共查询到20条相似文献,搜索用时 31 毫秒
1.
Olivier Poisson 《Mathematical Methods in the Applied Sciences》1999,22(9):773-790
Let 𝒩(μ) be the counting function of the eigenvalues associated with the self‐adjoint operator −∇(ρ(x, z)∇·) in the domain Ω = ℝ × ]0, h[, h > 0, with Neuman or Dirichlet conditions at z = 0, h. If ρ = 1 in the exterior of a bounded rectangular region 𝒪, that is, for ∣x∣ large, then 𝒩(μ) is known to be sublinear: the proof consists in the spectral analysis of a quadratic form obtained from a Green formula for −∇(ρ(x, z)∇·) on 𝒪. In our case, the medium is multistratified: the function ρ(x, z) satisfies ρ(x, z) = ρ(z) for ∣x∣ large. Since the direct use of the previous proof fails, we modify the quadratic form and obtain the estimate N(μ) ⩽ Cμ3/2. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
2.
3.
We prove the existence of smooth positive potentials V(t, x), periodic in time and with compact support in x, for which the Cauchy problem for the wave equation utt ? Δxu + V(t, x)u = 0 has solutions with exponentially growing global and local energy. Moreover, we show that there are resonances, z ∈ ?, |z| > 1, associated to V(t, x). © 2008 Wiley Periodicals, Inc. 相似文献
4.
James Renegar 《Mathematical Programming》1985,32(3):319-336
This work examines the computational complexity of a homotopy algorithm in approximating all roots of a complex polynomialf. It is shown that, probabilistically, monotonic convergence to each of the roots occurs after a determined number of steps. Moreover, in all subsequent steps, each rootz is approximated by a complex numberx, where ifx
0 =x, x
j
=x
j–1 –f(x
j–1)/f(x
j–1),j = 1, 2,, then |x
j
–z| < (1/|x
0 –z|)|x
j–1–z|2. 相似文献
5.
For an analytic function f (z) on the unit disk |z| < 1 with f (0) = f′(0) − 1 = 0 and f (z) ≠ 0, 0 < |z| < 1, we consider the power deformation f c (z) = z(f (z)/z) c for a complex number c. We determine those values c for which the operator maps a specified class of univalent functions into the class of univalent functions. A little surprisingly, we will see that the set is described by the variability region of the quantity zf′(z)/ f (z), |z| < 1, for most of the classes that we consider in the present paper. As an unexpected by-product, we show boundedness of strongly spirallike functions. 相似文献
6.
Jie Ming Wang 《数学学报(英文版)》2009,25(5):741-758
The stochastic comparison and preservation of positive correlations for Levy-type processes on R^d are studied under the condition that Levy measure v satisfies f{0〈|z|≤1)|z||v(x, dz) - v(x, d(-z))| 〈 ∞, x∈ R^d, while the sufficient conditions and necessary ones for them are obtained. In some cases the conditions for stochastic comparison are not only sufficient but also necessary. 相似文献
7.
Asymptotic properties of orthogonal Laurent (L-) polynomialsV n (z), associated with log-normal distributions, are derived by constructive methods. It is shown that the sequences {V 2n (z)} and {V 2n+1 (z)} converge separately (asn→∞) to functionsV (0) (z) andV (1) (z), respectively, both holomorphic in 0<|z|<∞. Explicit Laurent series expansions are obtained, from which it follows that each limit function has essential, isolated singularities atz=0 andz=∞. 相似文献
8.
Rajendra M. Pawale 《组合设计杂志》2007,15(1):49-60
The following results for proper quasi‐symmetric designs with non‐zero intersection numbers x,y and λ > 1 are proved.
- (1) Let D be a quasi‐symmetric design with z = y ? x and v ≥ 2k. If x ≥ 1 + z + z3 then λ < x + 1 + z + z3.
- (2) Let D be a quasi‐symmetric design with intersection numbers x, y and y ? x = 1. Then D is a design with parameters v = (1 + m) (2 + m)/2, b = (2 + m) (3 + m)/2, r = m + 3, k = m + 1, λ = 2, x = 1, y = 2 and m = 2,3,… or complement of one of these design or D is a design with parameters v = 5, b = 10, r = 6, k = 3, λ = 3, and x = 1, y = 2.
- (3) Let D be a triangle free quasi‐symmetric design with z = y ? x and v ≥ 2k, then x ≤ z + z2.
- (4) For fixed z ≥ 1 there exist finitely many triangle free quasi‐symmetric designs non‐zero intersection numbers x, y = x + z.
- (5) There do not exist triangle free quasi‐symmetric designs with non‐zero intersection numbers x, y = x + 2.
9.
Froim Marcus 《Israel Journal of Mathematics》1975,22(3-4):185-202
It is shown that Fubini’s theorem concerning the converse of Bianchi’s permutability theorem, published in 1940 in Annals of Mathematics, is true in general. There is a single exceptional case which is related to a theorem of H. Jonas, published in 1937 in Mathematische Annalen, concerningW congruences in which the necessary conditions of Fubini’s Theorem are not also sufficient. For this reason we reformulate Fubini’s theorem as follows: Letx(u, v),y(u, v) be two surfaces with a one-to-one mapping between them and such that the nets of curvesu, v on these surfaces are not osculating-related (following Jonas). If each of the three surfacesz(u, v),t(u, v),η(u, v) is a congruence transform of every one of the surfacesx(u, v),y(u, v), then the congruences generated by the lines (x, z +pt), (y, z +ρt),ρ=const are allW congruences. 相似文献
10.
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F n (f)}, where F n (x) = F(x) * δ n (x) and {δ n (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x ?s ln m |x| and x r is proved to exist and be equal to r m x ?rs ln m |x| for r, s, m = 2, 3…. 相似文献
11.
Mitsuhiro Nakao 《Journal of Differential Equations》2006,227(1):204-229
We show the existence, size and some absorbing properties of global attractors of the nonlinear wave equations with nonlinear dissipations like ρ(x,ut)=a(x)r|ut|ut. 相似文献
12.
Allen Weitsman 《Israel Journal of Mathematics》2001,124(1):327-331
Letw=f(z) be a univalent harmonic mapping of the annulus {ρ≤|z|≤1} onto the annulus {σ≤|w|≤1}. It is shown thatσ≤1/(1+(ρ
2/2)(logρ)2). 相似文献
13.
V. G. Petrosyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(6):305-312
The paper studies the rotation of the image of the sphere |z| = r under mappings by functions of the form w(z) − p(z), where w(z) is an entire meromorphic function, while p(z) is a polynomial. In terms of rotations, some analogs of the Nevanlinna Second Fundamental Theorem are established. 相似文献
14.
O.J. Boxma 《European Journal of Operational Research》1984,16(2):246-256
For the M/G/1 queue we study the joint distribution of the number of customers x present immediately before an arrival epoch and of the residual service time ζ of the customer in service at this epoch. The correlation coefficient ? (x, ζ) is shown to be positive (negative) when the service time distribution is DFR (IFR). The result for the joint distribution of x and ζ leads to the joint distribution of x, of the sojourn time s of the arriving customer and of the number of customers z left behind by this customer at his departure. ?(x, s), ?(z, s) and ?(x, z) are shown to be positive; ?(x, s) and ?(z, s) are compared in some detail.Subsequently the M/G/1 queue with finite capacity is considered; the joint distributions of x and ζ and of x and s are derived. These results may be used to study the cycle time distribution in a two-stage cyclic queue. 相似文献
15.
Alfred S. Carasso 《Mathematical Methods in the Applied Sciences》2013,36(3):249-261
Identifying sources of ground water pollution and deblurring astronomical galaxy images are two important applications generating growing interest in the numerical computation of parabolic equations backward in time. However, while backward uniqueness typically prevails in parabolic equations, the precise data needed for the existence of a particular backward solution is seldom available. This paper discusses previously unexplored non‐uniqueness issues, originating from trying to reconstruct a particular solution from imprecise data. Explicit 1D examples of linear and nonlinear parabolic equations are presented, in which there is strong computational evidence for the existence of distinct solutions wred(x,t) and wgreen(x,t), on 0 ≤ t ≤ 1. These solutions have the property that the traces wred(x,1) and wgreen(x,1) at time t = 1 are close enough to be visually indistinguishable, while the corresponding initial values wred(x,0) and wgreen(x,0) are vastly different, well‐behaved, physically plausible functions, with comparable L2 norms. This implies effective non‐uniqueness in the recovery of wred(x,0) from approximate data for wred(x,1). In all these examples, the Van Cittert iterative procedure is used as a tool to discover unsuspected, valid, additional solutions wgreen(x,0). This methodology can generate numerous other examples and indicates that multidimensional problems are likely to be a rich source of striking non‐uniqueness phenomena. Published 2012. This article is a US Government work and is in the public domain in the USA. 相似文献
16.
In this paper we prove a quantitative form of Landis’ conjecture in the plane. Precisely, let W(z) be a measurable real vector-valued function and V(z) ≥0 be a real measurable scalar function, satisfying ‖W‖ L ∞(R 2) ≤ 1 and ‖V‖ L ∞(R 2) ≤ 1. Let u be a real solution of Δu ? ?(Wu) ? Vu = 0 in R 2. Assume that u(0) = 1 and |u(z)| ≤exp (C 0|z|). Then u satisfies inf |z 0| =R sup |z?z 0| <1|u(z)| ≥exp (?CRlog R), where C depends on C 0. In addition to the case of the whole plane, we also establish a quantitative form of Landis’ conjecture defined in an exterior domain. 相似文献
17.
18.
This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex
plane of the form w(z) = exp(−|z|2 + Uμ(z)), where Uμ(z) is the logarithmic potential of a compactly supported positive measure μ. The equilibrium measure of the corresponding weighted energy problem is shown to be supported on subharmonic generalized
quadrature domains for a large class of perturbing potentials Uμ(z). It is also shown that the 2 × 2 matrix d-bar problem for orthogonal polynomials with respect to such weights is well-defined
and has a unique solution given explicitly by Cauchy transforms. Numerical evidence is presented supporting a conjectured
relation between the asymptotic distribution of the zeroes of the orthogonal polynomials in a semi-classical scaling limit
and the Schwarz function of the curve bounding the support of the equilibrium measure, extending the previously studied case
of harmonic polynomial perturbations with weights w(z) supported on a compact domain.
Submitted: July 25, 2008. Accepted: October 1, 2008.
Work supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds de recherche
sur la nature et les technologies du Québec (FQRNT). 相似文献
19.
C. H. Wilcox 《Mathematical Methods in the Applied Sciences》1983,5(1):276-291
Samples of biological tissue are modelled as inhomogeneous fluids with density ?(X) and sound speed c(x) at point x. The samples are contained in the sphere |x| ? δ and it is assumed that ?(x) ? ?0 = 1 and c(x) ? c0 = 1 for |x| ? δ, and |γn(x)| ? 1 and |?γ?(x)| ? 1 where γ?(x) = ?(x) ? 1 and γn(x) = c?2(x) ? 1. The samples are insonified by plane pulses s(x · θ0 – t) where x = |θ0| = 1 and the scattered pulse is shown to have the form |x|?1 es(|x| – t, θ, θ0) in the far field, where x = |x| θ. The response es(τ, θ, θ0) is measurable. The goal of the work is to construct the sample parameters γn and γ? from es(τ, θ, θ0) for suitable choiches of s, θ and θ0. In the limiting case of constant density: γ?(x)? 0 it is shown that Where δ represents the Dirac δ and S2 is the unit sphere |θ| = 1. Analogous formulas, based on two sets of measurements, are derived for the case of variable c(x) and ?(x). 相似文献
20.
Teodora-Liliana Dinu 《Journal of Mathematical Analysis and Applications》2006,322(1):382-392
We study the nonlinear elliptic problem −Δu=ρ(x)f(u) in RN (N?3), lim|x|→∞u(x)=?, where ??0 is a real number, ρ(x) is a nonnegative potential belonging to a certain Kato class, and f(u) has a sublinear growth. We distinguish the cases ?>0 and ?=0 and prove existence and uniqueness results if the potential ρ(x) decays fast enough at infinity. Our arguments rely on comparison techniques and on a theorem of Brezis and Oswald for sublinear elliptic equations. 相似文献