关于丢番图方程x~3±1=3·2~αpD_1y~2

设D_1=multiply from i=1 to s q_i(s=1或2),q_i≡-1(mod6)(i=1,2,…,s)是彼此不同的奇素数,p≡1(mod6)为奇素数.运用初等方法讨论了丢番图方程x~3±1=3·2~αpD_1y~2(α=0或1)的正整数解的情况.     

双循环半群上的同余关系

从双循环半群的同余关系出发,讨论了幂等元所在的同余类,证明了双循环半群上的一类同余ρd(d∈N)与其逆子半群之间的相互唯一确定关系,并对这种同余做成的集合进行了刻画,证明了这种同余做成的格与自然数集在某种偏序下做成的格同构,得到了一些有意义的结果.     

两个分块矩阵合同的充要条件

利用矩阵方程,给出了两个分块矩阵O AB C与O AB O合同的一个充分必要条件.     

关于Euler数一个猜想的证明

研究Euler数的猜想:对于任何素数p≡1 mod4,E(p-1)／20 mod p．根据Euler数本身的性质和Fourier级数对于Gauss和的应用,证明了这个猜想是成立的．     

分配半环上的可除半环同余

§ 1.　Introduction　　AsemiringSisanalgebraicsystem (S ,+ ,·)consistingofanon_emptysetStogetherwithtwobinaryoperations +and·onSsuchthat (S ,+ )and (S ,·)aresemigrolupscon nectedbyring_likedistributivity .AsemiringSiscalleddistributiveifinStheadditionisdis tributiveaboutmultiplication ,i.e .ab+c=(a+c) (b +c)anda+bc=(a +b) (a+c)holdforalla ,b ,c∈S .AsemiringSiscalleddivisibleif(S ,·)isagroup .AnequivalencerelationρonasemiringSiscalledacongruenceonS ,iffρisacongruenceon (S ,+ )and (…     

两个模糊子半群集合之间的同态

设S,T是半群,F(S)和F_s(S)分别表示S的所有模糊子集的集合和所有模糊子半群的集合。文中,讨论了F(S)(F_s(S))和F(T)(F_s(T))之间的模糊同态,建立了模糊商子半群的概念,把分明半群的基本同态定理推广到模糊子半群。     

半正定复方阵的Kronecker乘积

本文应用半正定（未必是Ｈｅｒｍｉｔｅ）复方阵在合同下的标准形给出两个半正定（未必是Ｈｅｒｍｉｔｅ）复方阵的Ｋｒｏｎｅｃｋｅｒ乘积为半正定的充要条件     

Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas

The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Categorical abstract algebraic logic: The categorical Suszko operator

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non‐protoalgebraic logics, paralleling the well‐known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so‐called, protoalgebraic π‐institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko operator to the π‐institution framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a subvariety of semi-De Morgan algebras

A characterization of principal congruences of the subvariety C of semi-DeMorgan algebras is given. This characterization is applied to determine the subdirectly irreducible algebras of the variety C and to describe a poset such that the lattice of its order ideals is isomorphic to the lattice of subvarieties of C. This revised version was published online in June 2006 with corrections to the Cover Date.