L-Fuzzy代数的L-Fuzzy代数同态(英文)

本文研究了L-fuzzy代数的L-fuzzy代数同态的定义及其性质.利用L-fuzzy集的水平截集,得到TL-fuzzy代数的L-fuzzy代数同态的若干等价刻画.     

On Ringel–Hall Algebras of Tame Hereditary Algebras

In this paper, the double Ringel–Hall algebras of tame hereditary algebras are decomposed as the quantized enveloping algebras of the infinite-dimensional Lie algebras, which are the central extensions of the affine loop algebras and the infinite-dimensional Heisenberg algebras. The numbers of the generators of the Heisenberg algebras are explicitly given at each dimensional level.     

Actions of Ore extensions and growth of polynomial H-identities

We show that if A is a finite-dimensional associative H-module algebra for an arbitrary Hopf algebra H, then the proof of the analog of Amitsur’s conjecture for H-codimensions of A can be reduced to the case when A is H-simple. (Here we do not require that the Jacobson radical of A is an H-submodule.) As an application, we prove that if A is a finite-dimensional associative H-module algebra where H is a Hopf algebra H over a field of characteristic 0 such that H is constructed by an iterated Ore extension of a finite-dimensional semisimple Hopf algebra by skew-primitive elements (e.g., H is a Taft algebra), then there exists integer PIexp^H(A). In order to prove this, we study the structure of algebras simple with respect to an action of an Ore extension.     

完备布尔代数商格的注

本文研究了完备布尔代数L的商格Q(L),建立 L上q-集构成的集合Q′(L)与Q(L)之间的同构,得出了完备布尔代数的商格仍是完备布尔代数,并给出了完备布尔代数范畴的某些性质.     

球面稳定同伦群中的一个新元素族$b_1g_0\tilde{\gamma}_s$

设$p\geq 7$素数,$A$为模$p$的Steenrod代数. 我们利用Adams谱序列证明了球面稳定同伦群$\pi_{\ast}S$中,存在由$b_1g_0\tilde{\gamma}_{s}\in Ext_A^{s+4,(s+1)p^2q+spq+sq+s-3}(Z_p,Z_p)$所表示的新的非平凡元素族,其中$q=2(p-1)$, $3\leq s相似文献   

不同种皮颜色花生糖含量近红外模型的构建

花生籽仁中的糖含量是影响食味品质的重要指标,建立快速测定糖含量的方法可有效提高食用型花生的检测效率。样品外观颜色是影响近红外分析的重要因素之一,按样品外观颜色分类定标(校正)更有利于提高模型的预测性能。研究选择不同糖含量的花生种质332个,采用色差仪将花生种质按种皮颜色分成黑紫色、红色和粉色三大类。采用3,5-二硝基水杨酸法、蒽酮乙酸乙酯法、蔗糖酶法分别测定籽粒中的总糖、可溶性糖及蔗糖含量。总糖含量分别在6.42%～39.53%(黑紫色籽粒)、 9.66%～39.71%(红色籽粒)和8.52%～38.84%(粉色籽粒)之间;可溶性糖含量分别在2.4%～14.32%(黑紫色籽粒)、 2.94%～13.75%(红色籽粒)和2.19%～14.53%(粉色籽粒)之间;蔗糖含量分别在0.92%～7.53%(黑紫色籽粒)、 1.05%～7.23%(红色籽粒)和0.95%～7.99%(粉色籽粒)之间,变异系数均在33%以上。采用瑞典波通DA7250型近红外分析仪(950～1 650 nm)采集籽粒的近红外光谱值,选用基于全波段的偏最小二乘回归法(PLSR),通过对比单一和复合预处理方法,对比模型的相...     

Periodicities in Cluster Algebras and Cluster Automorphism Groups

We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among (strict) direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A) for a cluster algebra A and the group AutMn(S) for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.     

A New Loop Algebra and Its Corresponding Multi-component Integrable Hierarchy

A type of new loop algebra $\tilde{G}_M$ is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.     

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi-component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.     

Matrix Lie Algebras and Integrable Couplings

Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.