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1.
§1. BasicDefinitionsLetXandYbesets,foragivingmappingf:X→Y,x|→y=f(x),amappingfonpowersetcanbeconductedbyf:f:P(X)→P(Y),A|→B=f(A)={y|x∈A,y=f(x)}. Notethatabinaryoperationisaspecialmappingonsets.GivenabinaryoperationonsetXsuchthat::X×X→X, (x,y)|→x… 相似文献
2.
3.
GroupGradedGammaRingsFanFusheng(樊复生)(DepartmentofMathematics,NortheasternUniversity,Shenyang,110006)GuoLingzhong(郭令忠)(Departm... 相似文献
4.
An associative algebra R over a field K is said to be right ?-prime if for every nonzero r ? R, there exists a finitely generated subalgebra S of R such that rSt = 0 implies t = 0. Clearly, strongly prime implies ?-prime and ?-prime implies prime. A large number of examples of group algebras are given which show that the concept of ?-prime lies strictly between prime and strongly prime. A complete characterization of ?-prime group algebras is given. It is proved that a group algebra KG of the group G over the field K is ?-prime if and only if Λ+(G) = (1). Intersection theorems play an important role in the study. In the process, a new intersection theorem for ?-prime group algebras is obtained. Elementwise characterization of the ?-prime radical is given and its relation with some well-known radicals is discussed. 相似文献
6.
Ricci Curvature and Fundamental Group 总被引:2,自引:0,他引:2
Yuanlong XIN 《数学年刊B辑(英文版)》2006,27(2):113-120
By refined volume estimates in terms of Ricci curvature, the two results due to J. Milnor (1968) are generalized. 相似文献
7.
L-fuzzyGroup(Ⅱ)¥JiangBaoqing;SunRongguang(HenanUniversity,Kaifeng,475001)(HenanUniversity,Kaifeng,475001)Abstract:Thispaperis... 相似文献
8.
Mathematical Notes - Riordan matrices are infinite lower triangular matrices corresponing to certain operators in the space of formal power series. In the paper, we introduce analogous matrices for... 相似文献
9.
§1. IntroductionLetΩbeaboundedsmoothdomainintheHeisenberggroupHn,weareconcernedwiththeproblemofsemilinearsubellipticLaplaceequation-ΔHnu=up+f(x,u),inΩ,u>0, inΩ,(1.1)u=0, onΩ,wherepisarealnumber,f(x,y)satisfiessuitableassumptions(seebelowsectio… 相似文献
10.
In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II. 相似文献
11.
A. N. Khisamiev 《Algebra and Logic》2012,51(1):89-102
We construct a family of Σ-uniform Abelian groups and a family of Σ-uniform rings. Conditions are specified that are necessary and sufficient for a universal Σ-function to exist in a hereditarily finite admissible set over structures in these families. It is proved that there is a set S of primes such that no universal Σ-function exists in hereditarily finite admissible sets \mathbbH\mathbbF(G) \mathbb{H}\mathbb{F}(G) and \mathbbH\mathbbF(K) \mathbb{H}\mathbb{F}(K) , where G = ⊕{Z p | p ∈ S} is a group, Z p is a cyclic group of order p, K = ⊕{F p | p ∈ S} is a ring, and F p is a prime field of characteristic p. 相似文献
12.
Oleg T. Izhboldin 《manuscripta mathematica》2000,102(1):41-52
Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 相似文献
13.
V. Maiorov 《Advances in Computational Mathematics》2006,25(4):435-450
We consider the manifolds H
n(φ) formed by all possible linear combinations of n functions from the set {φ(A⋅+b)}, where x→Ax+b is arbitrary affine mapping in the space ℝd. For example, neural networks and radial basis functions are the manifolds of type H
n(φ). We obtain estimates for pseudo-dimension of the manifold H
n(φ) for wide collection of the generator function φ. The estimates have the order O(d
2
n) in degree scale, that is the order is proportional to number of parameters of the manifold H
n(φ). Moreover the estimates for ɛ-entropy of the manifold H
n(φ) are obtained.
Mathematics subject classifications (2000) 41A46, 41A50, 42A61, 42C10
V. Maiorov: Supported by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel. 相似文献
14.
Let X be a compact metric space and let Lip(X) be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip(X), σπ(f) denotes the peripheral spectrum of f. We state that any map Φ from Lip(X) onto Lip(Y) which preserves multiplicatively the peripheral spectrum:
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
15.
Pierre Liardet 《Israel Journal of Mathematics》1981,39(4):303-325
LetS
φ be the skew product transformation(x, g)↦(Sx, gφ(x)) defined on Ω×G, where Ω is a compact metric space,G a compact metric group with its Haar measureh. IfS is a μ-continuous transformation where μ is a Borel measure on Ω, ergodic with respect toS, we study the setE
0 of μ-continuous applications φ:Ω→G such that μ⩀h is ergodic (with respect toS
φ). For example,E
0 is residual in the group of μ-continuous applications from Ω toG with the uniform convergence topology. We also study the weakly mixing case. Some arithmetic applications are given. 相似文献
16.
V. Yu. Protasov 《Functional Analysis and Its Applications》2011,45(1):46-55
We study continuous subadditive set-valued maps taking points of a linear space X to convex compact subsets of a linear space Y. The subadditivity means that φ(x
1 + x
2) ⊂ φ(x
1) + φ(x
2). We characterize all pairs of locally convex spaces (X, Y) for which any such map has a linear selection, i.e., there exists a linear operator A: X → Y such that Ax ∈ φ(x), x ∈ X. The existence of linear selections for a class of subadditive maps generated by differences of a continuous function is
proved. This result is applied to the Lipschitz stability problem for linear operators in Banach spaces. 相似文献
17.
Given a finite family F\mathcal{F} of linear forms with integer coefficients, and a compact abelian group G, an F\mathcal{F}-free set in G is a measurable set which does not contain solutions to any equation L(x)=0 for L in F\mathcal{F}. We denote by dF(G)d_{\mathcal{F}}(G) the supremum of μ(A) over F\mathcal{F}-free sets A⊂G, where μ is the normalized Haar measure on G. Our main result is that, for any such collection F\mathcal{F} of forms in at least three variables, the sequence
dF(\mathbb Zp)d_{\mathcal{F}}({\mathbb {Z}}_{p}) converges to
dF(\mathbb R/\mathbb Z)d_{\mathcal{F}}({\mathbb {R}}/{\mathbb {Z}}) as p→∞ over primes. This answers an analogue for ℤ
p
of a question that Ruzsa raised about sets of integers. 相似文献
18.
Let S be a fixed finite symmetric subset of SL
d
(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of π
q
(G) with respect to the generating set π
q
(S) form a family of expanders, where π
q
is the projection map Z→Z/q
Z. 相似文献
19.
Amos Nevo 《Israel Journal of Mathematics》1991,75(1):1-19
We prove a structure theorem for locally finite connected graphsX with infinitely many ends admitting a non-compact group of automorphisms which is transitive in its action on the space of
ends, Ω
X
. For such a graphX, there is a uniquely determined biregular treeT (with both valencies finite), a continuous representationφ : Aut(X) → Aut(T) with compact kernel, an equivariant homeomorphism λ : Ω
X
→ Ω
T
, and an equivariant map τ : Vert(X) → Vert(T) with finite fibers. Boundary-transitive trees are described, and some methods of constructing boundary-transitive graphs
are discussed, as well as some examples. 相似文献
20.
The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space 总被引:18,自引:0,他引:18
定光桂 《中国科学A辑(英文版)》2002,45(4):479-483
LetE andF be Hilbert spaces with unit spheresS
1(E) andS
1(F). Suppose thatV
0 S1(E) →S
1(F) is a Lipschitz mapping with Lipschitz constantk=1 such that −V
0[S
1(E)] ⊂V
0[S
1(E)]. Then V0 can be extended to a real linear isometric mappingV fromE intoF. In particular, every isometric mapping fromS
1(E) ontoS
1(F) can be extended to a real linear isometric mapping fromE ontoF. 相似文献