Jacobi fields and linear connections for arbitrary second-order ODEs

We discuss generalisations of Jacobi fields and Raychaudhuri’s equation from the geodesic case to that of an arbitrary system of second-order ODEs. Our results are obtained using a natural choice of linear connection on evolution space.     

五次完全幂的少位数三进制展开*

本文讨论了Michael Bennett [Bennett M, Bugeaud Y, Mignotte M. Perfect powers with few binary digits and related Diophantine problem [J]. Ann Sc Norm Super Pisa Cl Sci, 2013,XII:941–953.]中提出的一类丢番图方程, 即五次完全幂的少位数三进制展开. 作者证明了丢番图方程 3^a + 3^b + 2 = n⁵, a > b > 0 有唯一的正整数解$(a,b,n)=(3,1,2).     

含幺逆半群的半格上的同余格

本文证明了含幺逆半群Sα（α∈Y）的半格的容许同余格同构于半格S上同余格的一个子格。     

Structure of free strong doppelsemigroups

We consider strong doppelsemigroups which are sets with two binary associative operations satisfying axioms of strong interassociativity. Commutative dimonoids in the sense of Loday are examples of strong doppelsemigroups and two strongly interassociative semigroups give rise to a strong doppelsemigroup. The main aim of this paper is to construct a free strong doppelsemigroup, a free n-dinilpotent strong doppelsemigroup, a free commutative strong doppelsemigroup and a free n-nilpotent strong doppelsemigroup. We also characterize the least n-dinilpotent congruence, the least commutative congruence, the least n-nilpotent congruence on a free strong doppelsemigroup and establish that the automorphism group of every constructed free algebra is isomorphic to the symmetric group.     

On a congruence conjecture of Swisher

A congruence on a conjecture of van Hamme is established. This result confirms a particular case of a congruence conjecture of Swisher.     

On Solvable Congruences in Finitely Decidable Varieties

In this paper we establish the (1, 2)- and (2, 1)-transfer principles for finitely decidable locally finite varieties, where a class of structures is finitely decidable if the first order theory of its finite members is recursive. The transfer principles deal with the local structure of finite algebras and have strong global consequences. Mathematics Subject Classification : 08A05, 03C13, 08B05, 08B10.     

Normalizers of the congruence subgroups of the Hecke group

Let cos and let be the Hecke group associated to . In this article, we show that for a prime ideal in , the congruence subgroups of are self-normalized in .

     

Permutation congruent transformations of the freudenthal triangulation with minimum surface density

Linear transformations of the Freudenthal triangulation with permutation congruent simplexes are characterized, and within this class those transformations yielding minimum normalized surface density are identified. This research was partially supported by National Science Foundation Grants SOC 78-16811 and MCS 81-21838; and Department of Energy Contract AM03- 76F00326, PA# DE-AT03-76ER72018.     

On some congruence with application to exponential sums

We will study the solution of a congruence,x ≡g ^1/2)ωg(2 ⁿ ) mod 2 ⁿ , depending on the integersg andn, where ω _g (2 ⁿ ) denotes the order ofg modulo 2 ⁿ . Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.