TUHF代数上的Lie导子

证明了TUHF代数丁上的Lie导子L形如D l．其中D是T上的结合导子，l是从T到它的中心Z上的线性映射且零化T中的括积．     

扭的Multi-loop代数的triple导子

设G是三维实李代数so(3)的复化李代数,A=C[T_1~(±1),t_2~(±2)]为复数域上的多项式环.设L(t_1,t_2,1)=G(?)_cA,d_1,d_2为L(t_1,t_2,1)的度导子.最近我们研究了李代数L(t_1,t_2,1)的自同构群结构.研究扭的Multi-loop代数L(t_1,t_2,1)(?)(Cd_1(?)Cd_2)的导子以及triple导子结构.     

JBW-代数上的局部导子

本文证明了JBW-代数上的局部导子是导子,举反例说明了JBW-代数上的局部内导子未必是内导子,并且给出了JBW-代数的一个充要条件使得它上的局部内导子是内导子,     

CSL代数上的Lie导子

证明了不相关的有限宽度CSL代数上的每一个Lie导子都是内导子与作用在交换子上为零的中心值线性映射之和.     

von Neumann代数中套子代数上的Lie导子

本文对因子von Neumann代数中套子代数上的线性映射L:alg_Mβ→M满足L(AB—BA)=L(A)B-BL(A)+AL(B)-L(B)A( A,B∈alg_Mβ)进行了刻划,证明了存在线性函数h:alg_Mβ→C;且对任意A,B∈alg_Mβ,有h(AB—BA)=0和算子T∈M,使得对任意X∈alg_Mβ,都有L(X)=XT-TX+h(X)I.     

一类广义W型李超代数

构造了一类有限维广义Caxtan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

M_2(R)上的非线性Lie导子

设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和.     

某些算子代数的可加导子

本文主要研究非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数及两元生成格自反代数的可加导子的自动线性性和连续性问题．通过给出一个含无限维交换ＶｏｎＮｅｕｍａｎｎ子代数的代数上可加导子定理，证明了非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数上的可加导子是线性的，从而是自动连续的．这推广并简化证明了作者［１］中的主要结果．对于在非自伴算子代数研究中起重要的两元生成格自反代数，给出了所有可加导子是线性导子的充分必要条件．     

一类广义W型李超代数

构造了一类有限维广义Cartan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

Weyl型单代数

对于任意特征的域F上具有单位元的交换结合代数A和它的交换导子的子空间D的多项式代数F［Ｄ］,在张量空间A［Ｄ］=AÄF［Ｄ］中定义了Weyl型结合代数和Lie代数.证明了A［Ｄ］作为Lie代数(模去中心)或结合代数是单的充要条件是A为D-单的并且A［Ｄ］在A上的作用是忠实的.[KG*2]由此可构造出许多单代数.     

二次曲面和平面位置关系的判式

在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.     

Subspaces and quotients of Banach spaces with shrinking unconditional bases

The main result is that a separable Banach space with the weak* unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with a shrinking unconditional basis if and only if it is isomorphic to a quotient of a space with a shrinking unconditional basis, which solves a problem dating to the 1970s. The proof of the main result also yields that a uniformly convex space with the unconditional tree property is isomorphic to a subspace as well as a quotient of a uniformly convex space with an unconditional finite dimensional decomposition.     

Toader型平均与几种经典平均的确界

给出了最佳参数α_1,α_2,α_3,β_1,β_2,β_3∈R,使得双向不等式α_1Q(a,b)+(1-α_1)G(a,b)0且a≠b成立.其中A(a,b)=(a+b)/2,H(a,b)=2ab/(a+b),G(a,b)=(ab)~(1/2),Q(a,b)=((a~2+b~2)/2)~(1/2),C(a,b)=(a~2+b~2)/(a+b),T(a,b)=2/π∫_0~(π/2)(a~2cos~2t+b~2sin~2)~(1/2)tdt分别是两个正数a和b的算术平均,调和平均,几何平均,二次平均,反调和平均和Toader平均.     

On the intersections of circuits and cocircuits in matroids

Seymour has shown that a matroid has a triad, that is, a 3-element set which is the intersection of a circuit and a cocircuit, if and only if it is non-binary. In this paper we determine precisely when a matroidM has a quad, a 4-element set which is the intersection of a circuit and a cocircuit. We also show that this will occur ifM has a circuit and a cocircuit meeting in more than four elements. In addition, we prove that if a 3-connected matroid has a quad, then every pair of elements is in a quad. The corresponding result for triads was proved by Seymour.     

A Priori and A Posteriori: A Bootstrapping Relationship

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.     

图的分数κ-因子

给定图Ｇ＝（Ｖ,Ｅ）．设ａ和ｂ是两个非负整数．是一个函数．如果对所有的均成立,称 ｆ为 Ｇ的一个分数［ａ,ｂ］－ 因子． ａ＝ ｂ＝ κ时,称ｆ为 Ｇ的一个分数 ｋ＝因子．本文给出了一个图有分数 ｋ－因子的充分必要条件．     

A Decomposition of Markov Processes via Group Actions

We study a decomposition of a general Markov process in a manifold invariant under a Lie group action into a radial part (transversal to orbits) and an angular part (along an orbit). We show that given a radial path, the conditioned angular part is a nonhomogeneous Lévy process in a homogeneous space, we obtain a representation of such processes and, as a consequence, we extend the well-known skew-product of Euclidean Brownian motion to a general setting.      

关于伪准素环的注记

一个有单位元的交换环Ｒ称为伪准素环，如果Ｒ的每个非零理想都是某个准素理想之幂．本文证明了环Ｒ是伪准素环当且仅当Ｒ是准素环或Ｒ是两个域的直和或Ｒ是至多具有三个素理想的一维局部环，并且每个非零理想或是某个极小素理想之幂或是某个属于极大理想的准不比理想之幂.     

Graphs with disjoint dominating and paired-dominating sets

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating set and a paired-dominating set.