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1.
A closed expression is derived for the integral 0 /2 log n cosxlog p sinxdx, wheren andp are non-negative integers. As already remarked by Nielsen in a monograph on the generalized polylogarithms published early in this century, this integral is equal to times a homogeneous polynomial in (q) (the Riemann zeta function for integer arguments) and log 2, with rational coefficients. Explicit expressions for the integral are given for 0<n4, 0p4, most of which have been found from the general formula by means of a computer.Part of this work was done during the author's leave of absence at the Institute of Theoretical Physics at McGill University, Montreal, Quebec, Canada. This work was supported in part by the National Research Council of Canada.  相似文献   

2.
Paul Jolissaint 《K-Theory》1989,2(6):723-735
We associate to any length function L on a group a space of rapidly decreasing functions on (in the l 2 sense), denoted by H L (). When H L () is contained in the reduced C*-algebra C r * () of (), then it is a dense *-subalgebra of C r * () and we prove a theorem of A. Connes which asserts that under this hypothesis H L () has the same K-theory as C r * (). We introduce another space of rapidly decreasing functions on (in the l 1 sense), denoted by H L 1, (), which is always a dense *-subalgebra of the Banach algebra l 1(), and we show that H L 1, () has the same K-theory as l 1().  相似文献   

3.
Summary We define a constraint system , [0,0), which is a kind of family of vector fields on a manifold. This is a generalized version of the family of the equations , [0,0),x m ,y n . Finally, we prove a singular perturbation theorem for the system , [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday  相似文献   

4.
In this paper, we have proven that for the Jordan blockS() withS() (SI), i=1 n S() =S() (n) (n 1) has unique finite (SI) decomposition up to a similarity. As result, we obtain that ifV is a Volterra operator onH=L 2([0, 1]), thenV (n) has unique finite (SI) decomposition.This project was supported by National Natural Science Foundation of China.  相似文献   

5.
Let V: R N [0, ] be a measurable function, and >0 be a parameter. We consider the behaviour of the spectral bound of the operator 1/2–V as a function of . In particular, we give a formula for the limiting value as , in terms of the integrals of V over subsets of R N on which the Laplacian with Dirichlet boundary conditions has prescribed values. We also consider the question whether this limiting value is attained for finite .  相似文献   

6.
The symmetry properties of the spectral densitiesf (v)() of order v, equal to 4, 5, and 6 of a stationary stochastic process {(k), k Z} are studied. It is established that the fonctionf (v)(), Rv–1 is completely determined by its values on a set whose (v– 1)-dimensional volume is 4/6, 5/15, and 5/45 when v is equal to 4, 5, and 6, respectively. Results on the statistical estimation of the spectral densities of orders v equal to 3 and 4 with respect to samples of finite size are also given.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 1–4, 1988.  相似文献   

7.
We give some existence results of minima for a class of nonconvex functionals depending on the Laplacian. We minimize these functionals on the set of functionsu inW 2,p () W 0 1,p () such that u/n=0 on ,p>1, with either an annulus or the whole space n . Our approach allows us to deal with integrands without any regularity conditions. The results are obtained first by showing that the corresponding convexified problem has at least one radially symmetric solution via a rotation; then, by using a Liapunov's theorem on the range of a vector-valued measure, we construct a function that is a solution to our problem.The author wishes to thank Prof. A. Cellina for useful comments and Prof. G. Dal Maso for several helpful discussions during the preparation of this paper. He also is grateful to Prof. A. Salam and ICTP for the generous financial support that made this work possible.  相似文献   

8.
Alberto Marcone 《Order》2001,18(4):339-347
We pursue the fine analysis of the quasi-orderings and on the power set of a quasi-ordering (Q,). We set X Y if every xX is majorized in by some yY, and X Y if every yY is minorized in by some xX. We show that both these quasi-orderings are -wqo if and only if the original quasi-ordering is ( )-wqo. For this holds also restricted to finite subsets, thus providing an example of a finitary operation on quasi-orderings which does not preserve wqo but preserves bqo.  相似文献   

9.
Let (itk) (s) denote thek-th derivative of the Riemann Zeta-function,s=+it, ,t real numbers,k1 rational integers. Using ideas fromT. C. Titchmarsh and from a paper ofR. Spira, lower bounds are derived for |(itk)(s)|, |(itk)(1-s) for >1 and some infinitely many, sufficiently large values oft. Further let be an algebraic number of degreen and heightH; then a lower bound for |(itk)(its)|, dependent onn, H, k is established for alln,H1,k3, 2+7k/4 and all realt.  相似文献   

10.
Let n be n-dimensional Lobachevskii space, and {lx:x n} be a family of lines, parallel to a linel 0, 0n (in a given direction). Let {cx:Xn} be a family of circular cones in n of opening with axes lX and vertex X. Then, iff:nn(n>2) is a bijective mapping andf(Cx)=C f(x), it follows thatf is a motion in the space n.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 687–694, May, 1973.  相似文献   

11.
Let {X n,n1} be a strictly stationary sequence of weakly dependent random variables satisfyingEX n=,EX n 2 <,Var S n /n2 and the central limit theorem. This paper presents two estimators of 2. Their weak and strong consistence as well as their rate of convergence are obtained for -mixing, -mixing and associated sequences.Supported by a NSF grant and a Taft travel grant. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025.Supported by a Taft Post-doctoral Fellowship at the University of Cincinnati and by the Fok Yingtung Education Foundation of China. Hangzhou University, Hangzhou, Zhejiang, P.R. China and Department of Mathematics, National University of Singapore, Singapore 0511.  相似文献   

12.
Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in p , n , respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in n . The function c: p+n is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in n . Computational experiments show that the resulting algorithms work well for problems with smalln.  相似文献   

13.
Let be an inner function, let C, ¦¦=1. Then the harmonic function [(+)]/(–)] is the Poisson integral of a singular measure D. N. Clark's known theorem enables us to identify in a natural manner the space H2 H2 with the space L2 ( ).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 7–33, 1989.  相似文献   

14.
In this paper, we consider the problem: –u=N(N–2)u p– , u>0 on ; u=0 on , where is a smooth and bounded domain inR N, N3, p= , and >0. We prove a conjecture of H. Brezis and L.A. Peletier about the asymptotic behaviour of solutions of this problem which are minimizing for the Sobolev inequality as goes to zero. We give similar results concerning the related problem: –u=N(N–2)up+u, u>0 on ; u=0 on , for N is larger than 4.  相似文献   

15.
M. . , . , p () (). , , .  相似文献   

16.
For n2 we consider the Stokes problem in n, -u + p=f, -divu=g, in weighted Soboiev spaces H 6 m,r , where the weights are proportional to (1+|x|). We prove the existence of weak solutions for any K, whereK is a discrete set of critical values. Furthermore, we characterize the solutions of the homogeneous problem.This research was supported by the DFG research group Equations of Hydrodynamics, Universities of Bayreuth and Paderborn.  相似文献   

17.
Summary Given a stochastic matrixP on the state spaceI an ordering for measures inI can be defined in the following way: iff(f)(f) for allf in a sufficiently rich subcone of the cone of positiveP-subharmonic functions. It is shown that, if, are probability measures with , then in theP-process (X n)n0 having as initial distribution there exists a stopping time such thatX is distributed according to. In addition, can be chosen in such a way, that for every positive subharmonicf with(f)< the submartingale (f(X n))n0 is uniformly integrable.  相似文献   

18.
We prove by elementary means a regularity theorem for quasi-isometries of T x n (where T denotes an infinite tree), and of many other metric spaces with similar combinatorial properties, e.g. Cayley graphs of Baumslag–Solitar groups. For quasi-isometries of T x n, it states that the image of {x} x n (xT) is uniformly close to {y} x n for some yT, and there is a well-defined surjection . Even stronger, the image of a quasi-isometric embedding of n+1 in T x n is close to (a geodesic in T)T)x n.  相似文献   

19.
    
( « . III») - B p,q g(x) F p,q g(x) ( ) R n . --, . : , , , .  相似文献   

20.
The finite nth polylogarithm li n (z) /p(z) is defined as k=1 p–1 z k /k n . We state and prove the following theorem. Let Li k : p p be the p-adic polylogarithms defined by Coleman. Then a certain linear combination F n of products of polylogarithms and logarithms, with coefficients which are independent of p, has the property that p 1–n DF n (z) reduces modulo p>n+1 to li n–1((z)), where D is the Cathelineau operator z(1–z)d/dz and is the inverse of the p-power map. A slightly modified version of this theorem was conjectured by Kontsevich. This theorem is used by Elbaz-Vincent and Gangl to deduce functional equations of finite polylogarithms from those of complex polylogarithms.  相似文献   

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