, etc. Isotone fuzzy Galois connections and concept lattices provide an alternative to their antitone counterparts which are the fundamental structures behind formal concept analysis of data with fuzzy attributes. We show that hedges enable us to control the number of formal concepts in the associated concept lattice. We also describe the structure of the concept lattice and provide a counterpoint to the main theorem of concept lattices.     

Parallel algorithm for computing fixpoints of Galois connections

This paper presents a parallel algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. The algorithm results as a parallelization of CbO (Kuznetsov 1999) in which we process disjoint sets of fixpoints simultaneously. One of the distinctive features of the algorithm compared to other parallel algorithms is that it avoids synchronization which has positive impacts on its speed and implementation. We describe the parallel algorithm, prove its correctness, and analyze its asymptotic complexity. Furthermore, we focus on implementation issues, scalability of the algorithm, and provide an evaluation of its efficiency on various data sets.     

Note on generating fuzzy concept lattices via Galois connections

The aim of this paper is to compare an approach of creating fuzzy concept lattices proposed by Popescu with several other approaches. Particularly, we show that this approach is in some way equivalent to the approach of Kraj?i called generalized concept lattices. We also give a straightforward generalization of Popescu’s approach to non-homogeneous cases.     

On basic conditions to generate multi-adjoint concept lattices via Galois connections

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multi-adjoint sufficiency, possibility, and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.     

Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data

Fixpoints of Galois connections induced by object-attribute data tables represent important patterns that can be found in relational data. Such patterns are used in several data mining disciplines including formal concept analysis, frequent itemset and association rule mining, and Boolean factor analysis. In this paper we propose efficient algorithm for listing all fixpoints of Galois connections induced by object-attribute data. The algorithm, called FCbO, results as a modification of Kuznetsov’s CbO in which we use more efficient canonicity test. We describe the algorithm, prove its correctness, discuss efficiency issues, and present an experimental evaluation of its performance and comparison with other algorithms.     

Programming based learning algorithms of neural networks withself-feedback connections

Discusses the learning problem of neural networks with self-feedback connections and shows that when the neural network is used as associative memory, the learning problem can be transformed into some sort of programming (optimization) problem. Thus, the rather mature optimization technique in programming mathematics can be used for solving the learning problem of neural networks with self-feedback connections. Two learning algorithms based on programming technique are presented. Their complexity is just polynomial. Then, the optimization of the radius of attraction of the training samples is discussed using quadratic programming techniques and the corresponding algorithm is given. Finally, the comparison is made between the given learning algorithm and some other known algorithms     

Dynamic Galois Theory

Given a separable polynomial over a field, every maximal idempotent of its splitting algebra defines a representation of its splitting field. Nevertheless such an idempotent is not computable when dealing with a computable field if this field has no factorization algorithm for separable polynomials. Moreover, even when such an algorithm does exist, it is often too heavy. So we suggest to address the problem with the philosophy of lazy evaluation: make only computations needed for precise results, without trying to obtain a priori complete information about the situation. In our setting, even if the splitting field is not computable as a static object, it is always computable as a dynamic one. The Galois group has a very important role in order to understand the unavoidable ambiguity of the splitting field, and this is even more important when dealing with the splitting field as a dynamic object. So it is not astonishing that successive approximations to the Galois group (which is again a dynamic object) are a good tool for improving our computations. Our work can be seen as a Galois version of the Computer Algebra software D5 ( Della Dora et al., 1985).     

从C编程到C#控制台编程及窗体编程的教学实践研究

程序设计的发展与计算机语言的发展是相辅相成的,过程化编程是面向对象编程的基础,历史上程序设计经历了无数里程碑的跨越!以计算机语言为例,C家族就经历了C、C++、C#的发展演变。本文从教学的角度探讨从C语言编程跨越到C#控制台编程、再从C#控制台编程跨越到C#的Windows窗体编程。选择较优路径,采用比较教学法实现了轻松自然的过渡和跨越!本文对《C#程序设计》课程教学确有实用价值。     

Galois FCSR的内部状态分析

研究Galois FCSR状态序列的周期与互补性质及进位序列的互补性质。根据周期序列与有理数2-adic表达之间的关系,证明l-序列的状态序列是准周期的,且其周期与l-序列的周期相同。分析以q为极小连接数的l-序列a的状态序列s=(s0, s1,…, sn)及进位序列c=(c0, c1,…, cn),证明若s在t时刻进入周期,则i≥t时,si  si  T/2  , ci  ci  T/2  q ,其中,T = per(a), r = lb(q+1)。     

Multi-parameter Polynomials with Given Galois Group

We present a collection of multi-parameter polynomials for several mostly non-solvable permutation groups of small degree and describe their construction. As an application we are able to obtain totally real number fields with these Galois groups over the rationals, for example for the two small Mathieu groups M₁₁andM₁₂ .     

Galois Group Computation for Rational Polynomials

We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar’s algorithm. All computations are done in unramified p -adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar’s method and the absolute resolvent method.     

On cellular automata over Galois rings

In this paper we study the invertibility of one-dimensional cellular automata, determined by a local rule, acting on the space of all doubly-infinite sequences taking values in a finite Galois ring. We also compute the topological entropy of one-dimensional CA generated by additive local rule over a finite Galois ring. We conclude by showing that the topological entropy of an additive invertible CA over a finite Galois ring is equal to its inverse.     

Granular computing and dual Galois connection

A covering model for granular computing in a set-theoretic setting is studied in this paper. Under this model, a zooming-in operator is redefined. Combinations of the zooming-in and zooming-out operators form two pairs of approximation operators of the original and the granulated universe of discourse. Their properties are examined in detail. For the two pairs of lower and upper approximation operators, it is proved that the duality is always true. For a generalized approximation space, the approximation representations are just the combination operators formed on the basis of the zooming-out and zooming-in operators. Relationships between these combination operators and the dual Galois connection are also analyzed.     

Atomistic Galois insertions for flow sensitive integrity

Several program verification techniques assist in showing that software adheres to the required security policies. Such policies may be sensitive to the flow of execution and the verification may be supported by combinations of type systems and Hoare logics. However, this requires user assistance and to obtain full automation we shall explore the over-approximating nature of static analysis.We demonstrate that the use of atomistic Galois insertions constitutes a stable framework in which to obtain sound and fully automatic enforcement of flow sensitive integrity. The framework is illustrated on a concurrent language with local storage and polyadic synchronous communication.     

编程实现基于Oracle数据库的数据文件导出

提出了使用Developer编程将Oracle数据库中数据以特定文件格式 (如文本文件 )导出的方法 ,并通过一个工程勘测综合信息系统数据库中数据导出的实例 ,具体给出了实现过程中的重要步骤、设计方法和关键实现语句。     

Piecewise Polynomial Sequences over the Galois Ring

Problems of Information Transmission - We describe the construction of a piecewise polynomial generator over a Galois ring and prove a transitivity criterion for it. We give an estimate for the...     

有限域逆元算法的实现

在扩展欧几里得算法的基础上提出了有限域乘法逆元的计算方法。给出了该算法的硬件结构图，该算法的优点是时间复杂度和空间复杂度较优，便于VLSI的实现。