半序集的碰撞数与分层深度贪婪算法

设Ｐ＝（Ｘ，≤）是一个半序集，本文在关于碰撞数的深度贪婪算法的基础上，直接证明了对任意的Ｐ存在一个最优的ＤＬＧ扩张，给出了ＤＬＧ半序集的定义，并证明了半序集Ｐ是ＤＬＧ半序集的一个充分条件，最后给出了ＤＬＧ扩张算法。     

半连续格的半素极小集与序同态扩张

对完备格引入半素极小集的概念,证明完备格L为半连续格当且仅当L中的每个元在L中存在半素极小集,给出半连续格的两个序同态扩张定理.     

一个n有序集组的计数问题

In this paper, we discuss the counting problem of an order n-group of set (A1 ,A2 ,… ,An) which satisfies ∪^ni=1Ai={a,a2,…,am} and one of the following:(1)∩^ni=1Ai=Φ;(2)∩^ni=1Ai={b1,b2,…,bk};(3)∩^ni=1A1包含{b1,b2,…,bk};(4)Ai≠Φ(i=1,2,…,k），We solve these problems by element analytical method.     

模糊选择函数半序合理的充分条件

在G?del t-模下,研究了模糊选择函数的半序合理性.首先给出了模糊选择函数的合理性条件FA1.然后研究了该条件与模糊选择函数半序合理性之间的关系,得到了半序合理的一个充分条件.     

Georgescu模糊选择函数半序合理的一个充分条件

本文给出了Georgescu模糊选择函数的一些合理性条件FC1和FC2,并在G9del t-模下研究了Georgescu模糊选择函数半序合理性问题,得出了合理的模糊选择函数满足FC1和FC2仅仅是半序合理的充分条件,同时用实例说明了这些条件不再是必要条件。     

与Murty-Simon猜想相关的一个重要引理的推广

一个图G的无公共邻点的点对集定义为disj(G)={(u,v):N_G(u)∩N_G(v)=Φ}.Füredi在那篇对Murty-Simon猜想取得重大进展的文章中证明了一个重要的引理:对任意具有n个顶点的图G,|E(G)|+|disj(G)|≤「n~2/2」.本文对引理中的和|E(G)|+|disj(G)|做了一些更加深入的研究并对这个引理做了一些推广.     

半序概率度量空间中压缩条件下的三元重合点定理

在完备的半序概率度量空间中建立了自映射对G∶X×X×X→X与g∶X→X,满足一定非线性压缩条件下的三元重合点与三元不动点定理,所得结果推广了已有文献中的若干二元重合点与二元公共不动点定理.最后给出主要结果的一个应用.     

半序线性空间中混合单调映射不动点的存在唯一性

本文研究半序线性空间中一类混合单调映射不动点的存在唯一性及其迭代方法,对所述映射没作连续性或紧性假定．其推论改进了序Banach空间中增算子与减算子的某些已知结果．最后把所得结论用于常微分方程奇异边值问题．     

Remarks on the McKay Conjecture

The McKay Conjecture (MC) asserts the existence of a bijection between the (inequivalent) complex irreducible representations of degree coprime to p (p a prime) of a finite group G and those of the subgroup N, the normalizer of Sylow p-subgroup. In this paper we observe that MC implies the existence of analogous bijections involving various pairs of algebras, including certain crossed products, and that MC is equivalent to the analogous statement for (twisted) quantum doubles. Using standard conjectures in orbifold conformal field theory, MC is equivalent to parallel statements about holomorphic orbifolds V ^G , V ^N . There is a uniform formulation of MC covering these different situations which involves quantum dimensions of objects in pairs of ribbon fusion categories.     

Periodic Cyclic Homology as Sheaf Cohomology Dedicated to Daniel Quillen on his 60th Birthday

We study a noncommutative version of the infinitesimal site of Grothendieck. A theorem of Grothendieck establishes that the cohomology of the structure sheaf on the infinitesimal topology of a scheme of characteristic zero is de Rham cohomology. We prove that, for the noncommutative infinitesimal topology of an associative algebra over a field of characteristic zero, the cohomology of the structure sheaf modulo commutators is periodic cyclic cohomology. We also compute the noncommutative infinitesimal cohomology of other sheaves. For example, we show that infinitesimal hypercohomology with coefficients in K-theory gives the fiber of the Jones–Goodwillie character which goes from K-theory to negative cyclic homology.     

A Proof of Hozo's Conjecture on the Homology of a Class of Nilpotent Lie Algebras

LetPbe a rooted tree with rootrand vertex set {1, 2,…,n}. ConsiderPto be a poset by sayingu ≤ vifuis on the path fromrtov. LetZ[P] be the span of all matricesz_uvsuch thatu <_P v, wherez_uvis then × nmatrix with a 1 in theu, ventry and 0's elsewhere. Note thatZ[P] is a nilpotent Lie subalgebra of ?_n(). I. Hozo (Electron. J. Combin., to appear) studied the Laplacian of the Koszul complex for computing the Lie algebra homology ofZ[P]. He showed that the tree structure ofPforces significant simplifications in the Laplacian. He went on to conjecture that the eigenvalues of the Laplacian are indexed by certain labellings ofPby partitions. He gave a simple method for determining the eigenvalue indexed by a labelling. In this paper we prove Hozo's conjecture. As a consequence, we deduce that all eigenvalues of the Laplacian are integers.     

Homological symbols and the Quillen conjecture

We formulate a “correct” version of the Quillen conjecture on linear group homology for certain arithmetic rings and provide evidence for the new conjecture. In this way we predict that the linear group homology has a direct summand looking like an unstable form of Milnor K-theory and we call this new theory “homological symbols algebra”. As a byproduct, we prove the Quillen conjecture in homological degree two for the rank two and the prime 5.     

一个不等式猜想的证明及推广之注记

在最近的文章[一个不等式猜想的证明及推广.大学数学,2018,34(3):99-102]中,作者给出了三个定理并利用Jensen不等式证明了两个等价不等式及其推广形式.本注记说明作者的证明过程有误,并指出作者文章给出的三个定理中有两个定理是不成立的.     

On the singularity of Quillen metrics

Let π: X → S be a holomorphic map from a compact Kähler manifold (X,g _X ) to a compact Riemann surface S. Let Σ_π be the critical locus of π and let Δ  =  π(Σ_π) be the discriminant locus. Let (ξ, h _ξ) be a holomorphic Hermitian vector bundle on X. We determine the singularity of the Quillen metric on det Rπ_*ξ near Δ with respect to g _X | _TX/S and h _ξ.     

Comparison of the K-theories of Quillen and Volodin

A single proof of coincidence of K-theories of Quillen and Volodin is given for the linear, orthogonal and symplectic cases.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 93–105, 1989.     

The Overfull Conjecture and the Conformability Conjecture

In this paper we show that under some fairly general conditions the Overfull Conjecture about the chromatic index of a graph G implies the Conformability Conjecture about the total chromatic number of G. We also show that if G has even order and high maximum degree, then G is conformable unless the deficiency is very small.     

The Gaussian Moments Conjecture and the Jacobian Conjecture

We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. Note that the the Gaussian Moments Conjecture is a special case of [11, Conjecture 3.2]. The latter conjecture was referred to as the Moment Vanishing Conjecture in [7, Conjecture A] and the Integral Conjecture in [6, Conjecture 3.1] (for the one-dimensional case). We also give a counter-example to show that [11, Conjecture 3.2] fails in general for polynomials in more than two variables.