共查询到20条相似文献,搜索用时 31 毫秒
1.
Vladimir Varlamov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,196(3):957-985
The Ostrovsky equation governs the propagation of long nonlinear surface waves in the presence of rotation. It is related
to the Korteweg-de Vries (KdV) and the Kadomtsev-Petviashvili models. KdV can be obtained from the equation in question when
the rotation parameter γ equals zero. A fundamental solution of the Cauchy problem for the linear Ostrovsky equation is presented
in the form of an oscillatory Fourier integral. Another integral representation involving Airy and Bessel functions is derived
for it. It is shown that its asymptotic expansion as γ → 0 contains the KdV fundamental solution as the zero term. The Airy
transform is used to establish some of its properties. Higher-order asymptotics for γ → 0 on a bounded time interval are obtained
for both the fundamental solution and the solution of the linear Cauchy problem for the Ostrovsky equation. 相似文献
2.
The inversion formula for the short-time Fourier transform is usually considered in the weak sense, or only for specific combinations
of window functions and function spaces such as L2. In the present article the so-called θ-summability (with a function parameter θ) is considered which induces norm convergence
for a large class of function spaces. Under some conditions on θ we prove that the summation of the short-time Fourier transform
of ƒ converges to ƒ in Wiener amalgam norms, hence also in the Lp sense for Lp functions, and pointwise almost everywhere. 相似文献
3.
Vladimir Varlamov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(6):957-985
The Ostrovsky equation governs the propagation of long nonlinear surface waves in the presence of rotation. It is related
to the Korteweg-de Vries (KdV) and the Kadomtsev-Petviashvili models. KdV can be obtained from the equation in question when
the rotation parameter γ equals zero. A fundamental solution of the Cauchy problem for the linear Ostrovsky equation is presented
in the form of an oscillatory Fourier integral. Another integral representation involving Airy and Bessel functions is derived
for it. It is shown that its asymptotic expansion as γ → 0 contains the KdV fundamental solution as the zero term. The Airy
transform is used to establish some of its properties. Higher-order asymptotics for γ → 0 on a bounded time interval are obtained
for both the fundamental solution and the solution of the linear Cauchy problem for the Ostrovsky equation.
Received: November 23, 2004; revised: March 13, 2005
Research is supported by US Department of Defense, under grant No. DAAD19-03-1-0204 相似文献
4.
We study the inversion of weighted Radon transforms in two dimensions, Rρƒ(L)=ƒL =ƒ(·), where the weight function ρ(L, x), L a line and x ∈ L, has a special form. It was an important breakthrough when R.G.
Novikov recently gave an explicit formula for the inverse of Rρ when ρ has the form(1.2); in this case Rρ is called the attenuated Radon transform. Here we prove similar results for a somewhat larger class of ρ using completely
different and quite elementary methods. 相似文献
5.
Let ƒ be a polynomial automorphism of ℂk of degree λ, whose rational extension to ℙk maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙk of bidegree (1,1), we show that the sequence λ−n(ƒn)*S converges in the sense of currents on ℙk to a linear combination of the Green current T+ of ƒ and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms
of generalized Lelong numbers with respect to an invariant dynamical current for ƒ−1. 相似文献
6.
Let S′ be the class of tempered distributions. For ƒ ∈ S′ we denote by J
−α
ƒ the Bessel potential of ƒ of order α. We prove that if J
−α
ƒ ∈ BMO, then for any λ ∈ (0, 1), J
−α
(f)λ ∈ BMO, where (f)λ = λ−n
f(φ(λ−1)), φ ∈ S. Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order
α > 0 belongs to the VMO space. 相似文献
7.
We observe an unknown function of d variables ƒ(t), t ∈ [0, 1]d, in the white Gaussian noise of level ε > 0. We assume that {ie4526-01}, where {ie4526-02} is a ball in the Hilbert space
{ie4526-03} of tensor product structure. Under minimax setup, we consider two problems: estimate ƒ (for quadratic losses)
and detect ƒ, i.e., test the null hypothesis H0: ƒ = 0 against the alternatives {ie4526-04}. We are interested in the case {ie4526-05}. We study sharp, rate, and log-asymptotics
(as ε → 0 and d → ∞) in the problems. In particular, we show that log-asymptotics are essentially different for d ≪ log ε−1 and d ≫ log ε−1. Bibliography: 19 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 180–218. 相似文献
8.
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion
started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and
the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional
Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this
Bessel bridge stays below some fixed value. 相似文献
9.
Let ƒ be a birational map of C
d
,and consider the degree complexity or asymptotic degree growth rate δ(ƒ) = limn → ∞ (deg(ƒn))1/n.We introduce a family of elementary maps, which have the form ƒ = L o J, where L is (invertible) linear, and J(x
1
−1
,..., xd) = (x
1
−1
,...,x
d
−1
.We develop a method of regularization and show how it can be used to compute δ for an elementary map. 相似文献
10.
We generalize a theorem of Ky Fan about the nearest distance between a closed convex set D in a Banach space E and its image by a function ƒ:D→E, in several directions: (1) for noncompact sets D, when ƒ(D) precompact; (2) for compact D and upper semicontinuous multifunction ƒ and more generally, (3) for noncompact D and upper semicontinuous multifunction ƒ with ƒ(D) Hausdorff precompact.
In particular, we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions whose values are convex
closed bounded, thus not necessarily compact.
Received May 23, 2000, Accepted September 4, 2001 相似文献
11.
N. A. Krasovskii A. M. Taras’ev 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):174-185
We address the problem of optimal reconstruction of the values of a linear operator on ℝ
d
or ℤ
d
from approximate values of other operators. Each operator acts as the multiplication of the Fourier transform by a certain
function. As an application, we present explicit expressions for optimal methods of reconstructing the solution of the heat
equation (for continuous and difference models) at a given instant of time from inaccurate measurements of this solution at
other time instants. 相似文献
12.
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and
acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform.
However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the
main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints
in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem,
dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall
show, in general, the “fast Fourier” version of the optimization constraints produces a larger but sparser constraint matrix
and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem,
which is usually a good thing. 相似文献
13.
A. V. Voznyuk 《Journal of Mathematical Sciences》1994,69(5):1289-1295
The perturbation method and the Langer transform method are applied to obtain a second approximate solution of the problem with one and two cusp points. As an example, Langer type asymptotic formulas are derived for Bessel functions.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 67, pp. 42–50, 1989. 相似文献
14.
A new integral transform whose kernel is a Stokes stream function of an exact solution to the axisymmetric stationary Euler
equations is derived with its inverse by using a Coulomb wave function. In the process of its derivation, a set of integral
transforms with respect to the radial variable is also found. Each of them is different from the Hankel (the Fourier–Bessel)
transform. 相似文献
15.
A new integral transform whose kernel is a Stokes stream function of an exact solution to the axisymmetric stationary Euler
equations is derived with its inverse by using a Coulomb wave function. In the process of its derivation, a set of integral
transforms with respect to the radial variable is also found. Each of them is different from the Hankel (the Fourier–Bessel)
transform. 相似文献
16.
Luis Daniel Abreu 《Constructive Approximation》2008,28(2):219-235
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials,
which provide an abstract formulation of quantum (q-) Fourier-type systems.We prove Ismail’s conjecture regarding the existence
of a reproducing kernel structure behind these kernels, by establishing a link with Saitoh’s theory of linear transformations
in Hilbert space. The results are illustrated with Fourier kernels with ultraspherical, their continuous q-extensions and
generalizations. As a byproduct of this approach, a new class of sampling theorems is obtained, as well as Neumann-type expansions
in Bessel and q-Bessel functions. 相似文献
17.
A method for approximation of functions of two variables by a linear combination of nonnegative piecewise linear functions
with a compact support is presented. The crucial idea of this method consists in an “integral” calculation method for the
coefficients. The accuracy of the approximation in the spaces of continuous and integrable functions is proved to have the
same order as the best approximation by piecewise linear functions. 相似文献
18.
Manufacturing of steel involves thermal energy intensive processes with coal as the major input. Energy generated is a direct
function of ash content of coal and as such it weighs very high as regards the choice of coal. In this paper, we study a multiobjective
transportation problem to introduce a new type of coal in a steel manufacturing unit in India. The use of new type of coal
serves three non-prioritized objectives, viz. minimization of the total freight cost, the transportation time and the ratio
of ash content to the production of hot metal. It has been observed from the past data that the supply and demand points have
shown fluctuations around their estimated values because of changing economic conditions. To deal with uncertainties of supply
and demand parameters, we transform the past data pertaining to the amount of supply of the ith supply point and the amount of demand of the jth demand point using level (λ,ρ) interval-valued fuzzy numbers. We use a linear ranking function to defuzzify the fuzzy transportation problem. A transportation
algorithm is developed to find the non-dominated solutions for the defuzzified problem. The application of the algorithm is
illustrated by numerical examples constructed from the data provided by the manufacturing unit.
相似文献
19.
S. V. Konyagin 《Journal of Mathematical Sciences》2008,155(1):81-88
We show that if the module of continuity ω(ƒ, δ) of a 2π-periodic function ƒ ∈ {ie081-01} is o(1/ log log 1/δ) as δ → 0+, then there exists a rearrangement of the trigonometric Fourier series of ƒ converging uniformly to ƒ.
__________
Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 25, Theory of Functions, 2007. 相似文献
20.
We establish monotonicity inequalities for the r-area of a complete oriented properly immersed r-minimal hypersurface in Euclidean
space under appropriate quasi-positivity assumptions on certain invariants of the immersion. The proofs are based on the corresponding
first variational formula. As an application, we derive a degeneracy theorem for an entire r-minimal graph whose defining
function ƒ has first and second derivatives decaying fast enough at infinity: Its Hessian operator D2 ƒ has at least n − r null eigenvalues everywhere. 相似文献