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1.
Yoel Shkolnisky Mark Tygert Vladimir Rokhlin 《Applied and Computational Harmonic Analysis》2006,21(3):413-420
Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae. 相似文献
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A. A. Abramov S. V. Kurochkin 《Computational Mathematics and Mathematical Physics》2006,46(6):949-954
A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters. 相似文献
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Time-dependent reorientations of resorcinol-based acridinidione (ADR) dyes in glycerol were studied using steady-state and
time-resolved fluorescence studies. The difference between fluorescence anisotropy decays recorded at 460 nm when exciting
at 250 nm and those obtained when exciting at 394 nm are reported. When exciting at 394 nm, the fluorescence anisotropy decay
is bi-exponential, while on exciting at 250 nm a mono-exponential fluorescence anisotropy decay is observed. We interpret
this in terms of different directions of the absorption dipole at 394 and 250 nm with the emission dipole respectively, which
is experimentally validated and further analysed as a prolate model of ellipsoid. 相似文献
5.
J. Morais M. A. Pérez‐de la Rosa 《Mathematical Methods in the Applied Sciences》2015,38(17):4365-4387
Over the past few years, considerable attention has been given to the role played by the Lamé's Wave Functions (LWFs) in various problems of mathematical physics and mechanics. The LWFs arise via the method of separation of variables for the wave equation in ellipsoidal coordinates. The present paper introduces the Lamé's Quaternionic Wave Functions (LQWFs), which extend the LWFs to a non‐commutative framework. We show that the theory of the LQWFs is determined by the Moisil‐Theodorescu type operator with quaternionic variable coefficients. As a result, we explain the connections between the solutions of the Lamé's wave equation, on one hand, and the quaternionic hyperholomorphic and anti‐hyperholomorphic functions on the other. We establish analogues of the basic integral formulas of complex analysis such as Borel‐Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. We further obtain analogues of the boundary value properties of the LQWFs such as Sokhotski‐Plemelj formulae, the ‐hyperholomorphic extension of a given Hölder function and on the square of the singular integral operator. We address all the text mentioned earlier and explore some basic facts of the arising quaternionic function theory. We conclude the paper showing that the spherical, prolate, and oblate spheroidal quaternionic wave functions can be generated as particular cases of the LQWFs. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) . This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space . The quality of the spectral approximation and the choice of the parameter c when approximating a function in by its truncated PSWFs series expansion, are the main issues. By considering a function as the restriction to of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples. 相似文献
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A method is proposed to study the stress concentration around a shallow spheroidal crack in an infinite elastic body. The
stress concentration is due to the diffraction of a low-frequency plane longitudinal wave by the crack. The direction of wave
propagation is established in which the combined concentration of mode I and mode II stresses is maximum
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 70–77, January 2006. 相似文献