Self-maps of <Emphasis Type="Italic">S</Emphasis><Superscript>2</Superscript> homotopic to a smooth map with a single <Emphasis Type="Italic">n</Emphasis>-periodic point

We show for which (d,n) ∈ Z×N there exists a smooth self-map f:S² → S² so that deg(f)=d and Fix(fⁿ) is a point.     

Arithmetic properties of overpartition triples

Let p_3(n) be the number of overpartition triples of n. By elementary series manipulations,we establish some congruences for p_3(n) modulo small powers of 2, such as p_3(16 n + 14) ≡ 0(mod 32), p_3(8 n + 7) ≡ 0(mod 64).We also find many arithmetic properties for p_3(n) modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences: for any integers α≥ 1 and n ≥ 0, we have p_3 (3~(2α+1)(3n + 2))≡ 0(mod 9 · 2~4), p_3(4~(α-1)(56 n + 49)) ≡ 0(mod 7),p_3 (7~(2α+1)(7 n + 3))≡ p_3 (7~(2α+1)(7 n + 5))≡ p_3 (7~(2α+1)(7 n + 6))≡ 0(mod 7),and for r ∈ {1, 2, 3, 4, 5, 6},p_3(11 · 7~(4α-1)(7 n + r)≡ 0(mod 11).     

超富足半群及其子类

借助半群的Malcev积和公理化条件,对超富足半群及其子类进行了刻画,给出了超富足半群及其子类的若干特征.     

关于指数丢番图方程$(a^m-1)(b^n-1)=x^2$的注记

Let a and b be fixed positive integers.In this paper,using some elementary methods,we study the diophantine equation（a~m-1）（b~n-1）= x~2.For example,we prove that if a ≡ 2（mod 6）,b ≡ 3（mod 12）,then（a~n-1）（b~m-1）= x~2 has no solutions in positive integers n,m and x.     

On <Emphasis Type="Italic">n</Emphasis> × <Emphasis Type="Italic">m</Emphasis>-valued Łukasiewicz-Moisil algebras

n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM _n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM _n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM _n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM _n×m -algebra is computed.      

Applications of an Explicit Formula for the Generalized Euler Numbers

The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.     

On first order congruences of lines in ℙ4 with irreducible fundamental surface

In this article we study congruences of lines in ?ⁿ, and in particular of order one. After giving general results, we obtain a complete classification in the case of ?⁴ in which the fundamental surface F is in fact a variety, i.e. it is integral, and the congruence is the irreducible set of the trisecant lines of F. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A “Generalized Trace Formula” for Bell numbers

The nth Bell number B_n is the number of ways to partition a set of n elements into nonempty subsets. We generalize the “trace formula” of Barsky and Benzaghou [1], which asserts that for an odd prime p and an appropriate constant τ_p, the relation B_n=-Tr(^n-1-τ_p)B_τp holds in , where is a root of and is the trace form. We deduce some new interesting congruences for the Bell numbers, generalizing miscellaneous well-known results including those of Radoux [4].     

A class of congruences in partial Abelian semigroups

In this paper, by basing on the special morphism of Habil, we introduce and study a class of congruences in partial Abelian semigroups and obtain some interesting properties. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.