具有对称自同态与对称导子的环

本文研究具有对称自同态和对称导子的环. 利用性质nil(R[x]) =nil(R)[x], 我们证明了: 如果R是弱2-primal 环, 则R 是弱对称(σ, δ)-环当且仅当R[x] 是弱对称(σ,δ) -环. 本文结论拓展了关于对称环和弱对称环的研究.     

Cartan型模李超代数S(m,n;t)的中心扩张

本文研究了特征为素数p>2的有限维Special李超代数S(m,n;t)的中心扩张.通过计算从S(m,n;t)到S(m,n;t)^*的斜外导子,得到二阶上同调群H²(S(m,n;t),F)是平凡的.应用此结果,可得S(m,n;t)的中心扩张是平凡的.     

P*(k)线性互补问题基于新核函数的大步校正算法

本文研究了P_*(k)线性互补问题的大步校正原始-对偶内点算法.基于一个强凸且不同于通常的对数函数和自正则函数的新核函数,对具有严格可行初始点的该问题,算法获得的迭代复杂性为O((1+2k)√n(log n)² log (n)/(ε),该结果缩小了大步校正内点算法的实际计算与理论复杂性界之间的差距.     

多目标优化问题(ε,ε)-拟近似解的非线性标量化

本文研究了多目标优化问题的(ε,ε)-拟近似解.利用文献[1]给出的多目标优化问题统一的非线性标量化问题,在没有任何凸性条件下,研究了多目标优化问题的(ε,ε)-拟近似解的充分和必要条件.最后,利用文献[2]中给出的的范数,对多目标优化问题的(ε,ε)-拟近似解进行了非线性标量化刻画.本文第3节推广了文献[1]中的结果.     

On Cramer Approximations under Violation of Cramer's Condition

Let X ₁, X ₂,... be independent identically distributed random variables with distribution function F, S ₀ = 0, S _n = X ₁ + ⋯ + X _n , and Sˉ _n = max_1⩽k⩽n S _k . We obtain large-deviation theorems for S _n and Sˉ _n under the condition 1 − F(x) = P{X ₁ ⩾ x} = e^−l(x), l(x) = x ^α L(x), α ∈ (0, 1), where L(x) is a slowly varying function as x → ∞. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 447–456, October–December, 2005.     

辫子T-范畴的构造

本文首先引入了一类新的范畴_AYD_G^H, 这个范畴是一簇范畴{_AYD^H(α,β)}_(α,β)∈G的非交并, 获得了范畴{_AYD^H(α,β)}_(α,β)∈G是一个辫子T-范畴当且仅当(A,H,Q)是一个G-偶结构, 推广了2005年Panaite和Staic的主要结论. 最后, 当H是有限维时, 构造了一个拟三角T-余代数{A#H^*(α,β)}_(α,β)∈G, 它的表示范畴与{_AYD^H(α,β)}_(α,β)∈G是同构的.     

Degenerate principal series representations of Sp(<Emphasis Type="Italic">p,q</Emphasis>)

Letp>q and letG=Sp(p, q). LetP=LN be the maximal parabolic subgroup ofG with Levi subgroupL≅GL _q (ℍ)×Sp(p−q). Forsεℂ andμ a highest weight of Sp(p−q), let п_s,μ be the representation ofP such that its restriction toN is trivial and ⊠T _p-q ^μ , where det _q is the determinant character of GL _q (ℍ) andT _p-q ^μ is the irreducible representation of Sp(p−q) with highest weightμ. LetI _p,q(s, μ) be the Harish-Chandra module of the induced representation Ind _P ^G . In this paper, we shall determine the module structure and unitarity ofI _{p, q}(s, μ). Partially supported by NUS grant R-146-000-026-112.     

Universally L 1 good sequences with gaps tending to infinity

We construct a sequence (n _k ) such that n _{k + 1} − n _k → ∞ and for any ergodic dynamical system (X, Σ, μ, T) and f ε L ¹(μ) the averages converge to ∝ _X f dμ for μ almost every x. Since the above sequence is of zero Banach density this disproves a conjecture of J. Rosenblatt and M. Wierdl about the nonexistence of such sequences. Research supported by the Hungarian National Foundation for Scientific research T049727.     

三角范畴的coherent函子范畴的recollement

文章研究了三角范畴D及其coherent函子范畴A(D)的recollement之间的关系.利用D的recollement可以诱导A(D)的prerecollement,文章证明了该prerecollement是recollement的充分必要条件是D的recollement是可裂的;并且D的recollement可以诱导A(D)的prerecollement.     

Cyclotomic and simplicial matroids

We show that two naturally occurring matroids representable over ℚ are equal: thecyclotomic matroid μ_n represented by then ^th roots of unity 1, ζ, ζ², …, ζ^n-1 inside the cyclotomic extension ℚ(ζ), and a direct sum of copies of a certain simplicial matroid, considered originally by Bolker in the context of transportation polytopes. A result of Adin leads to an upper bound for the number of ℚ-bases for ℚ(ζ) among then ^th roots of unity, which is tight if and only ifn has at most two odd prime factors. In addition, we study the Tutte polynomial of μ_n in the case thatn has two prime factors. First author supported by NSF Postdoctoral Fellowship. Second author supported by NSF grant DMS-0245379.     

The cubic mapping graph for the ring of Gaussian integers modulo <Emphasis Type="Italic">n</Emphasis>

The article studies the cubic mapping graph Γ(n) of ℤ _n [i], the ring of Gaussian integers modulo n. For each positive integer n > 1, the number of fixed points and the in-degree of the elements [`1]\overline 1 and [`0]\overline 0 in Γ(n) are found. Moreover, complete characterizations in terms of n are given in which Γ₂(n) is semiregular, where Γ₂(n) is induced by all the zero-divisors of ℤ _n [i].     

Some remarks on universal graphs

LetΓ be a class of countable graphs, and let ℱ(Γ) denote the class of all countable graphs that do not contain any subgraph isomorphic to a member ofΓ. Furthermore, letTΓ andHΓ denote the class of all subdivisions of graphs inΓ and the class of all graphs contracting to a member ofΓ, respectively. As the main result of this paper it is decided which of the classes ℱ(TK ⁿ ) and ℱ(HK ⁿ ),n≦ℵ₀, contain a universal element. In fact, for ℱ(TK ⁴)=ℱ(HK ⁴) a strongly universal graph is constructed, whereas for 5≦n≦ℵ₀ the classes ℱ(TK ⁿ ) and ℱ(HK ⁿ ) have no universal elements. Dedicated to Klaus Wagner on his 75^th birthday     

Torsion in Boundary Coinvariants and K -Theory for Affine Buildings

Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion-free cocompact lattice in G. This article studies the coinvariants H ₀(Γ; C(Ω,Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H ₀(Γ; C(Ω, Z)) has finite order, with explicit bounds for the order. A similar statement applies to the K ₀ group of the boundary crossed product C ^*-algebra C(Ω)Γ. If the Tits system has type ? ₂, exact computations are given, both for the crossed product algebra and for the reduced group C ^*-algebra.     

Finite group actions and étale cohomology

If a finite group G acts on a quasi-projective variety X, then H*_c(X,Z/n), the étale cohomology with compact support of X with coefficients inZ/n, has aZ/n[G]-module structure. It is well known that there is a finer invariant, an object RΓ_c(X,Z/n) of the derived category ofZ/n[G]-modules, whose cohomology is H*_c(X,Z/n). We show that there is a finer invariant still, a bounded complex Λ_c(X,Z/n) of direct summands of permutationZ/n[G]-modules, well-defined up to chain homotopy equivalence, which is isomorphic to RΓ_c(X,Z/n) in the derived category. This complex has many properties analogous to those of the simplicial chain complex of a simplicial complex with a group action. There are similar results forl-adic cohomology.     

The isometric extension of the into mapping from the unit sphere S 1( E ) to S 1( l ∞(Γ))

This paper considers the isometric extension problem concerning the mapping from the unit sphere S ₁(E) of the normed space E into the unit sphere S ₁(l ^∞(Γ)). We find a condition under which an isometry from S ₁(E) into S ₁(l ^∞(Γ)) can be linearly and isometrically extended to the whole space. Since l ^∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are solved. More precisely, if E and F are two normed spaces, and if V ₀: S ₁(E) → S ₁(F) is a surjective isometry, where c ₀₀(Γ) ⊆ F ⊆ l ^∞(Γ), then V ₀ can be extended to be an isometric operator defined on the whole space. This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614)     

Estimates for the number of rational points on convex curves and surfaces

Let Γ ⊂ ℝ^d be a bounded strictly convex surface. We prove that the number k_n(Γ) of points of Γ that lie on the lattice satisfies the following estimates: lim inf k_n(Γ)/n^d−2 < ∞ for d ≥ 3 and lim inf k_n(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 174–189.     

The commuting graphs of some subsets in the quaternion algebra over the ring of integers modulo <Emphasis Type="Italic">N</Emphasis>

Let R be an arbitrary ring, S be a subset of R, and Z(S) = {s ∈ S | sx = xs for every x ∈ S}. The commuting graph of S, denoted by Γ(S), is the graph with vertex set S \ Z(S) such that two different vertices x and y are adjacent if and only if xy = yx. In this paper, let I _n , N _n be the sets of all idempotents, nilpotent elements in the quaternion algebra ℤ _n [i, j, k], respectively. We completely determine Γ(I _n ) and Γ(N _n ). Moreover, it is proved that for n ≥ 2, Γ(I _n ) is connected if and only if n has at least two odd prime factors, while Γ(N _n ) is connected if and only if n ∈ 2, 2², p, 2p for all odd primes p.     

Lower bounds at infinity of solutions of partial differential equations in the exterior of a proper cone

An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed convex proper cone inR ⁿ and −Γ′ be the antipodes of the dual cone of Γ. Let be a partial differential operator with constant coefficients inR ⁿ, whereQ(ζ)≠0 onR ⁿ−iΓ′ andP _i is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R ⁿ−iΓ′;P _j(ζ)=0, gradP _j(ζ)≠0} contains some real point on which gradP _j≠0 and gradP _j∉Γ∪(−Γ). LetC be an open cone inR ⁿ−Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in {ξ∈R ⁿ;P(ξ)=0}. Ifu∈ℒ′∩L _loc ² (R ⁿ−Γ) and the support ofP(−i∂/∂x)u is contained in Γ, then the condition implies that the support ofu is contained in Γ.     

The Dichotomy Between Traces on d-sets F in R^n and the Density of D（R^n／Г） in Function Spaces

A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are introduced and calculated.