涉及Domb数D_n的两个超同余式的研究

作者用一种新的方法证明了穆彦平和孙智伟证明的涉及Domb数的超同余式:设p> 3为素数,则■,并且给出了一个新的超同余式:■,其中q_p（a）代表的是费马商(a^p-1-1)/p.     

The minority game with incomplete strategies

This paper proposes a new model of Incomplete Minority Game (IMG), which features a default hierarchy of rules. This model introduces random bits into players’ individual strategies and is capable of applying the exception rules in the absence of the default one. Analysis of the numerical experiment results indicates that, in comparison with the standard Minority Game (SMG) model, this IMG model expands the maximum ensemble of uncorrelated strategies (MEUS) and excels in the effective strategy set and dynamic evolution of individual strategies, which enhance the overall performance by reaching an approximate ideal status in a shorter time with less memory steps and more stable combination of strategies. This paper also discusses the practical implication of the new IMG model.     

Hilbert-Enskog-Chapman expansion in the turbulent kinetic theory of gases. II

This is a continuation of the article (I) with the same title. [Tian-quan Chen, preceding articleJ. Stat. Phys. 25, 491 (1981).] We carry on with the Enskog-Chapman expansion here.     

A super hierarchy of coupled derivative nonlinear Schrödinger equations and conservation laws

By solving the zero-curvature equation associated with a 3 × 3 matrix spectral problem, a super hierarchy of coupled derivative nonlinear Schrödinger equations is proposed. The corresponding super bi-Hamiltonian structures are established by means of the super trace identity. Then, we derive infinite conservation laws of the super coupled derivative nonlinear Schrödinger equation with the aid of spectral parameter expansions.     

The Cayley–Dickson process for dialgebras

We adapt the algorithm of Kolesnikov and Pozhidaev, which converts a polynomial identity for algebras into the corresponding identities for dialgebras, to the Cayley–Dickson doubling process. We obtain a generalization of this process to the setting of dialgebras, establish some of its basic properties, and construct dialgebra analogues of the quaternions and octonions.     

Leibniz 2-Algebras and Twisted Courant Algebroids

Let Y be an integral projective curve whose singularities are of type A_k, i.e. with only tacnodes and planar (perhaps non-ordinary) cusps. Set g:= p_a(Y). Here we study the Brill - Noether theory of spanned line bundles on Y. If the singularities are bad enough, we show the existence of spanned degree d line bundles, L, with h⁰(Y, L) ≥ r + 1 even if the Brill - Noether number ρ(g, d, r) < 0. We apply this result to prove that genus g curves with certain singularities cannot be hyperplane section of a simple K3 surface S ? P ^g.     

A note on unimodular congruence of the Laplacian matrix of a graph

Let G be a simple connected graph and L(G) be its Laplacian matrix. In this note, we prove that L(G) is congruent by a unimodular matrix to its Smith normal form if and only if G is a tree.     

一类格序半群的同余

本文讨论了一类可换格序半群的同余性质。给出了这类格序半群同余的表示和同态分解定理。这个结论一般化了［１］和［２］中的结果。