3$\times$3阶上三角型算子矩阵的可能谱

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M（D,V,F） a 3×3 upper triangular operator matrix acting on Hi ＋H2＋ H3 of theform M（D,E,F）=（A D F 0 B F 0 0 C）.For given A ∈ B（H1）, B ∈ B（H2） and C ∈ B（H3）, the sets ∪D,E,F^σp（M（D,E,F））,∪D,E,F ^σr（M（D,E,F））,∪D,E,F ^σc（M（D,E,F）） and ∪D,E,F σ（M（D,E,F）） are characterized, where D ∈ B（H2,H1）, E ∈B（H3, H1）, F ∈ B（H3,H2） and σ（·）, σp（·）, σr（·）, σc（·） denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

A Connection Between the Logarithmic Capacity and the Sequence of the Analytical Function

Let E be a bounded closed set, d(E) be the logarithmic capacity of E. If A is any bounded set, then $[d(A) = \mathop {\sup }\limits_{E \in A} d(E)\]$ For each $Z_0 \in E$, and $\delta >0$, let $[\Delta = \Delta _{{Z_0}}^\delta = CE \cap (|Z - {Z_0}| < \delta )\]$ where CE is complement of E, then \Delta is an open set. By [{\bar \Delta ^0}\] we denote the interior of the closure A of A. Clearly,$\Delta \subset [{\bar \Delta ^0}\]$ and $d(\Delta) \leq d([{\bar \Delta ^0}\])$, and there exists an open set D such that d(D) 0, the equation $d(\Delta)=d([{\bar \Delta ^0}\])$ holds.     

图的邻点可区别全色数的一个上界

Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, where
C（u）={f（u）}∪{f（uv）｜uv∈E（G）}.
Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.     

Sobolev Spaces on Quasi-K\"ahler Complex Varieties

If $V$ is an irreducible quasi-K\"ahler complex variety and $E$ is a vector bundle over $\mathrm{reg}(V)$, the author proves that $W^{1,2}_{0}(\mathrm{reg}(V),E)=W^{1,2}(\mathrm{reg}(V),E)$, and that for $\dim_{\mathbb{C}}\mathrm{reg}(V)>1$, the natural inclusion $W^{1,2}(\mathrm{reg}(V),E)\hookrightarrow L^{2}(\mathrm{reg}(V),E)$ is compact, the natural inclusion $W^{1,2}(\mathrm{reg}(V),E)\hookrightarrow L^{\frac{2v}{v-1}}(\mathrm{reg}(V),E)$ is continuous.     

NASH EQUILIBRIUM OF TWO GAME MODELS ON THE RANDOM SOCIAL NETWORK

A graph $G$ is $k$-triangular if each of its edge is contained in at least $k$ triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph $G$ is a sequence of distinct triangles $T_1 T_2\cdots T_k$ in $G$ such that for $1\leq i\leq k-1, |E(T_i )\cap E(T_{i+1})|=1$ and $E(T_i)\cap E(T_j)=\emptyset$ if $j>i+1$. Two edges $e,e''\in E(G)$ are triangularly connected if there is a triangle-path $T_1,T_2,\cdots, T_k$ in $G$ such that $e\in E(T_1)$ and $e''\in E(T_k)$. Two edges $e,e''\in E(G)$ are equivalent if they are the same, parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component. In this paper, we prove that every 4-edge-connected triangular graph $G$ is ${\mathbb Z}_3$-connected, unless it has a triangularly connected component which is not ${\mathbb Z}_3$-connected but admits a nowhere-zero 3-flow.     

纯无限单的C*-代数通过某些C*-代数扩张的非稳定K-理论

设0→B■E■A→0是有单位元C~*-代数E的一个扩张,其中A是有单位元纯无限单的C~*-代数,B是E的闭理想.当B是E的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,证明了K_0(E)={[p]| p是E\B中的投影};当B是稳定C~*-代数时,证明了对任意紧的Hausdorff空间X,有■(C(X,E))/■_0(C(X,E))≌K_1(C(X,E)).     

Imaginaries in Boolean algebras

Given an infinite Boolean algebra B, we find a natural class of $\varnothing$‐definable equivalence relations $\mathcal {E}_{B}$ such that every imaginary element from B^eq is interdefinable with an element from a sort determined by some equivalence relation from $\mathcal {E}_{B}$. It follows that B together with the family of sorts determined by $\mathcal {E}_{B}$ admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean algebras, obtained in 10 .     

关于Witt代数基本子代数的一点注记

设g=W_1是特征p3的代数闭域k上的Witt代数.本文确定了g的极大基本子代数.进一步具体给出了最大维数的基本子代数的G共轭类,这里G是g的自同构群.从而证明了最大维数为(p-1)/2的基本子代数射影簇E((p-1)/2,g)是不可约的且是一维的.更进一步,证明了E(1,g)是不可约的,具有维数p-2,而E(2,g)是等维的,共有(p-3)/2个不可约分支,且每个不可约分支的维数是p-4.而当3≤r≤(p-3)/2时,E(r,g)是可约的.给出了E(r,g)(3≤r≤(p-3)/2)维数的一个下界.     

平面上随机级数的性质

研究了平面上系数{Xn,n≥0}为(?)-混合序列在满足,(q>1)等条件下的随机级数的增长性及值分布,得到了比较好的结果．     

Some descriptive set-theoretic properties of the isomorphism relation between Banach spaces

Consider the space of closed linear subspaces of a separable Banach space equipped with the standard Effros Borel structure. The isomorphism relation between Banach spaces being elements of  determines a partition of  . In this note we prove a result describing the complexity of analytic subsets of  intersecting a large enough number of the above-mentioned parts of  .

     

Cyclotomic Quotients of Two Conjugates of an Algebraic Number

Siberian Mathematical Journal - Let $ \alpha $ be an algebraic number of degree $ d\geq 2 $ . We consider the set $ E(\alpha) $ of positive integers&nbsp; $ n $ such that the primitive $ n $ th...     

非退化扩散过程的水平集和极集

设X(t)(t∈R )是一个d维非退化扩散过程．本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数．     

完全多部图的符号边控制数的界

$f: E(G)\rightarrow\{-1,1\}$称为图$G =(V,E)$的一个符号边控制函数 (简称SEDF),如果$f[e]=f(N[e])=\sum_{e''\in N[e]}f(e'')\geq1$对于图$G$的每条边$e\in E$都成立. $w(f)=\sum_{e\in E}f(e)$称为函数$f$的权. $G$的符号边控制数$\gamma_{s}\,''(G)$是指$G$的所有符号边控制函数的最小权.本文对完全多部图的符号边控制数进行研究.对于完全$r$-部图, 当$r$为偶数并且各部的顶点数相同的情况下,我们得到了这一参数的若干下界和上界.     

带有超线性项的混合单调算子的不动点定理及其应用

该文讨论了带有齐次超线性项μC和线性项D的混合单调算子A=B+μC+D的不动点的存在性.在不假设耦合下上解存在的条件下,得到了算子A的一个不动点定理,并且将所获结果应用到常微分方程两点边值问题、积分方程和椭圆型方程边值问题中,得到了新的结论.因而本质上推广和改进了已有的混合单调算子和相应的增算子的不动点定理.     

EXISTENCE AND NON-EXISTENCE OF GLOBAL SMOOTH SOLUTIONS FOR QUASILINEAR HYPERBOLIC SYSTEMS~*

Consider initial value probiom v_t-u_x=0, u_t+p(v)_x=0, (E), v(x, 0)=v_0(x), u(x, 0)=u_0(x), (I), where A≥0, p(v)=K~2v~(-γ), K>0, 0<γ<3. As 0<γ≤1, the authors give a sufficient condition for that (E), (I) to have a unique global smooth solution, As 1≤γ<3, a necessary condition is given for that.     

THE FOURIER SERIES EXPANSIONS OF FUNCTIONS DEFINED ON S-SETS

ＴＨＥＦＯＵＲＩＥＲＳＥＲＩＥＳＥＸＰＡＮＳＩＯＮＳＯＦＦＵＮＣＴＩＯＮＳＤＥＦＩＮＥＤＯＮＳＳＥＴＳＬＩＡＮＧＪＩＮＲＯＮＧＬＩＷＡＮＳＨＥＳＵＦＥＮＧＲＥＮＦＵＹＡＯＡｂｓｔｒａｃｔＬｅｔＥｂｅａｃｏｍｐａｃｔｓｓｅｔｓｏｆＲｎ．Ｔｈ...     

Degenerating families of rank two bundles

We construct families of rank two bundles on , in characteristic two, where for , is a sum of line bundles, and is non-split. We construct families of rank two bundles on , in characteristic , where for , is a sum of line bundles, and is non-split.

     

Notes on a -group generated by the Lévy Laplacian

In this paper we shall give some results on a -group generated by the Lévy Laplacian and operators approximating that group in the space of continuous linear operators defined on a certain locally convex space in

     

Equivalence of domains with isomorphic semigroups of endomorphisms

For two bounded domains in whose semigroups of analytic endomorphisms are isomorphic with an isomorphism , Eremenko proved in 1993 that there exists a conformal or anticonformal map such that for all .

In the present paper we prove an analogue of this result for the case of bounded domains in .

     

A perturbed elementary operator and range-kernel orthogonality

Let denote the algebra of operators on a Hilbert . If and are commuting normal operators, and and are commuting quasi-nilpotents such that , then define and by , , and . It is proved that and , where is some scalar and is the quasi-nilpotent part of the operator .