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1.
If (P, L) is a projective plane and is a triangle presentation compatible with a point-line correspondence :P L, then gives rise to a group and a thick building of typeà 2 on the vertices of which acts simply transitively. We find all triangle presentations (up to natural equivalence) compatible with some point-line correspondence :P L, when (P, L) is the projective plane of orderq=2 orq=3. For some, but not all, of these , is isomorphic to the building associated withG=PGL(3,K) whereK is a local field with discrete valuation and residual field of orderq. We identify the for which this is the case, and in these cases, find embeddings of intoG. We also describe the arithmetic nature of these groups.  相似文献   

2.
Summary Let (,, P) be a measurable space, and { t} be a filtration on (,). Then, given a fixed honest timeL a new filtrationG t} is defined, the smallest containing { t} and for whichL is a stopping time, and the martingales, semimartingales and stopping times of this new filtration are characterised.  相似文献   

3.
We give several complements to the paper The Bruhat order on symmetric varieties. Our main result shows that the partial order on the set of twisted involutions in the Weyl groupW, which was introduced in the earlier paper, agrees with the partial order on induced by the usual Bruhat order onW.R. W. Richardson died on 15 June. 1993.  相似文献   

4.
Let be a locally finite system of hyperplanes in d with the property that the cells of the induced cell complex decomposition of d have uniformly bounded diameters. If is simple and the density of the vertices in exists, then the density of thek-cells in exists and can be given explicitly (k = 1, ...,d). Also, the mean number ofj-faces of thek-cells in exists and can be calculated. For certain nonsimple systems , corresponding inequalities are obtained.  相似文献   

5.
We denote byK k ,k, 2, the set of allk-uniform hypergraphsK which have the property that every element subset of the base ofK is a subset of one of the hyperedges ofK. So, the only element inK 2 2 are the complete graphs. If is a subset ofK k then there is exactly one homogeneous hypergraphH whose age is the set of all finite hypergraphs which do not embed any element of . We callH -free homogeneous graphsH n have been shown to be indivisible, that is, for any partition ofH n into two classes, oue of the classes embeds an isomorphic copy ofH n . [5]. Here we will investigate this question of indivisibility in the more general context of-free homogeneous hypergraphs. We will derive a general necessary condition for a homogeneous structure to be indivisible and prove that all-free hypergraphs for K k with 3 are indivisible. The-free hypergraphs with K k 2 satisfy a weaker form of indivisibility which was first shown by Henson [2] to hold forH n . The general necessary condition for homogeneous structures to be indivisible will then be used to show that not all-free homogeneous hypergraphs are indivisible.This research has been supported by NSERC grant 69–1325.  相似文献   

6.
Let D be a subset of the s-dimensional lattice ZS, M=M(D) the number of elements in D, Dthe space of trigonometric polynomials on the torus TS with spectrum concentrated in D and having unit norm in L2(TS). In this paper we give the following bound for the Gel'fand diameter:d n( D,C(Ts))M/2–N/2. This bound is subsequently used for actual functional classes.Translated from Matematicheskie Zametki, Vol. 12, No. 4, pp. 413–419, October, 1972.  相似文献   

7.
We study homogeneous Riemannian structures belonging to the class 13 of the classification given by Tricerri and Vanhecke. The main result is the following: a connected, simply connected Riemannian manifoldM admits a homogeneous structureT of type 13,T3, if and only ifM is isometric to a hyperbolic space n .This work was partially supported by M.P.I.  相似文献   

8.
In a cyclotomic scheme over a finite field, there are some relations between the irreducible modules of the Terwilliger algebra and the Jacobi sums over the field. These relations were investigated in [3]. In this paper, we replace the finite field by a commutative local ring which is called a Galois ring of characteristic 4. Hence we want to find similar relations between the irreducible modules of the Terwilliger algebra and the Jacobi sums over the local ring. Specifically, if we let be a Galois ring of characteristic 4,X a cyclotomic scheme over with classD and the Terwilliger algebra ofX, then we show that most of the irreducible -modules have standard forms; otherwise, certain relations of the Jacobi sums hold. When the classD is three, we can completely determine the irreducible -modules using Jacobi sums.  相似文献   

9.
A bouquet of matroids is a combinatorial structure that generalizes the properties of matroids. Given an independence system, there exist several bouquets of matroids having the same family of independent sets. We show that the collection of these geometries forms in general a meet semi-lattice and, in some cases, a lattice (for instance, when is the family of the stable sets in a graph). Moreover, one of the bouquets that correspond to the highest elements in the meet semi-lattice provides the smallest decomposition of into matroidal families, such that the rank functions of the different matroids have the same values for common sets. In the last section, we give sharp bounds on the performance of the greedy algorithm, using parameters of some special bouquets in the semi-lattice.  相似文献   

10.
A limit theorem due to J. Kuelbs and M. Ledoux, valid for dilatation-stable laws on type 2-Banach spaces, is carried over to stable laws on simply connected step 2-nilpotent Lie groupsG. We show that for products of i.i.d. random variables in the of attraction of a nondegenerate semigroup onG, where is a one-parameter automorphism group acting contracting onG, a certain intermediate trimming procedure, together with a suitable norming, always yields a nondegenerate centered Gaussian limit.  相似文献   

11.
Let be a finite regular incidence-polytope. A realization of is given by an imageV of its vertices under a mapping into some euclidean space, which is such that every element of the automorphism group () of induces an isometry ofV. It is shown in this paper that the family of all possible realizations (up to congruence) of forms, in a natural way, a closed convex cone, which is also denoted by The dimensionr of is the number of equivalence classes under () of diagonals of , and is also the number of unions of double cosets ** *–1* ( *), where * is the subgroup of () which fixes some given vertex of . The fine structure of corresponds to the irreducible orthogonal representations of (). IfG is such a representation, let its degree bed G , and let the subgroup ofG corresponding to * have a fixed space of dimensionw G . Then the relations
  相似文献   

12.
Let be a Jacobian curve, defined over the global field K, and let g be the group of K-points on of finite order. In this note we give the local factorization of the coordinates of points from g.Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 827–832, December, 1973.  相似文献   

13.
Acontext is defined to be a triple (G, M, J) of setsG, M and an incidence relationJ G×M.A finite set ofn oriented lines in general position in the euclidean plane induces a cell decomposition of the plane. For a givenk-element subset of cells of dimension 2, we define an incidence relationJ × as follows:t i andl j are incident if and only ift i lies on the positive side with respect tol j .We call a context (G, M, J)represented in a line arrangement if and only if there are relation preserving bijections betweenG and ,M and , respectively. We study conditions for a context to be representable in a line arrangement.Especially, we provide a non-trivial infinite class of contexts which can not be represented in a line arrangement.  相似文献   

14.
Summary In this paper we establish a large deviations principle for the invariant measure of the non-Gaussian stochastic partial differential equation (SPDE) t v =v +f(x,v )+(x,v ) . Here is a strongly-elliptic second-order operator with constant coefficients, h:=DH xx-h, and the space variablex takes values on the unit circleS 1. The functionsf and are of sufficient regularity to ensure existence and uniqueness of a solution of the stochastic PDE, and in particular we require that 0<mM wherem andM are some finite positive constants. The perturbationW is a Brownian sheet. It is well-known that under some simple assumptions, the solutionv 2 is aC k (S 1)-valued Markov process for each 0<1/2, whereC (S 1) is the Banach space of real-valued continuous functions onS 1 which are Hölder-continuous of exponent . We prove, under some further natural assumptions onf and which imply that the zero element ofC (S 1) is a globally exponentially stable critical point of the unperturbed equation t 0 = 0 +f(x,0), that has a unique stationary distributionv K, on (C (S 1), (C K (S 1))) when the perturbation parameter is small enough. Some further calculations show that as tends to zero,v K, tends tov K,0, the point mass centered on the zero element ofC (S 1). The main goal of this paper is to show that in factv K, is governed by a large deviations principle (LDP). Our starting point in establishing the LDP forv K, is the LDP for the process , which has been shown in an earlier paper. Our methods of deriving the LDP forv K, based on the LDP for are slightly non-standard compared to the corresponding proofs for finite-dimensional stochastic differential equations, since the state spaceC (S 1) is inherently infinite-dimensional.This work was performed while the author was with the Department of Mathematics, University of Maryland, College Park, MD 20742, USA  相似文献   

15.
For a Rees matrix semigroupS with normalized sandwich matrix and C(S), the congruence lattice ofS, we consider the lattice generated by {itpTl, pK, pTr, ptl, pk, ptr}. HerepT 1 andpt l are the upper and lower ends of the interval which makes up the i -class of , i being the left trace relation onC(S). The remaining symbols have the analogous meaning relative to the kernel and the right trace relations. We also consider the lattice generated by {T l, K, Tr, tl, k, tr} where and are the equality and the universal relations onS, respectively. In both cases, we find lattices freest relative to these lattices and represent them as distributive lattices with generators and relations.With 3 Figures  相似文献   

16.
A study is presented of the relationship between the topological and uniformity properties of a group G and the spaces (G), (G) of all nonempty closed subsets and closed subgroups of G. A base for the neighborhood system of a closed subset X of G is formed by the sets S(X, U)={Y Y XU, X YU}, where U ranges over all neighborhoods of the identity in G. Criteria are obtained for the space (G) and some of its subspaces to be totally bounded and locally totally bounded. Some classes of groups with compact spaces (G) are described. It is proved that the spaces (G), (G) are complete in the case of projective metrizable groups G.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 542–549, April, 1990.  相似文献   

17.
Summary Arep-tiling is a self replicating, lattice tiling ofR n .Lattice tiling means a tiling by translates of a single compact tile by the points of a lattice, andself-replicating means that there is a non-singular linear mapø: R n Rn such that, for eachT , the imageø(T) is, in turn, tiled by . This topic has recently come under investigation, not only because of its recreational appeal, but because of its application to the theory of wavelets and to computer addressing. The paper presents an exposition of some recent results on rep-tiling, including a construction of essentially all rep-tilings of Euclidean space. The construction is based on radix representation of points of a lattice. One particular radix representation, called thegeneralized balanced ternary, is singled out as an example because of its relevance to the field of computer vision.  相似文献   

18.
Let (S nn>-1) be a random walk on a hypergroup ( + , *), i.e., a Markov chain with transition kernelN(x, A) = x * (A), where is a fixed probability measure on + such that the second moment exists. Then depending on the growth of the hypergroup two situations can occur: when ( + , *) is of exponential growth then it is shown thatS n is asymptotically normal. In the case of polynomial growth {more precisely, if the densityA of the Haar measure of ( + , *) satisfies lim[A()/A()]=}, the normalized variablesS n/[n Var()/(+1)]1/2 converge to a Rayleigh distribution with parameter .  相似文献   

19.
— [0,1] ,E — - e=1 [0,1]. I — E =1, E=L 2 x e =xL 2 x E.

This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund.  相似文献   

20.
We define a class p (M,N) of Sobolev maps from a manifoldM into a manifoldN, in such a way that each mapu p (M, N) has a well defined [p]-homotopy type, providedN satisfies a topological hypothesis. Using this, we prove the existence of minimizers in [p]-homotopy classes for some polyconvex variational problems.  相似文献   

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