共查询到20条相似文献,搜索用时 15 毫秒
1.
For classical Neumann eigenvalue, buckling eigenvalue and clamped plate eigenvalue, we give the corresponding Rellich type identities. As an application of these results, then, we obtain a new necessary and sufficient condition for a domain without the Pompeiu property. 相似文献
2.
A Wiener-Tauberian theorem is proven on the Laguerre hypergroup [M.M. Nessibi, K. Trimèche, Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets, J. Math. Anal. Appl. 208 (1997) 337-363]. As consequence of this theorem we establish a Pompeiu type-theorem and we study some of its applications. 相似文献
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We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains Ω⊂Rd of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians. 相似文献
6.
The isometries of the hyperspace of a compact subset of the real line endowed with the generalized Pompeiu metric are considered. It is proved that any such an isometry is generated by an isometry of the base space.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 163–170.Original Russian Text Copyright © 2005 by V. V. Aseev, A. V. Tetenov, A. P. Maksimova. 相似文献
7.
Stephen A. Williams 《Journal of Mathematical Analysis and Applications》2002,274(1):296-304
If a nonconstant solution u of the Helmholtz equation exists on a bounded domain with u satisfying overdetermined boundary conditions (u and its normal derivative both required to be constant on the boundary), then under certain assumptions the boundary of the domain is proved to be real-analytic. Under weaker assumptions, if a real-analytic portion of the boundary has a real-analytic extension, then that extension must also be part of the boundary. Also, an explicit formula for u is given and a condition (which does not involve u) is given for a bounded domain to have such a solution u defined on it. Both of these last results involve acoustic single- and double-layer potentials. 相似文献
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9.
Michael Mörs 《Journal of Combinatorial Theory, Series A》1981,31(2):126-130
Zarankiewicz (Colloq. Math.2 (1951), 301) raised the following problem: Determine the least positive integer z(m, n, j, k) such that each 0–1-matrix with m rows and n columns containing z(m, n, j, k) ones has a submatrix with j rows and k columns consisting entirely of ones. This paper improves a result of Hylten-Cavallius (Colloq. Math.6 (1958), 59–65) who proved: . We prove that exists and is equal to . For the special case where k = 2 resp. k = 3 this result was proved earlier by Kövari, Sos and Turan (Colloq. Math.3 (1954), 50–57) resp. Hylten-Cavallius. 相似文献
10.
Stephen A. Williams 《Mathematische Annalen》1976,223(2):183-190
A nonempty bounded open subset D of
n
is said to have the Pompeiu property if and only if for every continuous complex-valued function f on
n
which does not vanish identically there is a rigid motion of
n
onto itself — taking D onto (D) — such that the integral of f over (D) is not zero. This article gives a partial solution of the Pompeiu problem, the problem of finding all sets D with the Pompeiu property.In the special case that D is the interior of a homeomorphic image of an(n–1)-dimensional sphere, the main result states that if D has a portion of an(n–1)-dimensional real analytic surface on its boundary, then either D has the Pompeiu property or any connected real analytic extension of the surface also lies on the boundary of D. Thus, for example, any such region D having a portion of a hyperplane as part of its boundary must have the Pompeiu property, since the entire hyperplane cannot lie in the boundary of the bounded set D.The research for this paper was done in part while on sabbatical at the Courant Institute of Mathematical Sciences, New York University. 相似文献
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V. V. Volchkov 《Mathematical Notes》1996,59(5):482-489
The Pompeiu problem is studied for functions defined on a ballB
n
and having zero integrals over all sets congruent to a given compact setK B. The problem of finding the least radiusr=r(K) ofB for whichK is a Pompeiu set is considered. The solution is obtained for the cases in whichK is a cube or a hemisphere.Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 671–680, May, 1996. 相似文献
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In this work we consider a Cauchy problem for a nonlinear viscoelastic equation. Under suitable conditions on the initial data and the relaxation function, we prove a finite-time blow-up result. 相似文献
15.
Kerris W. Thompson 《Aequationes Mathematicae》1992,44(1):42-47
Summary In this article we continue our study of the following problem posed by Lawrence Zalcman in 1972. LetS be the closed unit square. For eachz in the interior,S
0, ofS letS(z) be the largest closed square inS with centroidz, and for each in the interval (0, 1] letS
(z) be the square homothetic toS(z) with linear ratio . Iff is a continuous function such that its integral overS
(z) vanishes for allz in S0, is f =0? We show that the answer is yes if 3/4 < 1. 相似文献
16.
V. V. Volchkov 《Ukrainian Mathematical Journal》1993,45(10):1623-1628
Functions are investigated whose integrals over a given collection of sets are zero. Pompeiu sets are described in terms of the approximation of their indicators by linear combinations of the indicators of balls with special radii.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1444–1448, October, 1993. 相似文献
17.
Milton Ferreira R. Sren Kraußhar M. Manuela Rodrigues Nelson Vieira 《Mathematical Methods in the Applied Sciences》2019,42(10):3633-3653
In this paper, we develop a fractional integro‐differential operator calculus for Clifford algebra‐valued functions. To do that, we introduce fractional analogues of the Teodorescu and Cauchy‐Bitsadze operators, and we investigate some of their mapping properties. As a main result, we prove a fractional Borel‐Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge‐type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann‐Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order. 相似文献
18.
It is proposed here to study the free boundary of the obstacle problem in the case of an elastic plate. Under a nondegeneracy assumption, we prove a stability theorem which relates the variations of the contact zone to the variations the external forces. The statement of this result obtained and the steps in the proof are very close to those given by D.G. Schaeffer in 1975, except for the very important fact that the present study deals with the biharmonic operator. 相似文献
19.
R. Ben-Hador 《Applied Mathematics Letters》1999,12(8):65-72
Cagniard problem refers to the class of linear reflection and transmission problem for pulsed line and point sources, which have solution methods leading to exact algebraic representations of the wave fields. All previous methods have relied heavily on integral or differential transforms. We present in this paper a new and direct approach to the problem which involves only the wave equation and its associated characteristic equation. We illustrate the new method by applying it to the problem of the reflection and transmission of acoustic waves radiating from a line source in the vicinity of a plane boundary separating two uniform acoustic media. 相似文献
20.
David Conlon 《Journal of Graph Theory》2008,58(4):351-356
We consider the following question: how large does n have to be to guarantee that in any two‐coloring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In the late 1970s, Irving showed that it was sufficient, for k large, that n ≥ 2k ? 1 (k ? 1) ? 1. Here we improve upon this bound, showing that it is sufficient to take where the log is taken to the base 2. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 351–356, 2008 相似文献