共查询到20条相似文献,搜索用时 15 毫秒
1.
Luc Devroye 《Journal of multivariate analysis》1982,12(1):72-79
If X1,…,Xn are independent identically distributed Rd-valued random vectors with probability measure μ and empirical probability measure μn, and if is a subset of the Borel sets on Rd, then we show that P{supA∈|μn(A)?μ(A)|≥ε} ≤ cs(, n2)e?2n∈2, where c is an explicitly given constant, and s(, n) is the maximum over all (x1,…,xn) ∈ Rdn of the number of different sets in {{x1…,xn}∩A|A ∈}. The bound strengthens a result due to Vapnik and Chervonenkis. 相似文献
2.
M. Delgado 《European Journal of Operational Research》1983,13(2):165-172
A resolution method for multiobjective problems, based on a maximin criterion, is developed. Given the multiobjective problem Max{Ax=b,x?0}{cix; i = 1,2,…,k}, we suppose that the decisor can construct, for each i, a function hi: → (or hi:n→-), such that hi(ci,x) is his satisfaction degree produced by the value cix, and we substitute the original problem by Max{Ax=b,x?0~mini{hi(cix)}. We analize its resolution and basic properties. 相似文献
3.
Fopke Klok 《Journal of Differential Equations》1984,55(1):101-134
A real-valued function L on the tangent bundle of n gives rise to variational problems as follows: for two points x0, x1 in n and a time interval [0, T] to determine a curve γ: [O,T] → n, connecting x0 with x1 which minimizes ∫0TL(γ(t), gg(t)) dt. We consider the associated Hamiltonian vectorfield on the cotangent bundle. If L is not convex on each fibre then the corresponding Hamiltonian vectorfield is not continuous. For homogeneous L and n = 2 restriction to an energy level gives an essentially three-dimensional vectorfield. In this case we list the possible discontinuities for generic L. Then we observe that there exits an open class of such variational problems, which admit no minimizing solution. 相似文献
4.
Let φ and ψ be any norms on m and n respectively. We study a subgradient method for computing the associated bound norm Sφψ(A) = sup{φ(Ax), ψ(x)?1} (a nonconvex optimization problem). It is proved that homodual method converges when one of the norms φ and ψ is polyhedral. 相似文献
5.
B.G. Pittel 《Stochastic Processes and their Applications》1980,10(1):33-48
Let X1,X2,… be i.i.d. random variables with a continuous distribution function. Let R0=0, Rk=min{j>Rk?1, such that Xj>Xj+1}, k?1. We prove that all finite-dimensional distributions of a process , converge to those of the standard Brownian motion. 相似文献
6.
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
7.
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
8.
Donald C. Solmon 《Journal of Mathematical Analysis and Applications》1979,71(2):351-358
Let Π be a k-dimensional subspace of Rn, n ? 2, and write x = (x′, x″) with x′ in Π and x″ in the orthogonal complement Π⊥. The k-plane transform of a measurable function ? in the direction Π at the point x″ is defined by . In this article certain a priori inequalities are established which show in particular that if , , then ? is integrable over almost every translate of almost every k-space. Mapping properties of the k-plane transform between the spaces Lp(Rn), p ? 2, and certain Lebesgue spaces with mixed norm on a vector bundle over the Grassmann manifold of k-spaces in Rn are also obtained. 相似文献
9.
Kai Wang 《Journal of Number Theory》1984,18(3):306-312
For a positive integer m, let and let n = |A|. For an integer x, let R(x) be the least positive residue of x modulo m and if (x, m) = 1, let x′ be the inverse of x modulo m. If m is odd, then |R(ab′)|a,b∈A = ?21?n(∏χ(Σa = 1m ? 1aχ(a))), where χ runs over all the odd Dirichlet characters modulo m. 相似文献
10.
The probability measure of X = (x0,…, xr), where x0,…, xr are independent isotropic random points in n (1 ≤ r ≤ n ? 1) with absolutely continuous distributions is, for a certain class of distributions of X, expressed as a product measure involving as factors the joint probability measure of (ω, ?), the probability measure of p, and the probability measure of . Here ω is the r-subspace parallel to the r-flat η determined by X, ? is a unit vector in ω⊥ with ‘initial’ point at the origin [ω⊥ is the (n ? r)-subspace orthocomplementary to ω], p is the norm of the vector z from the origin to the orthogonal projection of the origin on η, and , where α is a scale factor determined by p. The probability measure for ω is the unique probability measure on the Grassmann manifold of r-subspaces in n invariant under the group of rotations in n, while the conditional probability measure of ? given ω is uniform on the boundary of the unit (n ? r)-ball in ω⊥ with centre at the origin. The decomposition allows the evaluation of the moments, for a suitable class of distributions of X, of the r-volume of the simplicial convex hull of {x0,…, xr} for 1 ≤ r ≤ n. 相似文献
11.
Jorge L.C Sanz Thomas S Huang 《Journal of Mathematical Analysis and Applications》1984,104(1):302-308
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function f(z1…,zn), zi ? , i=1, …, n, is uniquely determined from the magnitude of f(x1…,xn): | f(x1…,xn)|, xi ? , i=1,…, n, except for (1) linear shifts: i(α1z1+…+αn2n+β), β, αi?, i=1,…, n; and (2) conjugation: . 相似文献
12.
We investigate the asymptotic properties of posterior distributions when the model is misspecified, i.e. it is contemplated that the observations x1,…,xn might be drawn from a density in a family where , while the actual distribution of the observations may not correspond to any of the densities hσ. A concentration property around a fixed value of the parameter is obtained as well as concentration properties around the maximum likelihood estimate. To cite this article: C. Abraham, B. Cadre, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 495–498. 相似文献
13.
K. Inoue 《Journal of multivariate analysis》1976,6(2):295-308
We consider two Gaussian measures P1 and P2 on (C(G), ) with zero expectations and covariance functions R1(x, y) and R2(x, y) respectively, where Rν(x, y) is the Green's function of the Dirichlet problem for some uniformly strongly elliptic differential operator A(ν) of order , on a bounded domain G in d (ν = 1, 2). It is shown that if the order of A(2) ? A(1) is at most , then P1 and P2 are equivalent, while if the order is greater than , then P1 and P2 are not always equivalent. 相似文献
14.
Following the lines of [13] we introduce the classes of mixed smoothness αp(Rn), αp(Zn) for a multi-index α = (α1,…, αn). Such classes are naturally tied up with the study of semi-elliptic differential and difference equations.Besides a brief presentation of such classes, we concentrate our research on the study of mixed homogeneous multipliers with homogeneity β = (β1, …, βn) and their preservation of mixed homogeneous Hölder classes α∞, for a different multi-index α.In the last paragraph we apply the results to produce various improvements of the classical Schauder's estimates, for differential and difference equations, in the parabolic and elliptic case. 相似文献
15.
Béla Uhrin 《Journal of Number Theory》1981,13(2):192-209
Given a lattice and a bounded function g(x), x ∈ Rn, vanishing outside of a bounded set, the functions ?(x)maxu∈Λg(u +x), ?(x)?Σu∈Λ g(u +x), and ?+(x)?Σu∈Λ maxv∈Λ min {g(v + x); g(u + v + x)} are defined and periodic mod Λ on Rn. In the paper we prove that ?(x) + ?+(x) ? 2?(x) ≥ ?(x) + h?+(x) ? 2?(x) holds for all x ∈ Rn, where h(x) is any “truncation” of g by a constant c ≥ 0, i.e., any function of the form h(x)?g(x) if g(x) ≤ c and h(x)?c if g(x) > c. This inequality easily implies some known estimations in the geometry of numbers due to Rado [1] and Cassels [2]. Moreover, some sharper and more general results are also derived from it. In the paper another inequality of a similar type is also proved. 相似文献
16.
Susanne M. Kuen Krzysztof P. Rybakowski 《Journal of Mathematical Analysis and Applications》1985,112(2):378-390
Let b: [?1, 0] → be a nondecreasing, strictly convex C2-function with b(? 1) = 0, and let g: n → n be a locally Lipschitzian mapping, which is the gradient of a function G: n → . Consider the following vector-valued integro-differential equation of the Levin-Nohel type . (E) This equation is used in applications to model various viscoelastic phenomena. By LaSalle's invariance principle, every bounded solution x(t) goes to a connected set of zeros of g, as time t goes to infinity. It is the purpose of this paper to give several geometric criteria assuring the boundedness of solutions of (E) or some of its components. 相似文献
17.
Allan M Krall 《Journal of Differential Equations》1977,24(2):253-267
This article discusses linear differential boundary systems, which include nth-order differential boundary relations as a special case, in np[0,1] × np[0,1], 1 ? p < ∞. The adjoint relation in nq[0,1] × nq[0,1], , is derived. Green's formula is also found. Self-adjoint relations are found in n2[0,1] × n2[0,1], and their connection with Coddington's extensions of symmetric operators on subspaces of np[0,1] × n2[0,1] is established. 相似文献
18.
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
19.
Detlef Müller 《Journal of Functional Analysis》1982,47(2):247-280
Let F1(Rn) denote the Fourier algebra on n, and (n) the space of test functions on n. A closed subset E of n is said to be of spectral synthesis if the only closed ideal J in F1(Rn) which has E as its hull is the ideal . We consider sufficiently regular compact subsets of smooth submanifolds of n with constant relative nullity. For such sets E we give an estimate of the degree of nilpotency of the algebra , where j(E) denotes the smallest closed ideal in F1(Rn) with hull E. Especially in the case of hypersurfaces this estimate turns out to be exact. Moreover for this case we prove that k(E)∩D(Rn) is dense in k(E). Together this solves the synthesis problem for such sets. 相似文献
20.
Yasuhiro Takeuchi Norihiko Adachi 《Journal of Mathematical Analysis and Applications》1981,79(1):141-162
This paper presents sufficient conditions for the existence of a nonnegative and stable equilibrium point of a dynamical system of Volterra type, (1) , for every q = (q1,…, qn)T?Rn. Results of a nonlinear complementarity problem are applied to obtain the conditions. System (1) has a nonnegative and stable equilibrium point if (i) f(x) = (f1(x),…,fn(x))T is a continuous and differentiable M-function and it satisfies a certain surjectivity property, or (ii), f(x) is continuous and strongly monotone on R+0n. 相似文献