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1.
We prove the following result for a not necessarily symmetrizable Kac–Moody algebra: Let x,y W with x y, and let P+. If n=l(x)-l(y), then Ext C() n (M(x·),L(y·))=1.  相似文献   

2.
Contact Riemannian manifolds (M, ,g) satisfying the condition (1) =0, where is the torsion introduced byChern andHamilton [6] and is the characteristic vector field, have interesting geometric properties (see [6], [9], [11]). In this paper we give a variational characterization of compact contact Riemannian manifolds which satisfy (1). Moreover we study the tangent sphere bundles (T 1 M, , g), where (,g) is the standard contact Riemannian structure, which satisfy the condition (1); in particular in the 3-dimensional case we find a surprising result (see Corollary 5.3).Supported by funds of the M.U.R.S.T.  相似文献   

3.
Pair algebras which have a non degenerate (left- and right-) invariant bilinear form and for which the inner derivation algebra is completely reducible are characterised by pairs (C,), where C is a n×n matrix satisfying certain conditions and is a sequence of n integers equal to 0 or 1. They occur as pair algebras of type (S(C,)–1,S(C,)1), xuy=[[x,u],y], where (S(C,)r)r is the gradation induced by . in the Kac-Moody algebraS(C). If C is an affin Cartan matrix (as in the case of Lie triple systems), there exists a finite dimensional simple Lie algebrag and a Aut (g), ord =m< such that the pair algebra is isomorphic to the pair algebra (g –1,g 1), xuy=[[x,u],y] (product ing), whereg i. is the eigenspace of of eigenvalue i, a primitive m-th root of unity.  相似文献   

4.
Let G=A ut(T) be the group of automorphisms of a homogeneous tree and let d(v,gv) denote the natural tree distance. Fix a base vertex e in T. The function (g)=exp(–d(e,ge)), being positive definte on G, gives rise to a semigroup of states on G whose infinitesimal generator d/d|=0=log() is conditionally positive definite but not positive definite. Hence, log() corresponds to a nontrivial cocycle (g): GH in some representation space H . In contrast with the case of PGL(2,), the representation is not irreducible.Let o (g) be the derivative of the spherical function corresponding to the complementary series of A ut(T). We show that –d(e,ge) and o (g) come from cohomologous cocycles. Moreover, o is associated to one of the two (irreducible) special representations of A ut(T).  相似文献   

5.
w a(x)=exp(–xa), xR, a0. , N n (a,p,q) — (2), n P nwap, CNn(a,p, q)Pnwaq. , — , {P n}, .

This material is based upon research supported by the National Science Foundation under Grant No. DMS-84-19525, by the United States Information Agency under Senior Research Fulbright Grant No. 85-41612, and by the Hungarian Ministry of Education (first author). The work was started while the second author visited The Ohio State University between 1983 and 1985, and it was completed during the first author's visit to Hungary in 1985.  相似文献   

6.
Summary We consider the set of random measures which consists of measurable maps from [0, 1] to the set of measures on . As it is the dual space ofL 1 ([0, 1];C()), we can equip this space with the weak* topology. We construct a special random measure , which appears as the weak* limit of a sequence of Dirac random measures , where (X n ) n is a bounded sequence inL p [0, 1], (1p<2). The special form of this random measure, which oscillates randomly between twoq-stable standard measures on with different normalizations (p<q<2) allows us to prove two properties of (X n ) n is equivalent to the unit vector basis ofl q and has no almost symmetric subsequence.  相似文献   

7.
Let G be a finite permutation group on a set with no fixed points in and let m and k be integers with 0 < m < k. For a finite subset of the movement of is defined as move() = maxgG| g \ |. Suppose further that G is not a 2-group and that p is the least odd prime dividing |G| and move() m for all k-element subsets of . Then either || k + m or k (7m – 5) / 2, || (9m – 3)/2. Moreover when || > k + m, then move() m for every subset of .  相似文献   

8.
Summary LetB=(B t,t0) be a planar Brownian motion and let >0. For anyt0, the pointz=B t is called a one-sided cone point with angle if there exist >0 and a wedgeW(,z) with vertexz and angle such thatB sW(,z) for everys[t, t+]. Burdzy and Shimura have shown independently that one-sided cone points with angle exist when >/2 but not when   相似文献   

9.
We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (1, ..., n ) = 1(1) + ... + n ( n ), where i ( i ) are ordinary moduli of continuity that depend on one variable. In the case where i ( i ) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L 2 for (1, ..., n ) = 1(1) + ... + n ( n ); (ii) in the integral metric L p (p 1) for (1, ..., n ) = c 11 + ... + c n n ; (iii) in the integral metric L (2, ..., 2, 2r) (r = 2, 3, ...) for (1, ..., n ) = 1(1) + ... + n – 1( n – 1) + c n n .  相似文献   

10.
The problem of tiling space by translates of certain star bodies, called crosses and semicrosses, is intimately connected with finding a subsetA of a finite abelian groupG such that for a particular subset of the integersS each non-zero element ofG is uniquely expressible in the forms·g withs inS andg inA. This paper examines some of the algebraic questions raised; in particular it obtains bounds on the number of elements inS, constructs factorizations ofZ p n , and presents an example of a setS that factors no group.  相似文献   

11.
In this article we examine the minimaxity and admissibility of the product limit (PL) estimator under the loss function% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGmbGaaiikai% aadAeacaGGSaGabmOrayaajaGaaiykaiabg2da9maapeaabaGaaiik% aiaadAeacaGGOaGaamiDaiaacMcaaSqabeqaniabgUIiYdGccqGHsi% slceWGgbGbaKaacaGGOaGaamiDaiaacMcacaGGPaWaaWbaaSqabeaa% caaIYaaaaOGaamOramaaCaaaleqabaaccmGae8xSdegaaOGaaiikai% aadshacaGGPaGaaiikaiaaigdacqGHsislcaWGgbGaaiikaiaadsha% caGGPaGaaiykamaaCaaaleqabaGaeqOSdigaaOGaamizaiaadEfaca% GGOaGaamiDaiaacMcaaaa!5992!\[L(F,\hat F) = \int {(F(t)} - \hat F(t))^2 F^\alpha (t)(1 - F(t))^\beta dW(t)\].To avoid some pathological and uninteresting cases, we restrict the parameter space to ={F: F(ymin) }, where (0, 1) and y 1,...y,n are the censoring times. Under this set up, we obtain several interesting results. When y 1=···=y n, we prove the following results: the PL estimator is admissible under the above loss function for , {–1, 0}; if n=1, ==–1, the PL estimator is minimax iff dW ({y})=0; and if n2, , {–1, 0}, the PL estimator is not minimax for certain ranges of . For the general case of a random right censorship model it is shown that the PL estimator is neither admissible nor minimax. Some additional results are also indicated.Partially supported by the Governor's Challenge Grant.Part of the work was done while the author was visiting William Paterson College.  相似文献   

12.
We investigate the asymptotic behaviour of the summatory functions of z(n, ), k(n, ) z (n) and k(n, ) z (n).  相似文献   

13.
The following statement is proved. Letu be a subharmonic function in the region and u the associated measure. Then there exists a functionf holomorphic in and such that if f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= u and for= f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

. . .  相似文献   

14.
H={h 1,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h (I),I} . , , . L p .

Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.  相似文献   

15.
Summary Consider a Wiener process {W(t),t0}, letM(t)=max |W(s)| andv(t) be the location of the maximum of the absolute value of in [0,t] i.e.|W(v(t))|=M(t). We study the limit points of ( t M(t), t v(t)) ast where t and t are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval ofM(t).Research supported by Hungarian National Foundation for Scientific Research Grant n. 1808  相似文献   

16.
. . . : sn(x) — , n-(, 1)- n L 2. , . , : a k l 2 n () [0,1] , (*) , (**) . a k l 2 u n () [0,1] , (**), (*) .  相似文献   

17.
The paper considers statistical models with real-valued observations i.i.d. by F(x, 0) from a family of distribution functions (F(x, ); ), R s , s 1. For random quantizations defined by sample quantiles (F n –1 (1),, F n –1 ( m–1)) of arbitrary fixed orders 0 < 1 < m-1 < 1, there are studied estimators ,n of 0 which minimize -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F –1 (1,0),, F –1 ( m–1, 0)). Moreover, the Fisher information matrix I m (0, ) of the latter model with the equidistant orders = ( j = j/m : 1 j m – 1) arbitrarily closely approximates the Fisher information J(0) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type.  相似文献   

18.
On a measurable space (T, , ) we choose an additive measure: Z (Z is a Banach space) with the following property: for alle , we have ; this measure defines an indefinite integral over the measure onL 2 (T, ,). We prove that if { n (t)} n =1/ is an orthonormal basis inL 2 and n (e)=e n (t) d, then any additive measure: Z whose Radon-Nikodým derivatived/d belongs toL 2 is uniquely expandable in a series(e)= n =1/ n n(e) that converges to(e) uniformly with respect toe can be differentiated term-by-term, and satisfies n =1/ n /2 <. In the caseL 2[0,2],Z=, the Fourier series of a 2-periodic absolutely continuous functionF(t) such thatF'(t) L 2[0, 2] is superuniformly convergent toF(t).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 180–184, August, 1998.  相似文献   

19.
Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfyingX n+1 =f(X n )+(X n ) n+1 , wheref, are measurable, { n } are i.i.d. with a (common) positive density,E| n |>. In the special casef(x)/x has limits, , asx– andx+, respectively, it is shown that <1, <1, <1 is sufficient for geometric ergodicity, and that <-1, 1, 1 is necessary for recurrence.  相似文献   

20.
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional : n , such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map n n , which is functional increasing (i.e. for each x n (which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)( u))( 2(u))... n (u)). Under quite general conditions one finds that the sequence { n (u)} n converges tov=v(u). As a consequence one obtains the inequality (u)(v).  相似文献   

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