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1.
在这篇文章中, 我们引入了$Pm$-可分解拓扑群的概念. 令$G$是一个拓扑群, 若对于$G$到一个可度空间$M$上的每一个连续函数$f: Grightarrow M$, 都存在第二可数拓扑群$K$ 以及完备同态映射$pi: Grightarrow K$ 和连续函数$g: Krightarrow M$使得$f=gcircpi$, 那么我们称$G$是$Pm$-可分解拓扑群. 我们证明了一个拓扑群$G$是$Pm$-可分解拓扑群当且仅当$G$是$Pmathbb{R}$-可分解拓扑群. 并且我们证明了: 若$G$是$Pm$-可分解拓扑群, $K$是任一紧拓扑群, 则$Gtimes K$ 是$Pm$-可分解拓扑群. 相似文献
2.
The $mathbb{Z}_{+}$-ring is an important invariant in the theory of tensor category. In this paper, by using matrix method, we describe all irreducible $mathbb{Z}_{+}$-modules over a $mathbb{Z}_{+}$-ring $mathcal{A}$, where $mathcal{A}$ is a commutative ring with a $mathbb{Z}_{+}$-basis{$1$, $x$, $y$, $xy$} and relations: $$ x^{2}=1,;;;;; y^{2}=1+x+xy.$$We prove that when the rank of $mathbb{Z}_{+}$-module $ngeq5$, there does not exist irreducible $mathbb{Z}_{+}$-modules and when the rank $nleq4$, there exists finite inequivalent irreducible $mathbb{Z}_{+}$-modules, the number of which is respectively 1, 3, 3, 2 when the rank runs from 1 to 4. 相似文献
3.
本文主要研究了$mathbb{Z}^{k}$-作用一维子系统的跟踪性质. 文中运用两种等价的方式引入了$mathbb{Z}^{k}$-作用一维子系统的伪轨以及跟踪性的概念. 对于一个闭黎曼流形上的光滑$mathbb{Z}^{k}$-作用$T$, 我们通过诱导的非自治动力系统提出了Anosov方向的概念. 借助Bowen几何的方法, 我们证明了$T$沿着任意Anosov方向具有Lipschitz跟踪性. 相似文献
4.
Christine Scharlach Luc Vrancken 《Proceedings of the American Mathematical Society》1998,126(1):213-219
For (positive) definite surfaces in there is a canonical choice of a centroaffine normal plane bundle, which induces a centroaffine invariant Ricci-symmetric connection . We classify all surfaces in with planar -geodesics. It turns out that the resulting class of surfaces is umbilical with projectively flat induced connection and flat normal plane bundle.
5.
In this paper (weakly) separating maps between spaces of bounded continuous functions over a nonarchimedean field are studied. It is proven that the behaviour of these maps when is not locally compact is very different from the case of real- or complex-valued functions: in general, for -compact spaces and , the existence of a (weakly) separating additive map implies that and are homeomorphic, whereas when dealing with real-valued functions, this result is in general false, and we can just deduce the existence of a homeomorphism between the Stone-Cech compactifications of and . Finally, we also describe the general form of bijective weakly separating linear maps and deduce some automatic continuity results.
6.
In this paper, we present a $mathbb{P}_N × mathbb{P}_N$ spectral element method and a detailedcomparison with existing methods for the unsteady incompressible Navier-Stokes equations.The main purpose of this work consists of: (i) detailed comparison and discussionof some recent developments of the temporal discretizations in the frame of spectral elementapproaches in space; (ii) construction of a stable $mathbb{P}_N × mathbb{P}_N$ method together witha $mathbb{P}_N → mathbb{P}_{N-2}$post-filtering. The link of different methods will be clarified. The keyfeature of our method lies in that only one grid is needed for both velocity and pressurevariables, which differs from most well-known solvers for the Navier-Stokes equations.Although not yet proven by rigorous theoretical analysis, the stability and accuracy ofthis one-grid spectral method are demonstrated by a series of numerical experiments. 相似文献
7.
We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.
8.
In this paper,a new type of entropy,directional preimage entropy including topological and measure theoretic versions for■-actions,is introduced.Some of their properties including relationships and the invariance are obtained.Moreover,several systems including■-actions generated by the expanding maps,■-actions defined on finite graphs and some infinite graphs with zero directional preimage branch entropy are studied. 相似文献
9.
Genevra Neumann 《Transactions of the American Mathematical Society》2005,357(8):3133-3167
The valence of a function at a point is the number of distinct, finite solutions to . Let be a complex-valued harmonic function in an open set . Let denote the critical set of and the global cluster set of . We show that partitions the complex plane into regions of constant valence. We give some conditions such that has empty interior. We also show that a component is an -fold covering of some component . If is simply connected, then is univalent on . We explore conditions for combining adjacent components to form a larger region of univalence. Those results which hold for functions on open sets in are first stated in that form and then applied to the case of planar harmonic functions. If is a light, harmonic function in the complex plane, we apply a structure theorem of Lyzzaik to gain information about the difference in valence between components of sharing a common boundary arc in .
10.
Yuan-chung Sheu 《Proceedings of the American Mathematical Society》1999,127(12):3721-3728
Consider an -superdiffusion on , where is an uniformly elliptic differential operator in , and . The -polar sets for are subsets of which have no intersection with the graph of , and they are related to the removable singularities for a corresponding nonlinear parabolic partial differential equation. Dynkin characterized the -polarity of a general analytic set in term of the Bessel capacity of , and Sheu in term of the restricted Hausdorff dimension. In this paper we study in particular the -polarity of sets of the form , where and are two Borel subsets of and respectively. We establish a relationship between the restricted Hausdorff dimension of and the usual Hausdorff dimensions of and . As an application, we obtain a criterion for -polarity of in terms of the Hausdorff dimensions of and , which also gives an answer to a problem proposed by Dynkin in the 1991 Wald Memorial Lectures.
11.
给出了某类解析簇上具有非孤立奇点的函数芽f在某种等价关系下的C~0-R_V-V(f)-充分性及它的某些形变平凡性的充分条件.它推广了具有非孤立奇点的函数芽的R-Z-充分性的一个判别准则. 相似文献
12.
Based on matrix spectral problems associated with the real special orthogonal Lie algebra so(3,$mathbb{R}$), a Dirac-type equation is derived by virtue of the zero-curvature equation. Further, an N-fold Darboux transformation for the Dirac-type equation is constructed by means of the gauge transformation. Finally, as its application, some exact solutions and their figures are obtained via symbolic computation software (Maple).Correction: The authors were supported by the Nature Science Foundation of China (No. 11701334). 相似文献
13.
Stefan Papadima Laurentiu Paunescu 《Transactions of the American Mathematical Society》2007,359(6):2777-2786
We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré -algebra, in classical terms (discriminant and local invariants). When the algebra is -connected, we show that this property is the only obstruction to realizing it by a smooth closed manifold, in dimension . We analyse the homogeneous artinian complete intersections over realized by smooth closed manifolds of dimension , and their signatures.
14.
S. Mrowka 《Proceedings of the American Mathematical Society》2000,128(12):3701-3709
Answering a question of Arhangel'skii, we show - under GCH - that for most cardinals there exists an -compact space such that but does not embed in a closed fashion into the product of copies of .
15.
Julie T.-Y. Wang 《Transactions of the American Mathematical Society》1996,348(8):3379-3389
For the number field case we will give an upper bound on the number of the -integral points in
. The main tool here is the explicit upper bound of the number of solutions of -unit equations (Invent. Math. 102 (1990), 95--107). For the function field case we will give a bound on the height of the -integral points in . We will also give a bound for the number of ``generators" of those -integral points. The main tool here is the -unit Theorem by Brownawell and Masser (Proc. Cambridge Philos. Soc. 100 (1986), 427--434).
. The main tool here is the explicit upper bound of the number of solutions of -unit equations (Invent. Math. 102 (1990), 95--107). For the function field case we will give a bound on the height of the -integral points in . We will also give a bound for the number of ``generators" of those -integral points. The main tool here is the -unit Theorem by Brownawell and Masser (Proc. Cambridge Philos. Soc. 100 (1986), 427--434).
16.
17.
Over the complex numbers, Plücker's formula computes the number of inflection points of a linear series of fixed degree and projective dimension on an algebraic curve of fixed genus. Here, we explore the geometric meaning of a natural analog of Plücker's formula and its constituent local indices in -homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field. 相似文献
18.
Sandra L. Shields 《Transactions of the American Mathematical Society》1996,348(11):4653-4671
We examine the relationship between codimension one foliations that are covered by a trivial product of hyperplanes and the branched surfaces that can be constructed from them. We present a sufficient condition on a branched surface constructed from a foliation to guarantee that all perturbations of the foliation are covered by a trivial product of hyperplanes. We also show that a branched surface admits a strictly positive weight system if and only if it can be constructed from a fibration over .
19.
William M. Kantor Michael E. Williams 《Transactions of the American Mathematical Society》2004,356(3):895-938
There are lovely connections between certain characteristic 2 semifields and their associated translation planes and orthogonal spreads on the one hand, and -linear Kerdock and Preparata codes on the other. These inter-relationships lead to the construction of large numbers of objects of each type. In the geometric context we construct and study large numbers of nonisomorphic affine planes coordinatized by semifields; or, equivalently, large numbers of non-isotopic semifields: their numbers are not bounded above by any polynomial in the order of the plane. In the coding theory context we construct and study large numbers of -linear Kerdock and Preparata codes. All of these are obtained using large numbers of orthogonal spreads of orthogonal spaces of maximal Witt index over finite fields of characteristic 2.
We also obtain large numbers of ``boring' affine planes in the sense that the full collineation group fixes the line at infinity pointwise, as well as large numbers of Kerdock codes ``boring' in the sense that each has as small an automorphism group as possible.
The connection with affine planes is a crucial tool used to prove inequivalence theorems concerning the orthogonal spreads and associated codes, and also to determine their full automorphism groups.
20.
Florin P. Boca Alexandru Zaharescu 《Transactions of the American Mathematical Society》2006,358(4):1797-1825
Let denote the repartition of the -level correlation measure of the finite set of directions , where is the fixed point and is an integer lattice point in the square . We show that the average of the pair correlation repartition over in a fixed disc converges as . More precisely we prove, for every and , the estimate
We also prove that for each individual point , the -level correlation diverges at any point as , and we give an explicit lower bound for the rate of divergence.
We also prove that for each individual point , the -level correlation diverges at any point as , and we give an explicit lower bound for the rate of divergence.