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1.
We consider an evolution process in a Gaussian random field V(q) with the mean ‹V(q)› = 0 and the correlation function W(|qq|) ‹V(q)V(q)›, where q d and d is the dimension of the Euclidean space d . For the value ‹G(q,t;q 0)›, t > 0, of the Green's function of the evolution equation averaged over all realizations of the random field, we use the Feynman–Kac formula to establish an integral equation that is invariant with respect to a continuous renormalization group. This invariance property allows using the renormalization group method to find an asymptotic expression for ‹G(q,t;q 0)› as |qq 0| and t .  相似文献   

2.
LetE be an ample vector bundle of rankr on a compact complex manifoldX of dimension 3 with detE=–K x, andi(X) the index ofX. Then it is proved in this note thati(X)r unless (X,E)(1 × 2,p*O(1) q*), wherep,q are the projections and is isomorphic toO(2) O(1) or the tangent bundleT of 2. This result gives a counterexample to the conjecture formed by T. Peternell.  相似文献   

3.
Two-parameter Vilenkin systems will be investigated. First we give a general sufficient condition for multipliers to be bounded between two-dimensional Hardy spaces H q(0<q1). By means of interpolation and duality argument, this theorem can be extended to other spaces. As a consequence, we can prove the (H q , L q)-boundedness of the Sunouchi operator U with respect to two-parameter Vilenkin systems for all 0 <q 1. Moreover, the equivalence f{Hq} ~ Ufq (f Hq)follows for 1/2<q 1.  相似文献   

4.
Dupoiron  K.  Mathieu  P.  San Martin  J. 《Potential Analysis》2004,21(1):7-33
Soit X une diffusion uniformément elliptique sur R d ,F une fonction dans H loc 1(R d ) et la loi initiale de la diffusion. On montre que si l'intégrale |F|2(x)U(x)dx est finie, oùU désigne le potentiel de la mesure , alors F(X) est un processus de Dirichlet. Si de plus, F appartient àH 2 loc(R d ) et si les intégrales |F|2(x)U(x)dx et |f k |2(x)U(x)dx sont finies, pour les dérivées faibles f k de F, alors on peut écrire une formule d'Itô. En particulier, on définit l'intégrale progressive F(X)dX et on prouve l'existence des covariations quadratiques [f k (X),X k ].  相似文献   

5.
Summary Let T be an infinite homogeneous tree of order a+1. We study Markov chains {X n} in T whose transition functions p(x, y)=A[d(x,y)] depend only on the shortest distance between x and y in the graph. The graph T can be represented as a symmetric space of a p-adic matrix group; we prove a series of results using essentially the spherical functions of this symmetric space. Theorem 1. d(X n,x) n a.s., where >0 if A(0) 1, X 0=x. Assuming {X n} is strongly aperiodic, Theorem 2. p 2(x, y)CRn/n3/2 for fixed x, y where R=(d) A(d)<1, and if E[d(X1, X0)2]<, Theorem 3. R(1–u, x, y) = (1–u)npn(x, y)=Ca–d[exp(–du/)+od(1)] as d=d(x,y) uniformly for 0u2. Using Theorem 3, we calculate the Martin boundary Dirichlet kernel of p(x, y) on T, which turns out to be independent of {itA(d)}. We also consider a stepping-stone model of a randomly-mating-and-migrating population on the nodes of T. If initially all individuals are distinct, then in generation n approximately half of the individuals of a given type are within n of a typical one and essentially all are within 2n.This work was partially supported by the National Science Foundation under grant number MCS 75-08098-A01For the academic year 1977–78: Department of Mathematics GN-50, University of Washington, Seattle, Washington 98195 USA  相似文献   

6.
LetY = (X, {R i } oid) denote aP-polynomial association scheme. By a kite of lengthi (2 i d) inY, we mean a 4-tuplexyzu (x, y, z, u X) such that(x, y) R 1,(x, z) R 1,(y, z) R 1,(u, y) R i–1,(u, z) R i–1,(u, x) R i. Our main result in this paper is the following.  相似文献   

7.
The aim of this paper is to illustrate the use of topological degree for the study of bifurcation in von Kármán equations with two real positive parameters and for a thin elastic disk lying on the elastic base under the action of a compressing force, which may be written in the form of an operator equation F(x, , ) = 0 in some real Banach spaces X and Y. The bifurcation problem that we study is a mathematical model for a certain physical phenomenon and it is very important in the mechanics of elastic constructions. We reduce the bifurcation problem in the solution set of equation F(x, , ) = 0 at a point (0, 0, 0) X × IR + 2 to the bifurcation problem in the solution set of a certain equation in IR n at a point (0, 0, 0) IR n × IR + 2, where n = dim Ker F x (0, 0, 0) and F x (0, 0, 0): X Y is a Fréchet derivative of F with respect to x at (0, 0, 0). To solve the bifurcation problem obtained as a result of reduction, we apply homotopy and degree theory.  相似文献   

8.
Summary LetF: n + 1 be a polynomial. The problem of determining the homology groupsH q (F –1 (c)), c , in terms of the critical points ofF is considered. In the best case it is shown, for a certain generic class of polynomials (tame polynomials), that for allc,F –1 (c) has the homotopy type of a bouquet of - c n-spheres. Here is the sum of all the Milnor numbers ofF at critical points ofF and c is the corresponding sum for critical points lying onF –1 (c). A second best case is also discussed and the homology groupsH q (F –1 (c)) are calculated for genericc. This case gives an example in which the critical points at infinity ofF must be considered in order to determine the homology groupsH q (F –1 (c)).  相似文献   

9.
Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier.  相似文献   

10.
Summary This paper studies annihilating properties of operators generated by spherical convolution over the unit sphere 2q of Cq. Its specific aim is to answer the following question: given a complex number , ||1, to determine what functions of L2(2q) have zero average over every section w,q :={ z 2q: <z,w> = } of 2q . Here, <.,.>stands for the usual inner product of Cq.  相似文献   

11.
Let X2, X2 be Hilbert spaces, X2 X1, X2 is dense in X1, the imbedding is compact,m X2, dimH i m and h(i)(m) are the Hausdorff dimension and the limit capacity (information dimension) of the setm with respect to the metrics of the spaces Xi (i=1, 2). Two examples are constructed. 1) An example of a setm bounded in X2, such that: a) h(1)(m) < (and, consequently, dimH 1 m); b)m cannot be covered by a countable collection of sets, compact in X2 (and, consequently, dimH 2 m=). 2) an Example of a setm, compact in X2, such that h(1)(m) < and h(2)(m)=.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 154–165, 1987.  相似文献   

12.
Let M n =X1+...+Xn be a martingale with bounded differences Xm=Mm-Mm-1 such that {|Xm| m}=1 with some nonnegative m. Write 2= 1 2 + ... + n 2 . We prove the inequalities {M nx}c(1-(x/)), {M n x} 1- c(1- (-x/)) with a constant . The result yields sharp inequalities in some models related to the measure concentration phenomena.  相似文献   

13.
The imaginary powersA it of a closed linear operatorA, with inverse, in a Banach spaceX are considered as aC 0-group {exp(itlogA);t R} of bounded linear operators onX, with generatori logA. Here logA is defined as the closure of log(1+A) – log(1+A –1). LetA be a linearm-sectorial operator of typeS(tan ), 0(/2), in a Hilbert spaceX. That is, |Im(Au, u)| (tan )Re(Au, u) foru D(A). Then ±ilog(1+A) ism-accretive inX andilog(1+A) is the generator of aC 0-group {(1+A) it ;t R} of bounded imaginary powers, satisfying the estimate (1+A) it exp(|t|),t R. In particular, ifA is invertible, then ±ilogA ism-accretive inX, where logA is exactly given by logA=log(1+A)–log(1+A –1), and {A it;t R} forms aC 0-group onX, with the estimate A it exp(|t|),t R. This yields a slight improvement of the Heinz-Kato inequality.  相似文献   

14.
In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x 0 1 i /p} on [0, 1] fori=0, 1,..., (p–1)p–1–1, i.e. in current terminology, generators given byx n+1 1 x n mod p wheren=0, 1,..., (p–1)p –1–1,p is any odd prime, (x 0,p)=1, 1 is a primitive root modp 2, and 1 is any positive integer.We derive the expectationsE(X, ),E(X 2, ),E(X nXn+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of 1 for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.  相似文献   

15.
Let X be a smooth, projective, d-dimensional subvariety of n (). Barth's theorem says that H q (X, p X )=0 when pq and q+p2dn (if p=0 we must have q>0). It is very interesting to look for analogous vanishing theorems for H q (X, p X (m)), m (see [S-S], [F], [S]). In this paper we prove some vanishing theorems for H q (X, p X (1)), for H q (X, p X (m)) when m–1, and, if dim(X)=n–2, for H q (X, 2 X (m)) and H q (X, S k 1 X (m)). We use standard techniques and some of our previous results.  相似文献   

16.
Let X be a compact subset of the n-dimensional Euclidean space R n . A theorem of G. Björck implies the existence of a unique probability measure 0 which maximizes the value X X d 2(x, y) d(x) d(y), where ranges over all probability measures on X and d 2 denotes the Euclidean distance on R n . In this paper we introduce and investigate an algorithm which is easy to describe and which inductively constructs a sequence = x 1, x 2,... in X such that is uniformly distributed with respect to 0. Geometrical and topological interpretations and applications, and concrete numerical examples are given.  相似文献   

17.
Let Xn denote the set of quadratic forms in n variables over a finite field Fq of characteristic 2, and Xn the association scheme on Xn by defining the relations with respect to the type of quadratic forms. We prove that every automorphism of Xn is of the form X PtXP + Y for all X Xn, where P GLn(Fq), is an automorphism of Fq, and Y Xn.2000 Mathematics Subject Classification: 05E30Supported by the National Natural Science Foundation of China (10271039), Hobei Natural Science Foundation (102132) and Hebei Education Committee.  相似文献   

18.
We consider the function space B p l () of functionsf(x), defined on the domain of a certain class and characterized by specific differential-difference properties in Lp(). We prove a theorem on the embedding B p,q l () Lq in the case whenl=n/p –n/q >0 and its generalization for vectorl, p, q.Translated from Matematicheski Zametki, Vol. 6, No. 2, pp. 129–138, August, 1969.  相似文献   

19.
The projected gradient methods treated here generate iterates by the rulex k+1=P (x k s k F(x k )),x 1 , where is a closed convex set in a real Hilbert spaceX,s k is a positive real number determined by a Goldstein-Bertsekas condition,P projectsX into ,F is a differentiable function whose minimum is sought in , and F is locally Lipschitz continuous. Asymptotic stability and convergence rate theorems are proved for singular local minimizers in the interior of , or more generally, in some open facet in . The stability theorem requires that: (i) is a proper local minimizer andF grows uniformly in near ; (ii) –F() lies in the relative interior of the coneK of outer normals to at ; and (iii) is an isolated critical point and the defect P (xF(x)) –x grows uniformly within the facet containing . The convergence rate theorem imposes (i) and (ii), and also requires that: (iv)F isC 4 near and grows no slower than x4 within the facet; and (v) the projected Hessian operatorP F 2 F()F is positive definite on its range in the subspaceF orthogonal toK . Under these conditions, {x k } converges to from nearby starting pointsx 1, withF(x k ) –F() =O(k –2) and x k – =O(k –1/2). No explicit or implied local pseudoconvexity or level set compactness demands are imposed onF in this analysis. Furthermore, condition (v) and the uniform growth stipulations in (i) and (iii) are redundant in n .  相似文献   

20.
Summary A characterization of compact sets in Lp (0, T; B) is given, where 1P and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method, the point is to obtain compactness in a space Lp (0,T; B) from estimates with values in some spaces X, Y or B where XBY with compact imbedding XB. Using the present characterization for this kind of situations, sufficient conditions for compactness are given with optimal parameters. As an example, it is proved that if {fn} is bounded in Lq(0,T; B) and in L loc 1 (0, T; X) and if {fn/t} is bounded in L loc 1 (0, T; Y) then {fn} is relatively compact in Lp(0,T; B), p相似文献   

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