共查询到20条相似文献,搜索用时 31 毫秒
1.
Andr Goldman Pierre Calka 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2003,39(6):90-1082
Denote by (t)=∑n1e−λnt, t>0, the spectral function related to the Dirichlet Laplacian for the typical cell
of a standard Poisson–Voronoi tessellation in
. We show that the expectation E(t), t>0, is a functional of the convex hull of a standard d-dimensional Brownian bridge. This enables us to study the asymptotic behaviour of E(t), when t→0+,+∞. In particular, we prove that the law of the first eigenvalue λ1 of
satisfies the asymptotic relation lnP{λ1t}−2dωdj(d−2)/2d·t−d/2 when t→0+, where ωd and j(d−2)/2 are respectively the Lebesgue measure of the unit ball in
and the first zero of the Bessel function J(d−2)/2. 相似文献
2.
Yang Wang 《Journal of Approximation Theory》2001,113(2):207
We consider the two-scale refinement equation f(x)=∑Nn=0 cnf(2x−n) with ∑n c2n=∑n c2n+1=1 where c0, cN≠0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 0<c0, cN<1 and the greatest common divisor of S={n: cn>0} is 1. We prove the conjecture for a large class of refinement equations. 相似文献
3.
Among all integration rules with n points, it is well-known that n-point Gauss–Legendre quadrature rule∫−11f(x) dx∑i=1nwif(xi)has the highest possible precision degree and is analytically exact for polynomials of degree at most 2n−1, where nodes xi are zeros of Legendre polynomial Pn(x), and wi's are corresponding weights.In this paper we are going to estimate numerical values of nodes xi and weights wi so that the absolute error of introduced quadrature rule is less than a preassigned tolerance ε0, say ε0=10−8, for monomial functionsf(x)=xj, j=0,1,…,2n+1.(Two monomials more than precision degree of Gauss–Legendre quadrature rules.) We also consider some conditions under which the new rules act, numerically, more accurate than the corresponding Gauss–Legendre rules. Some examples are given to show the numerical superiority of presented rules. 相似文献
4.
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)1 be a measurable function defined on a domain ΩRn, n2, and such that exp(βK(x))Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|nK(x)J(x,f) for a.e. xΩ and such that the Jacobian determinant J(x,f) is locally in L1 log−c1(n)βL. Then automatically J(x,f) is locally in L1 logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion. Namely, we obtain novel results on the size of removable singularities for bounded mappings of finite distortion, and on the area distortion under this class of mappings. 相似文献
5.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1994,46(3):290-303
For the equationL
0
x(t)+L
1x(t)+...+L
n
x
(n)(t)=O, whereL
k,k=0,1,...,n, are operators acting in a Banach space, we establish criteria for an arbitrary solutionx(t) to be zero provided that the following conditions are satisfied:x
(1–1) (a)=0, 1=1, ..., p, andx
(1–1) (b)=0, 1=1,...,q, for - <a< b< (the case of a finite segment) orx
(1–1) (a)=0, 1=1,...,p, under the assumption that a solutionx(t) is summable on the semiaxista with its firstn derivatives.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 279–292, March, 1994.This research was supported by the Ukrainian State Committee on Science and Technology. 相似文献
6.
We consider functions represented by series ∑g G cgψ(g − 1(x)) of wavelet-type, where G is a group generated by affine functions L1,…,Ln and ψ is piecewise affine. By means of those functions we characterize the class of self-affine fractal functions, previously studied by Barnsley et al. We compute their global and local Hölder exponents and investigate points of non-differentiability. Wavelet-representations for various continuous nowhere differentiable and singular functions are presented. Another application is the construction of functions with prescribed local Hölder exponents at each point. 相似文献
7.
Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables 总被引:1,自引:0,他引:1
Consider Z+d (d2)—the positive d-dimensional lattice points with partial ordering , let {Xk,kZ+d} be i.i.d. random variables with mean 0, and set Sn=∑knXk, nZ+d. We establish precise asymptotics for ∑n|n|r/p−2P(|Sn||n|1/p), and for
, (0δ1) as 0, and for
as
. 相似文献
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8.
Summability of spherical h-harmonic expansions with respect to the weight function ∏j=1d |xj|2κj (κj0) on the unit sphere Sd−1 is studied. The main result characterizes the critical index of summability of the Cesàro (C,δ) means of the h-harmonic expansion; it is proved that the (C,δ) means of any continuous function converge uniformly in the norm of C(Sd−1) if and only if δ>(d−2)/2+∑j=1d κj−min1jd κj. Moreover, it is shown that for each point not on the great circles defined by the intersection of the coordinate planes and Sd−1, the (C,δ) means of the h-harmonic expansion of a continuous function f converges pointwisely to f if δ>(d−2)/2. Similar results are established for the orthogonal expansions with respect to the weight functions ∏j=1d |xj|2κj(1−|x|2)μ−1/2 on the unit ball Bd and ∏j=1d xjκj−1/2(1−|x|1)μ−1/2 on the simplex Td. As a related result, the Cesàro summability of the generalized Gegenbauer expansions associated to the weight function |t|2μ(1−t2)λ−1/2 on [−1,1] is studied, which is of interest in itself. 相似文献
9.
Hans-Dietrich O. F. Gronau 《Journal of Combinatorial Theory, Series A》1981,30(3):298-316
Let nc,d(r, k) denote the maximal cardinality of Sperner families
(i.e., XY for all X, Y ε
) on an r-element set satisfying c X d for all X ε
and in which no k sets have an empty intersection. nc,d(r, k) was determined by Frankl (J. Combin. Theory Ser. A 20 (1976), 1–11) if c r/k, and, if c = 0 and d = r, by Frankl and the author (J. Combin. Theory Ser. A 28 (1980), 54–63; Acta Cybernet. 4 (1978), 213–220 for all r and k with exception of 60 values of r if k = 3. In this paper we solve the problem of determination of nc,d(r, 3) in nearly all unknown cases. In particular, we obtain n0,r(r, 3) for 33 of the exceptional cases. 相似文献
10.
Let τ=σ+ν be a point mass perturbation of a classical moment functional σ by a distribution ν with finite support. We find necessary conditions for the polynomials {Qn(x)}∞n=0, orthogonal relative to τ, to be a Bochner–Krall orthogonal polynomial system (BKOPS); that is, {Qn(x)}∞n=0 are eigenfunctions of a finite order linear differential operator of spectral type with polynomial coefficients: LN[y](x)=∑Ni=1 ℓi(x) y(i)(x)=λny(x). In particular, when ν is of order 0 as a distribution, we find necessary and sufficient conditions for {Qn(x)}∞n=0 to be a BKOPS, which strongly support and clarify Magnus' conjecture which states that any BKOPS must be orthogonal relative to a classical moment functional plus one or two point masses at the end point(s) of the interval of orthogonality. This result explains not only why the Bessel-type orthogonal polynomials (found by Hendriksen) cannot be a BKOPS but also explains the phenomena for infinite-order differential equations (found by J. Koekoek and R. Koekoek), which have the generalized Jacobi polynomials and the generalized Laguerre polynomials as eigenfunctions. 相似文献
11.
Christian Elbert 《Journal of Approximation Theory》2001,109(2):708
For the horizontal generating functions Pn(z)=∑nk=1 S(n, k) zk of the Stirling numbers of the second kind, strong asymptotics are established, as n→∞. By using the saddle point method for Qn(z)=Pn(nz) there are two main results: an oscillating asymptotic for z(−e, 0) and a uniform asymptotic on every compact subset of
\[−e, 0]. Finally, an Airy asymptotic in the neighborhood of −e is deduced. 相似文献
12.
Stanis
aw Lewanowicz 《Journal of Computational and Applied Mathematics》2003,150(2):193-327
Let {pk(x; q)} be any system of the q-classical orthogonal polynomials, and let be the corresponding weight function, satisfying the q-difference equation Dq(σ)=τ, where σ and τ are polynomials of degree at most 2 and exactly 1, respectively. Further, let {pk(1)(x;q)} be associated polynomials of the polynomials {pk(x; q)}. Explicit forms of the coefficients bn,k and cn,k in the expansions are given in terms of basic hypergeometric functions. Here k(x) equals xk if σ+(0)=0, or (x;q)k if σ+(1)=0, where σ+(x)σ(x)+(q−1)xτ(x). The most important representatives of those two classes are the families of little q-Jacobi and big q-Jacobi polynomials, respectively.Writing the second-order nonhomogeneous q-difference equation satisfied by pn−1(1)(x;q) in a special form, recurrence relations (in k) for bn,k and cn,k are obtained in terms of σ and τ. 相似文献
13.
Persistence, contractivity and global stability in logistic equations with piecewise constant delays
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2002,270(2):1532-635
We establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium N*=1/(a+∑i=0mbi) of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, ∑i=0mbi>0, bi0, i=0,1,2,…,m, and a+∑i=0mbi>0. These new conditions depend on a,b0 and ∑i=1mbi, and hence these are other type conditions than those given by So and Yu (Hokkaido Math. J. 24 (1995) 269–286) and others. In particular, in the case m=0 and r(t)≡r>0, we offer necessary and sufficient conditions for the persistence and contractivity of solutions. We also investigate the following differential equation with nonlinear delay terms: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, 1−ax−g(x,x,…,x)=0 has a unique solution x*>0 and g(x0,x1,…,xm)C1[(0,+∞)×(0,+∞)××(0,+∞)]. 相似文献
14.
Gil Kalai 《Discrete and Computational Geometry》1988,3(1):1-14
Lets(d, n) be the number of triangulations withn labeled vertices ofS
d–1, the (d–1)-dimensional sphere. We extend a construction of Billera and Lee to obtain a large family of triangulated spheres. Our construction shows that logs(d, n)C
1(d)n
[(d–1)/2], while the known upper bound is logs(d, n)C
2(d)n
[d/2] logn.Letc(d, n) be the number of combinatorial types of simpliciald-polytopes withn labeled vertices. (Clearly,c(d, n)s(d, n).) Goodman and Pollack have recently proved the upper bound: logc(d, n)d(d+1)n logn. Combining this upper bound forc(d, n) with our lower bounds fors(d, n), we obtain, for everyd5, that lim
n(c(d, n)/s(d, n))=0. The cased=4 is left open. (Steinitz's fundamental theorem asserts thats(3,n)=c(3,n), for everyn.) We also prove that, for everyb4, lim
d(c(d, d+b)/s(d, d+b))=0. (Mani proved thats(d, d+3)=c(d, d+3), for everyd.)Lets(n) be the number of triangulated spheres withn labeled vertices. We prove that logs(n)=20.69424n(1+o(1)). The same asymptotic formula describes the number of triangulated manifolds withn labeled vertices.Research done, in part, while the author visited the mathematics research center at AT&T Bell Laboratories. 相似文献
15.
By using Krasnoselskii's fixed point theorem and upper and lower solutions method, we find some sets of positive values λ determining that there exist positive T-periodic solutions to the higher-dimensional functional difference equations of the form where A(n)=diag[a1(n),a2(n),…,am(n)], h(n)=diag[h1(n),h2(n),…,hm(n)], aj,hj :Z→R+, τ :Z→Z are T -periodic, j=1,2,…,m, T1, λ>0, x :Z→Rm, f :R+m→R+m, where R+m={(x1,…,xm)TRm, xj0, j=1,2,…,m}, R+={xR, x>0}. 相似文献
16.
Li-Xin Zhang 《Journal of multivariate analysis》2001,78(2):27
Let {Xn, n1} be a sequence of stationary negatively associated random variables, Sj(l)=∑li=1 Xj+i, Sn=∑ni=1 Xi. Suppose that f(x) is a real function. Under some suitable conditions, the central limit theorem and the weak convergence for sums
are investigated. Applications to limiting distributions of estimators of Var Sn are also discussed. 相似文献
17.
The predictive ratio is considered as a measure of spread for the predictive distribution. It is shown that, in the exponential families, ordering according to the predictive ratio is equivalent to ordering according to the posterior covariance matrix of the parameters. This result generalizes an inequality due to Chaloner and Duncan who consider the predictive ratio for a beta-binomial distribution and compare it with a predictive ratio for the binomial distribution with a degenerate prior. The predictive ratio at x1 and x2 is defined to be pg(x1)pg(x2)/[pg(
)]2 = hg(x1, x2), where pg(x1) = ∫ ƒ(x1θ) g(θ) dθ is the predictive distribution of x1 with respect to the prior g. We prove that hg(x1, x2) ≥ hg*(x1, x2) for all x1 and x2 if ƒ(xθ) is in the natural exponential family and Covgx(θ) ≥ Covg*x(θ) in the Loewner sense, for all x on a straight line from x1 to x2. We then restrict the class of prior distributions to the conjugate class and ask whether the posterior covariance inequality obtains if g and g* differ in that the “sample size” 相似文献
18.
Marco Buratti 《Journal of Combinatorial Theory, Series A》2000,90(2):353
A Z-cyclic triplewhist tournament for 4n+1 players, or briefly a TWh(4n+1), is equivalent to a n-set {(ai, bi, ci, di) | i=1, …, n} of quadruples partitioning Z4n+1−{0} with the property that ni=1 {±(ai−ci), ±(bi−di)}=ni=1 {±(ai−bi), ±(ci−di)}=ni=1 {±(ai−di), ±(bi−ci)}=Z4n+1−{0}. The existence problem for Z-cyclic TWh(p)'s with p a prime has been solved for p1 (mod 16). I. Anderson et al. (1995, Discrete Math.138, 31–41) treated the case of p≡5 (mod 8) while Y. S. Liaw (1996, J. Combin. Des.4, 219–233) and G. McNay (1996, Utilitas Math.49, 191–201) treated the case of p≡9 (mod 16). In this paper, besides giving easier proofs of these authors' results, we solve the problem also for primes p≡1 (mod 16). The final result is the existence of a Z-cyclic TWh(v) for any v whose prime factors are all≡1 (mod 4) and distinct from 5, 13, and 17. 相似文献
19.
We investigate some geometrical aspects of the discriminant functions of the kindfp(x)=∑pk=1 ckτ(a′kx) for suitable constantsak, ckwhereτis a sigmoidal transformation. This function is realized by a multilayer perceptron with one hidden layer. These results are applied in the analysis of the discriminating power offp. In particular, we prove that the class of finite populationsΩ1andΩ2that can be distinguished byfpis monotonically increasing inpand we give a minimal sufficientpleading to a complete separation betweenΩ1andΩ2. 相似文献
20.
This paper is concerned with an iterative functional differential equation
c1x(z)+c2x′(z)+c3x″(z)=x(az+bx′(z))