共查询到20条相似文献,搜索用时 46 毫秒
1.
Pierrette Cassou-Noguès 《Journal of Number Theory》1982,14(1):32-64
In this paper, we are studying Dirichlet series Z(P,ξ,s) = Σn?1rP(n)?s ξn, where P ∈ + [X1,…,Xr] and ξn = ξ1n1 … ξrnr, with ξi ∈ , such that |ξi| = 1 and ξi ≠ 1, 1 ≦ i ≦ r. We show that Z(P, ξ,·) can be continued holomorphically to the whole complex plane, and that the values Z(P, ξ, ?k) for all non negative integers, belong to the field generated over by the ξi and the coefficients of P. If, there exists a number field K, containing the ξi, 1 ≦ i ≦ r, and the coefficients of P, then we study the denominators of Z(P, ξ, ?k) and we define a -adic function Z(P, ξ,·) which is equal, on class of negative integers, to Z(P, ξ, ?k). 相似文献
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3.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1981,81(2):437-452
We show that if F, X are two locally convex spaces and are two convex functionals satisfying h(y) = ?(y, x0) (y?F) for some x0?X, then, under suitable assumptions, the computation of inf h(F) can be reduced to the computation of inf ?(H) on certain hyperplanes H of F × X. We give some applications. 相似文献
4.
Thomas I Seidman 《Journal of Differential Equations》1985,60(2):151-173
We obtain a strict coercivity estimate, (generalizing that of T. I. Seidman [J. Differential Equations 19 (1975), 242–257] in considering spatial variation) for second order elliptic operators A: u ? ?▽ · γ(·, ▽u) with γ “radial in the gradient” ?γ(·, ξ) = a(·, |ξ|)ξ for ξ ? m. The estimate is then applied to obtain existence of solutions of boundary value problems: with Dirichlet conditions. 相似文献
5.
M.Francesca Betta Friedman Brock Anna Mercaldo M.Rosaria Posteraro 《Comptes Rendus Mathematique》2002,334(6):451-456
In this paper we prove a comparison result for weak solutions to linear elliptic problems of the type where is an open set of (n?2), ?(x)=(2π)?n/2exp(?|x|2/2), aij(x) are measurable functions such that aij(x)ξiξj??(x)|ξ|2 a.e. , and f(x) is a measurable function taken in order to guarantee the existence of a solution of (1.1). We use the notion of rearrangement related to Gauss measure to compare u(x) with the solution of a problem of the same type, whose data are defined in a half-space and depend only on one variable. To cite this article: M.F. Betta et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 451–456. 相似文献
6.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献
7.
Jean François Mertens Shmuel Zamir 《Journal of Mathematical Analysis and Applications》1977,60(2):550-558
Given P and Q convex compact sets in RkandRs, respectively, and u a continuous real valued function on P × Q, we consider the following pair of dual problems: Problem I—Minimize ? so that ?: . Problem II—Maximize g so that g: P × Q → R and g ? Vexq × Cavpmin(u, g). Here Cavp is the operation of concavification of a function with respect to the variable p?P (for each fixed q?Q). Similarly, Vexq is the operation of convexification with respect to q?Q. Maximum and minimum are taken here in the partial ordering of pointwise comparison: . It is proved here that both problems have the same solution which is also the unique simultaneous solution of the following pair of functional equations: (i) . (ii) . The problem arises in game theory, but the proof here is purely analytical and makes no use of game-theoretical concepts. 相似文献
8.
Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. 相似文献
9.
B. P. Kharlamov 《Journal of Mathematical Sciences》1981,16(2):1005-1027
The product of spaces Φ × D is considered, where Φ is the set of all continuous, nondecreasing functions ?:[0,∞)→(0,∞), ?(0)=0, ?(t)→∞(t→∞), and D is the set of all right continuous functions ξ:(0,∞)→X; here X is some metric space. Two mappings are defined: the first is the projection q(?,ξ)=ξ, and the second is the change of time U(?,ξ)=ξº?. The following equivalence relation is defined on D: $$\xi _1 \sim \xi _2 \Leftrightarrow \exists _{\varphi _1 , \varphi _1 } \in \Phi :\xi _1 ^\circ \varphi _1 = \xi _2 ^\circ \varphi _2 $$ . Let? be the set of all equivalence classes, and let L be the mapping ξ4~ξ2, Lξ is called the curve corresponding to ξ. The following theorem is proved: two stochastic processes with probability measures P1 and P2 on D possess identical random curves (i.e.,P1ºL?1=P2ºL?1) if and only if there exist two changes of time (i.e., probability measures Q1 and Q2 on ?×D for which P1=Q1ºq?1, P2=Q2ºq?1 which take these two processes into a process with measure \(\tilde P\) (i.e., Q1ºu?1=Q2ºu?1,=~P) If (P x 1 )x∈X and (P x 2 )x∈X are two families of probability measures for which P x 1 ºL?1=P x 2 ºL?1?x∈X then for each x ε X the corresponding measures Q X 1 andQ X 2 can be found in the following manner. The set of regenerative times of the family \(\left( {\tilde P_x } \right)_{x \in X} \) contains all stopping times which are simultaneously regenerative times of the families (p x 1 )x∈X and (P x 2 )x∈X and possess a certain special property of first intersection. 相似文献
10.
Ronald Evans 《Journal of Number Theory》1977,9(1):61-62
Let P(X) be a homogeneous polynomial in X = (x, y), Q(X) a positive definite integral binary quadratic form, and G the group of integral automorphs of Q(X). Let A(m) = {N ∈ × : Q(N) = m}. It is shown that if ΣN∈A(m)P(N) = 0 for each m = 1, 2, 3,… then ΣU∈GP(UX) ≡ 0. 相似文献
11.
This paper presents a demonstrably convergent method of feasible directions for solving the problem min{φ(ξ)| gi(ξ)?0i=1,2,…,m}, which approximates, adaptively, both φ(x) and ▽φ(x). These approximations are necessitated by the fact that in certain problems, such as when , a precise evaluation of φ(x) and ▽φ(x) is extremely costly. The adaptive procedure progressively refines the precision of the approximations as an optimum is approached and as a result should be much more efficient than fixed precision algorithms.It is outlined how this new algorithm can be used for solving problems of the form under the assumption that Ωmξ={x|gi(x)?0, j=1,…,s} ∩n, Ωy={y|ζi(y)?0, i-1,…,t} ∩ m, with f, gj, ζi continuously differentiable, f(x, ·) concave, ζi convex for compact. 相似文献
12.
This paper deals with the class of Q-matrices, that is, the real n × n matrices M such that for every q ∈ n×1, the linear complementarity problem , , has a solution. In general, the results are of two types. First, sufficient conditions are given on a matrix M so that M ∈ Q. Second, conditions are given so that M ? Q. 相似文献
13.
Hasse Carlsson Stephen Wainger 《Journal of Mathematical Analysis and Applications》1984,100(1):316-322
Let X be a random variable on Rn, n ? 2, having a density. Assume X has a finite exponential moment and non-zero mean vector, μ. Let ν be the corresponding renewal measure, and Q a cube. We obtain an asymptotic formula for ν(x + Q) as x → ∞ which is uniform in a small cone about the mean vector. This formula depends on moments of arbitrarily high order but depends only on the first and second moments of X in a region . 相似文献
14.
B. Roth 《Journal of Functional Analysis》1975,18(4):329-337
Let [(Ω)]p be the Cartesian product of the space of real-valued infinitely differentiable functions on a connected open set Ω in n with itself p-times. The finitely generated submodules of [(Ω)]p are of the form im(F) where F: [(Ω)]q → [(Ω)]p is a p × q matrix of infinitely differentiable functions on Ω. Let . The main results of the present paper are that for Ω ? n, if the finitely generated submodule im(F) is closed in [(Ω)]p, then for every x?ω with rank(F(x)) < r there exists an r × r sub-matrix A of F such that x is a zero of finite order of det(A), and for Ω ? 1 the converse also holds. 相似文献
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David Chillingworth 《Journal of Functional Analysis》1980,35(2):251-278
Let C be a Banach space, H a Hilbert space, and let F(C,H) be the space of C∞ functions f: C × H → R having Fredholm second derivative with respect to x at each (c, x) ?C × H for which ; here we write for . Say ? is of standard type if at all critical points of ?c it is locally equivalent (as an unfolding) to a quadratic form Q plus an elementary catastrophe on the kernel of Q. It is proved that if f?F (A × B, H) satisfies a certain ‘general position’ condition, and dim B ? 5, then for most a?A the function fo?F(B,H) is of standard type. Using this it is shown that those f?F(B,H) of standard type form an open dense set in F(B,H) with the Whitney topology. Thus both results are Hilbert-space versions of Thom's theorem for catastrophes in n. 相似文献
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J. V. Brawley 《Linear algebra and its applications》1975,10(3):199-217
Let F=GF(q) denote the finite field of order q, and let . Then f(x) defines, via substitution, a function from Fn×n, the n×n matrices over F, to itself. Any function which can be represented by a polynomialf(x)?F[x] is called a scalar polynomial function on Fn×n. After first determining the number of scalar polynomial functions on Fn×n, the authors find necessary and sufficient conditions on a polynomial in order that it defines a permutation of (i) n, the diagonalizable matrices in Fn×n, (ii)n, the matrices in Fn×n all of whose roots are in F, and (iii) the matric ring Fn×n itself. The results for (i) and (ii) are valid for an arbitrary field F. 相似文献
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Charles R. Baker 《Journal of Mathematical Analysis and Applications》1979,69(1):115-123
Let () and be probability spaces, with measurable map. Define μXY on β × by μXY(A) = μX ? μN{(x, y): (x, f(x, y)) ?A}, and let μY = (μX ? μN)of?1. An expression is determined for computing the Shannon information in the measure μXY. This expression is used to compute the information for the non-linear additive Gaussian channel, and can be used to solve the channel capacity problem. 相似文献