Again Sharpening of a Negative ExponentGeometric Inequality in the Space E~n

DerinitionInageometricinequalitybyaftersimplify,ifturnupgeometricmetricinde-nominatorofafractor,butnoturnupgeometricmetricinnumerator,thencallednegativeex-ponentgeometricinequalitysuchgeometicinequality,isnegativeexponentgecmetricinequalityforshort-LetrandR.denotetheinradiusandcircumradiusofsimplexXinthen-dimensionalEuc-tideanspaceEw,respectively.LetPbearbitraryPOintinsidethe8implexX,andd,,d,,..',d. ,bethedistancefrompointPton lthen-l-dimensionalhyperplane,article[ljobtainanegativeexponent…     

Revêtements modérés et groupe fondamenttal de graphe de groupes

Let R be a discrete complete valuation ring, with algebraically closedresidue field. Let X be a semi-stable R-curve, with smooth generic fibre. In this paper we study tame coverings of X.     

RESEARCH ANNOUNCEMENTS The Pure Exponential Diophantine Equation ax+by=Cz for Generalized Pythagorean Triplets

Let N+ be the set of all positive integers.Let a,b,c be fixed coprime positive integers with min(a,b,c)＞1.     

Discrete Differential Calculus on Simplicial Complexes and Constrained Homology*

Let V be a finite set. Let K be a simplicial complex with its vertices in V .In this paper, the author discusses some differential calculus on V . He constructs some constrained homology groups of K by using the differential calculus on V . Moreover, he defines an independence hypergraph to be the complement of a simplicial complex in the complete hypergraph on V . Let L be an independence hypergraph with its vertices in V .He constructs some constrained cohomology groups of L by using the differential calculus on V .     

On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups

Russian Mathematics - Let $${\cal K}$$ be a root class of groups closed under taking quotient groups, G be a free product of groups A and B with amalgamated subgroups H and K. Let also H be normal...     

Special precovered categories of Gorenstein categories

Let A be an abelian category and P(A)be the subcategory of A consisting of projective objects.Let C be a full,additive and self-orthogonal subcategory of A with P(A)a generator,and let G(C)be the Gorenstein subcategory of A.Then the right 1-orthogonal category G(C)~⊥1 of G(C)is both projectively resolving and injectively coresolving in A.We also get that the subcategory SPC(G(C))of A consisting of objects admitting special G(C)-precovers is closed under extensions and C-stable direct summands(*).Furthermore,if C is a generator for G(C)~⊥1,then we have that SPC(G(C))is the minimal subcategory of A containing G(C)~⊥1∪G(C)with respect to the property(*),and that SPC(G(C))is C-resolving in A with a C-proper generator C.     

On Weak Well-posedness of the Nearest Point and Mutually Nearest Point Problems in Banach Spaces

Let G be a nonempty closed subset of a Banach space X. Let B(X) be the family of nonempty bounded closed subsets of X endowed with the Hausdorff distance and ■, where the closure is taken in the metric space(B(X), H). For x ∈ X and F ∈ BG(X), we denote the nearest point problem inf ■ by min(x, G) and the mutually nearest point problem inf■ by min(F, G). In this paper, parallel to well-posedness of the problems min(x, G) and min(F, G) which are defined by De Blasi et al., we further introduce the weak well-posedness of the problems min(x, G) and min(F, G). Under the assumption that the Banach space X has some geometric properties, we prove a series of results on weak well-posedness of min(x, G) and min(F, G). We also give two sufficient conditions such that two classes of subsets of X are almost Chebyshev sets.     

Invariant metrics of positive Ricci curvature on principal bundles

Let be a compact connected Riemannian manifold with a metric of positive Ricci curvature. Let be a principal bundle over with compact connected structure group . If the fundamental group of is finite, we show that admits a invariant metric with positive Ricci curvature so that is a Riemannian submersion. Received 14 January 1997     

The decomposition of permutation module for infinite Chevalley groups

Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module M(tr) = kG ■tr(where tr is the trivial B-module) for any field k.     

Strong Approximation for a Toric Variety

Let X be a toric variety over a number field k with k[X]~×=k~×.Let W ■ X be a closed subset of codimension at least 2.We prove that X \ W satisfies strong approximation with algebraic Brauer-Manin obstruction.     

The double Coxeter arrangement

Let V be Euclidean space. Let be a finite irreducible reflection group. Let be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For choose such that . The arrangement is known to be free: the derivation module is a free S-module with generators of degrees equal to the exponents of W. In this paper we prove an analogous theorem for the submodule of defined by . The degrees of the basis elements are all equal to the Coxeter number. The module may be considered a deformation of the derivation module for the Shi arrangement, which is conjectured to be free. The proof is by explicit construction using a derivation introduced by K. Saito in his theory of flat generators. Received: March 13, 1997     

On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph

Acta Mathematicae Applicatae Sinica, English Series - Let G be a simple connected graph with order n. Let $$\mathcal{L}(G)$$ and $$\mathcal{Q}(G)$$ be the normalized Laplacian and normalized...     

Symplectic orthogonality spaces

Let E be a finite dimensional vector space over the Galois field GF(2). Let lin(E) denote the set of one-dimensional subspaces of E. Let Φ be the symplectic inner product on E. Consider the elements of lin(E) as vertices of a graph, two vertices being connected exactly when they are distinct and orthogonal with respect to Φ. This graph is characterized abstractly.     

The local structure of characters

Let G be a connected real semisimple Lie group with Lie algebra g. Let g = t? + s be the Cartan decomposition and K the maximal compact subgroup with Lie algebra t?. Let Θ be the character of an irreducible representation. Then Θ has an asymptotic expansion at zero (in the sense of Taylor series). As consequences of this expansion we obtain results about the asymptotic directions in which the K-types occur and about the Gelfand-Kirillov dimension of the representation.     

On C-small conjugacy classes in a reductive group

Let G be an almost simple reductive group with Weyl group W. Let B be a Borel subgroup of G. Let w be an elliptic element of W which has minimal length in its conjugacy class. We show that in almost all cases there exists a semisimple class in G whose intersection with BwB has dimension dim(B).     

區域的映照半徑與格林函數

<正> §1.設a_1,a_2是z平面上兩個不同的有限點,G_1和G_2是z平面上不相重疊的兩個單連區域,a_i∈G_i,i=1,2.記R(a_i,G_i)是區域G_i關於a_i真的映照半徑.記     

Witt型单李超代数

设F是特征p〉2的域,A是F上结合的超交换的代数,D是域为F上A的超交换的导子.设A×D=A[D]为Witt型李超代数.从环论的角度得到了Witt型李超代数为单代数的充分必要条件.     

Banach空间中极大单调算子零点的迭代构造

设E为实光滑、一致凸Banach空间,E*为其对偶空间,TE×E*为极大单调算子且T-10≠φ.本文引入了一种新迭代格式,利用Lyapunov泛函和广义投影算子等技巧,在Banach空间中证明了迭代序列弱收敛于极大单调算子T的零点的结论.     

实可分Banach空间中K正定算子方程的逼近解

设E是带严格凸对偶空间的实可分Banach空间，设A：D（A）包含于E→E是一K正定算子。对任意f∈E，我们构造了强收敛于算子方程Ax=f唯一解的新的带误差的迭代过程。我们的工作推广了文[1,3-4]中的结果。     

Banach空间中渐近非扩张映象的修正Reich-Takahashi型迭代法的强收敛性

设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的.设D是E的非空有界闭凸子集,T:→D是渐近非扩张映象.该证明了,在一些适当的条件下,修正的Reich-Takahashi型迭代法强收敛到渐近非扩张映象T的不动点