共查询到20条相似文献,搜索用时 171 毫秒
1.
The problem of scattering of Love waves due to the presence of a rigid barrier of finite depth in the crusfal layer of the earth is studied in the present paper. The barrier is in the slightly dissipative surface layer and the surface of the layer is a free surface. The Wiener-Hopf technique is the method of solution. Evaluation of the integrals along appropriate contours in the complex plane yields the reflected, transmitted and the scattered waves. The scattered waves behave as a decaying cylindrical wave at distant points. Numrical computations for the amplitude of the scattered waves have been made versus the wave number. The amplitude falls off rapidly as the wave number increases very slowly. 相似文献
2.
The paper presents a theoretical formulation for studying scattering of Rayleigh waves due to the presence of rigid barriers in oceanic waters. The Wiener-Hopf technique has been employed to solve the problem. Exact solution has been obtained in terms of Fourier integrals whose evaluation gives the reflected, transmitted and scattered waves. The scattered waves have the behaviour of cylindrical waves originating at the edge of the barrier. Numerical results for the amplitude of the scattered waves have been obtained for small depth of the barrier. 相似文献
3.
L. A. Molotkov 《Journal of Mathematical Sciences》2011,175(6):672-684
Along the boundary between elastic and fluid media, the surface Rayleigh wave propagates. The velocity of this wave v
R0 in the case of a plane boundary is less than the velocity of the Rayleigh wave v
R
on a free plane boundary of an elastic medium and less than the velocity v
P0 in a fluid medium. To investigate the velocity v
R0 in the case of curvilinear boundaries, the propagation of Rayleigh waves under consideration along cylindrical and spherical
surfaces is studied. The velocity of the Rayleigh wave depends on the curvature of the wave trajectory and the curvature in
the direction perpendicular to the trajectory. Furthermore this velocity depends on the presence or absence of a fluid medium.
Bibliography: 5 titles. 相似文献
4.
In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic σ≤ 0 is given, that generalizes a result of Borodin on plane graphs. As a consequence, it is proved that every such graph without i-circuits for 4 ≤ i ≤ 11 - 3σ is 3-choosable, that offers a new upper bound to a question of Y. Zhao. 相似文献
5.
In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t > 0 and obtain an explicit formula for the solution of the mixed initial boundary value problem, the boundary data being
prescribed in the sense of Bardos-Leroux and Nedelec. We also get an explicit formula for the solution of weighted Burgers
equation in a strip. 相似文献
6.
J. Yoon 《Constructive Approximation》2001,17(2):227-247
A new multivariate approximation scheme on R
d
using scattered translates of the “shifted” surface spline function is developed. The scheme is shown to provide spectral
L
p
-approximation orders with 1 ≤ p ≤ ∞, i.e., approximation orders that depend on the smoothness of the approximands. In addition, it applies to noisy data
as well as noiseless data. A numerical example is presented with a comparison between the new scheme and the surface spline
interpolation method. 相似文献
7.
We consider Finsler spaces with a Randers metric F=α+β, on the three dimensional real vector space, where α is the Euclidean metric and β=bdx
3
is a 1-form with norm b,0≤b<1. By using the notion of mean curvature for immersions in Finsler spaces introduced by Z. Shen, we get the ordinary differential
equation that characterizes the minimal surfaces of rotation around the x
3
axis. We prove that for every b,0≤b<1, there exists, up to homothety, a unique forward complete minimal surface of rotation. The surface is embedded, symmetric
with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve. Moreover, for every
there are non complete minimal surfaces of rotation, which include explicit minimal cones.
Received: 30 November 2001 / Published online: 10 February 2003
RID="⋆"
ID="⋆" Partially supported by CAPES
RID="⋆⋆"
ID="⋆⋆" Partially supported by CNPq and PROCAD. 相似文献
8.
N. Ya. Kirpichnikova 《Journal of Mathematical Sciences》2008,155(3):409-418
The solutions of equations of elasticity theory that have a discontinuity only on a boundary free of tensions (Rayleigh waves)
are considered. Initial data for the complex intensity of the surface Rayleigh waves are found in two simple media. The first
elastic medium fills a half-space with Lamé parameters and density dependent on depth. The second medium is bounded by a curve
determined by a natural equation. The parameters of the second medium depend on the arc length along the curve. Bibliography:
12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 132–149. 相似文献
9.
A. S. Serdyuk 《Ukrainian Mathematical Journal》2005,57(8):1275-1296
We find asymptotic equalities for upper bounds of approximations by partial Fourier sums in the uniform metric on classes
of Poisson integrals of periodic functions belonging to the unit balls in the spaces L
p
, 1 ≤ p ≤ ∞. We generalize the results obtained to the classes of (ψ,
)-differentiable (in the sense of Stepanets) functions that admit an analytic extension to a fixed strip of the complex plane.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1079 – 1096, August, 2005. 相似文献
10.
If on a surface Σ bounding an electromagnetic field, the Leontovich boundary conditions with a pure imaginary exponent are
fulfilled, then surface electromagnetic waves propagating along Σ may exist. These waves have much in common with the Rayleigh
waves in elasticity theory. In the paper, the ray theory of this electromagnetic analog of the Rayleigh waves is constructed.
Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 5–19. 相似文献
11.
A. S. Serdyuk 《Ukrainian Mathematical Journal》2005,57(10):1635-1651
We establish asymptotic equalities for upper bounds of approximations by partial Fourier sums in the metrics of the spaces
L
p
, 1 ≤ p ≤ ∞, on classes of Poisson integrals of periodic functions belonging to the unit ball of the space L
1. The results obtained are generalized to the classes of
-differentiable (in the sense of Stepanets) functions that admit an analytic extension to a fixed strip of the complex plane.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1395–1408, October, 2005. 相似文献
12.
E. G. Kir’yatskii 《Russian Mathematics (Iz VUZ)》2010,54(2):84-86
Let a set B have the following properties: if z ∈ B, then z ± 2π ∈ B and the intersection of B with the vertical strip 0 ≤ Re x ≤ π is a closed and bounded set. In this paper we study the approximation of a continuous on B and 2π-periodic function f(z) by trigonometric polynomials T
n
(z). We establish the necessary and sufficient conditions for the function f(z) to be entire and specify a formula for calculating its order. In addition, we describe some metric properties of periodic
sets in a plane. 相似文献
13.
Existing bounds on the minimum weight d
⊥ of the dual 7-ary code of a projective plane of order 49 show that this must be in the range 76 ≤ d
⊥ ≤ 98. We use combinatorial arguments to improve this range to 88 ≤ d
⊥ ≤ 98, noting that the upper bound can be taken to be 91 if the plane has a Baer subplane, as in the desarguesian case. A
brief survey of known results for the minimum weight of the dual codes of finite projective planes is also included.
Dedicated to Dan Hughes on the occasion of his 80th birthday. 相似文献
14.
Tian Liang Tu 《数学学报(英文版)》2002,18(4):631-646
Let D be a smooth domain in the complex plane. In D consider the simultaneous approximation to a function and its ith (0 ≤i≤q) derivatives by Hermite interpolation. The orders of uniform approximation and approximation in the mean, are obtained under
some domain boundary conditions. Some known results are included as particular cases of the theorems of this paper.
Received May 25, 2000, Revised November 3, 2000, Accepted December 7, 2000 相似文献
15.
Shu-hongWu 《应用数学学报(英文版)》2005,21(1):77-80
A two-point boundary value problem with a non-negative parameter Q arising in the study of surface tension induced flow of a liquid metal or semiconductor is studied. We prove that the problem has at least one solution for Q≥0.This improves a recent result that the problem has at least one solution for 0 ≤Q≤13.21. 相似文献
16.
We consider a parabolic Signorini boundary value problem in a thick plane junction Ω
ε
which is the union of a domain Ω0 and a large number of ε−periodically situated thin rods. The Signorini conditions are given on the vertical sides of the thin rods. The asymptotic
analysis of this problem is done as ε → 0, i.e., when the number of the thin rods infinitely increases and their thickness tends to zero. With the help of the
integral identity method we prove a convergence theorem and show that the Signorini conditions are transformed (as ε → 0) in differential inequalities in the region that is filled up by the thin rods in the limit passage. Bibliography: 31
titles. Illustrations: 1 figure. 相似文献
17.
Dambaru D. Bhatta 《Journal of Applied Mathematics and Computing》2005,18(1-2):171-182
An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the nonhomogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only. 相似文献
18.
The general theme of this note is illustrated by the following theorem:Theorem 1.
Suppose K is a compact set in the complex plane and 0belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo morphic in a neighborhood
of K and f(0) = 0.Also for any givenpositive integer m, let A(m, K) denote the space of all f such that f is holomorphic in a neighborhood of
K and f(0) =f′(0) = ... =f
(m)(0) = 0.Then A(m, K) is dense in A(K) under the supre mum norm on K provided that there exists a sector W = re
iθ; 0≤r≤ δ,α≤ θ≤ β
such that W ∩ K = 0. (This is the well- known Poincare’s external cone condition). We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.
Dedicated to Prof. Ashoke Roy on his 62nd birthday 相似文献
19.
E. A. Zernyshkina 《Proceedings of the Steklov Institute of Mathematics》2009,264(Z1):199-213
We study the sharp constant in the inequality between the L
p
-mean (p ≥ 0) of a 2π-periodic function with zero mean value and the L
q
-norm (q ≥ 1) of the positive cutoff of its derivative. We obtain estimates of the constant from below for 0 ≤ p ≤ ∞ and from above for 1 ≤ p ≤ ∞ for an arbitrary 1 ≤ q ≤ ∞. We write out the values of the sharp constant in the cases p = 2, 1 ≤ q ≤ ∞ and p = ∞, 1 ≤ q ≤ ∞. 相似文献
20.
For a (smooth irreducible) curveC of genus g and Clifford indexc>2 with a linear seriesg
d
r
computing c (so
) it is well known thatc + 2 ≤d ≤2 (c + 2), and if
then 2c + 1 ≤g ≤ 2c + 4 unlessd = 2c + 4 in which caseg = 2c + 5.
Let c ≥ 0 andg be integers. If 2c + 1 ≤g ≤2c + 4 we prove that for any integerd <g such thatd ≡c mod 2 andc + 2 ≤d < 2(c + 2) there exists a curve of genus g and Clifford index c with a gd
r computing c. Ford ≥c + 6 (i.e.r ≥ 3) we construct this curve on a surface of degree 2r-2 in ℙr, and ford ≥c + 8 (i.e.r ≥ 4) we show that such a curve cannot be found on a surface in ℙr of smaller degree. In fact, if gd
r computes the Clifford index c of C such thatc + 8 ≤d ≤ 2c + 3 then the birational morphism defined by this series cannot map C onto a (maybe, singular) curve contained in a surface
of degree at most 2r-3 in ℙr. 相似文献