共查询到20条相似文献,搜索用时 640 毫秒
1.
V. M. Babich 《Journal of Mathematical Sciences》1996,79(4):1166-1168
The equation for SH-waves is considered for the following parameters μ and ρ: μ=a(x)·b(y), ρ=a(x)b(y)(c(x)+d(y)) (a,b,c,d
are known functions). For such μ and ρ the variables in this equation can be separated. An explicit solution of the problem
of the interaction of a whispering gallery wave with a vertical interface of two media is obtained. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 12–16.
Translated by N. S. Zabavnikova. 相似文献
2.
Angelo Miele 《Journal of Optimization Theory and Applications》1967,1(1):70-82
This paper considers the minimization of the product of the powers ofn integrals, each of which depends on a functiony(x) and its derivative
. The necessary conditions for the extremum are derived within the frame of the Mayer-Bolza formulation of the calculus of variations, and it is shown that the extremal arc is governed by a second-order differential equation involvingn undetermined multipliers related to the unknown values of the integrals. After the general solution is combined with the definitions of the multipliers and the end conditions, a system ofn+2 algebraic equations is obtained; it involvesn+2 unknowns, that is, then undetermined multipliers and two integration constants.The procedure discussed here can be employed in the study of shapes which are aerodynamically optimum at supersonic, hypersonic, and free-molecular flow velocities, that is, wings and fuselages having the maximum lift-to-drag ratio or the minimum drag. The problem of a slender body of revolution having the minimum pressure drag in Newtonian hypersonic flow is developed as an example. First, a general solution is derived for any pair of conditions imposed on the length, the thickness, the wetted area, and the volume. Then, a particular case is treated, that in which the thickness and the wetted area are given, while the length and the volume are free; the shape minimizing the pressure drag is a cone.This research, supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67, is a condensed version of the investigation described in Ref. 1. The author is indebted to Messrs. H. Y. Huang, J. C. Heideman, and J. N. Damoulakis for analytical and numerical assistance. 相似文献
3.
R. R. Salimov 《Siberian Mathematical Journal》2012,53(4):739-747
Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point. 相似文献
4.
E. Bolthausen 《Stochastic Processes and their Applications》1984,16(2):199-204
Let ξt, t ? 0, be a d-dimensional Brownian motion. The asymptotic behaviour of the random field ??∫t0?(ξs) ds is investigated, where ? belongs to a Sobolev space of periodic functions. Particularly a central limit theorem and a law of iterated logarithm are proved leading to a so-called universal law of iterated logarithm. 相似文献
5.
The main result in this paper states that if a one-parameter Gaussian process has C
2k
paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class C
k
. The methods leading to this theorem permit also to give bounds on the successive derivatives of the distribution of the
maximum and to study their asymptotic behaviour as the level tends to infinity.
Received: 14 May 1999 / Revised version: 18 October 1999 / Published online: 14 December 2000 相似文献
6.
P. Dubey 《International Journal of Game Theory》1975,4(3):131-139
L.S. Shapley [1953] showed that there is a unique value defined on the classD of all superadditive cooperative games in characteristic function form (over a finite player setN) which satisfies certain intuitively plausible axioms. Moreover, he raised the question whether an axiomatic foundation could be obtained for a value (not necessarily theShapley value) in the context of the subclassC (respectivelyC′, C″) of simple (respectively simple monotonic, simple superadditive) gamesalone. This paper shows that it is possible to do this. Theorem I gives a new simple proof ofShapley's theorem for the classG ofall games (not necessarily superadditive) overN. The proof contains a procedure for showing that the axioms also uniquely specify theShapley value when they are restricted to certain subclasses ofG, e.g.,C. In addition it provides insight intoShapley's theorem forD itself. Restricted toC′ orC″, Shapley's axioms donot specify a unique value. However it is shown in theorem II that, with a reasonable variant of one of his axioms, a unique value is obtained and, fortunately, it is just theShapley value again. 相似文献
7.
Let u be a solution to the obstacle problem
in a domain Ω⊂ℝ
n
. In this paper, the behavior of the free boundary in a neighborhood of ϖΩ is studied. It is proved that under some conditions
the free boundary touches ϖΩ at contact points. Bibliography:4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 5–19.
Translated by T. N. Rozhkovskaya. 相似文献
8.
Julien Roth 《Annals of Global Analysis and Geometry》2008,33(3):293-306
In this article, we prove new pinching theorems for the first eigenvalue λ1(M) of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound
for λ1(M) in terms of higher order mean curvatures H
k
. We show that under a suitable pinching condition, the hypersurface is diffeomorpic and almost-isometric to a standard sphere.
Moreover, as a corollary, we show that a hypersurface of the Euclidean space which is almost-Einstein is diffeomorpic and
almost-isometric to a standard sphere.
相似文献
9.
Kristen A. Beck 《代数通讯》2013,41(4):1640-1653
Let A be a differential graded (DG) algebra with a trivial differential over a commutative unital ring. This paper investigates the image of the totaling functor, defined from the category of complexes of graded A-modules to the category of DG A-modules. Specifically, we exhibit a special class of semifree DG A-modules which can always be expressed as the totaling of some complex of graded free A-modules. As a corollary, we also provide results concerning the image of the totaling functor when A is a polynomial ring over a field. 相似文献
10.
Alexander Domoshnitsky Robert Hakl Bedřich Půža 《Czechoslovak Mathematical Journal》2012,62(4):1033-1053
Consider the homogeneous equation $$u'(t) = l(u)(t){\rm{ for a}}{\rm{.e}}{\rm{. }}t \in [a,b]$$ where ?: C([a, b];?) → L([a, b];?) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations. 相似文献
11.
Ya V. Vasyl’kiv 《Ukrainian Mathematical Journal》1999,51(11):1635-1642
We establish that, for a Blaschke product B(z) convergent in the unit disk, the condition - ∞ < \smallint 01 log(1 - t)n(t,B)dt\smallint _0^1 \log (1 - t)n(t,B)dt is sufficient for the total variation of logB to be bounded on a circle of radiusr, 0 <r < 1. For products B(z) with zeros concentrated on a single ray, this condition is also necessary. Here, n(t, B) denotes the number of zeros of the functionB (z) in a disk of radiust. 相似文献
12.
Randolf Arnold 《Monatshefte für Mathematik》1993,115(1-2):1-11
LetF be a closed convex hypersurface in Euclideand-space with almost constantq-th mean curvatureH
q (q=1, ...,d–1). The deviation ofF from a suitable sphere is estimated explicitely in terms of geometric quantities ofF. The proof depends on a new stability result on the Aleksandrov-Fenchel inequality, which improves a theorem of Schneider. 相似文献
13.
Let X1, ... , Xn be i.i.d. integral valued random variables and Sn their sum. In the case when X1 has a moderately large tail of distribution, Deshouillers, Freiman and Yudin gave a uniform upper bound for max k ∊ ℤ Pr{Sn = k} (which can be expressed in term of the Lévy Doeblin concentration of Sn), under the extra condition that X1 is not essentially supported by an arithmetic progression. The first aim of the paper is to show that this extra condition cannot be simply ruled out. Secondly, it is shown that if X1 has a very large tail (larger than a Cauchy-type distribution), then the extra arithmetic condition is not sufficient to guarantee a uniform upper bound for the decay of the concentration of the sum Sn. Proofs are constructive and enhance the connection between additive number theory and probability theory.À Jean-Louis Nicolas, avec amitié et respect2000 Mathematics Subject Classification: Primary—60Fxx, 60Exx, 11Pxx, 11B25 相似文献
14.
In this article a linear operator, K, defined on a Hilbert space equipped with a chain of orthoprojectors is considered. It is proved that if K enjoys a particular property with respect to the chain of orthoprojectors, then the series ∑n = 0∞Kn converges in the uniform operator norm. The proof uses purely algebraic techniques and does not require compactness of K. As such, it is a significant generalization of the well-known Volterra principle of inversion. 相似文献
15.
The assertion that the Salem test [5] for the uniform convergence of a trigonometric Fourier series is improvable, is proved. In particular, an example of a continuous function, which does not fulfill the condition of the Salem test but satisfies the condition of the generalized Salem test [10], is constructed.Besides, the theorem which improves Golubov’s [3,4] result for continuous functions of two variables, is given. 相似文献
16.
Boaz Nadler 《Journal of multivariate analysis》2011,102(2):363-371
The ratio of the largest eigenvalue divided by the trace of a p×p random Wishart matrix with n degrees of freedom and an identity covariance matrix plays an important role in various hypothesis testing problems, both in statistics and in signal processing. In this paper we derive an approximate explicit expression for the distribution of this ratio, by considering the joint limit as both p,n→∞ with p/n→c. Our analysis reveals that even though asymptotically in this limit the ratio follows a Tracy-Widom (TW) distribution, one of the leading error terms depends on the second derivative of the TW distribution, and is non-negligible for practical values of p, in particular for determining tail probabilities. We thus propose to explicitly include this term in the approximate distribution for the ratio. We illustrate empirically using simulations that adding this term to the TW distribution yields a quite accurate expression to the empirical distribution of the ratio, even for small values of p,n. 相似文献
17.
We study conditions under which the characteristic vector of a normal lcQS-manifold is a torsion-forming or even a concircular vector field. We prove that the following assertions are equivalent:
- An lcQS-structure is normal, and its characteristic vector is a torsion-forming vector field.
- An lcQS-structure is normal, and its characteristic vector is a concircular vector field.
- An lcQS-structure is locally conformally cosymplectic and has a closed contact form.
18.
On the validity of the Ginzburg-Landau equation 总被引:1,自引:0,他引:1
A. van Harten 《Journal of Nonlinear Science》1991,1(4):397-422
Summary The famous Ginzburg-Landau equation describes nonlinear amplitude modulations of a wave perturbation of a basic pattern when
a control parameterR lies in the unstable regionO(ε
2) away from the critical valueR
c for which the system loses stability. Hereε>0 is a small parameter. G-L's equation is found for a general class of nonlinear evolution problems including several classical
problems from hydrodynamics and other fields of physics and chemistry. Up to now, the rigorous derivation of G-L's equation
for general situations is not yet completed. This was only demonstrated for special types of solutions (steady, time periodic)
or for special problems (the Swift-Hohenberg equation). Here a mathematically rigorous proof of the validity of G-L's equation
is given for a general situation of one space variable and a quadratic nonlinearity. Validity is meant in the following sense.
For each given initial condition in a suitable Banach space there exists a unique bounded solution of the initial value problem
for G-L's equation on a finite interval of theO(1/ε2)-long time scale intrinsic to the modulation. For such a finite time interval of the intrinsic modulation time scale on which
the initial value problem for G-L's equation has a bounded solution, the initial value problem for the original evolution
equation with corresponding initial conditions, has a unique solutionO(ε2) — close to the approximation induced by the solution of G-L's equation. This property guarantees that, for rather general
initial conditions on the intrinsic modulation time scale, the behavior of solutions of G-L's equation is really inherited
from solutions of the original problem, and the other way around: to a solution of G-L's equation corresponds a nearby exact
solution with a relatively small error. 相似文献
19.
Pomirchi L. M. Ryzhov V. N. Tareyeva E. E. 《Theoretical and Mathematical Physics》2001,130(1):101-110
In the framework of the two-dimensional melting theory based on the density functional approach, we use a Monte Carlo computer simulation to study melting of a two-dimensional hard disk system with a rectangular-well attraction potential. We show that depending on the attraction radius, the melting can occur via a single first-order transition as well as continuously in accordance with the Kosterlitz–Thouless–Halperin–Nelson–Young theory. 相似文献
20.
G. V. Kuz'mina 《Journal of Mathematical Sciences》1982,19(6):1715-1726
Let ck, k=1,...,4, be arbitrary distinct points of . LetD be the family of all systems of simply connected domains in. By R(Dk, ck) we denote the conformal radius of the domain Dk, relative to the point ck. We prove that in the familyD one has the sharp inequality, (1) where a=(+i)/(–1), being the cross-ratio of the points c1,c2, c3, c4: E(–1, 1,a) is the continuum of least capacity containing the points –1,1,a. An explicit expression for capE(–1,1,a.) in terms of elliptic Jacobi functions has been obtained earlier by the author [Tr. Mat. Inst. Akad. Nauk SSSR,94, 47–65, 1968]. On the basis of the well-known properties of continua of least capacity, one shows that the largest value of the right-hand side of (1) is attained for a=± i3 and it is equal to 4–8/3·32. One gives all the configurations for which equality prevails in the obtained estimates.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 100, pp. 131–145, 1980. 相似文献