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51.
本文推导了包含自衍射及非线性吸收影响、用以描述空间电荷场建立过程的微分方程组,阐明了周期性的空间电荷场与光强干涉条纹之间的相位差在建立过程中所起的作用,并推导了描述条纹倾斜和弯曲的微分方程。通过数值计算找到了硅酸铋(BSO)晶体中能量转移的规律,讨论了材料特性对过程快慢的影响,提出了用CW激光来探讨瞬态过程快慢的可能性。 相似文献
52.
We consider a composite material composed of fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mathematical modelling of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. In this paper, we are interested in the computation of approximate solutions. We propose a family of discretized problems depending on two parameters (β1, β2) ε [0, 1]2 which split the linear and non‐ linear terms in implicit and explicit parts. We prove the stability and convergence of the discretization for any (β1, β2) ε [½, 1 ] × [0, 1]. We present also some numerical results. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
53.
Shigeki Aida 《Journal of Functional Analysis》2007,251(1):59-121
We determine the limit of the bottom of spectrum of Schrödinger operators with variable coefficients on Wiener spaces and path spaces over finite-dimensional compact Riemannian manifolds in the semi-classical limit. These are extensions of the results in [S. Aida, Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space, J. Funct. Anal. 203 (2) (2003) 401-424]. The problem on path spaces over Riemannian manifolds is considered as a problem on Wiener spaces by using Ito's map. However the coefficient operator is not a bounded linear operator and the dependence on the path is not continuous in the uniform convergence topology if the Riemannian curvature tensor on the underling manifold is not equal to 0. The difficulties are solved by using unitary transformations of the Schrödinger operators by approximate ground state functions and estimates in the rough path analysis. 相似文献
54.
55.
Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data. 相似文献
56.
Sergio Albeverio Yeneng Sun Jiang-Lun Wu 《Transactions of the American Mathematical Society》2007,359(2):517-527
It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.
57.
In this paper κ-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed. 相似文献
58.
The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym2(g)× sym2(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym2(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym2(g). 相似文献
59.
Tim R. Dargaville Julie M. Elliott Mathew Celina 《Journal of Polymer Science.Polymer Physics》2006,44(22):3253-3264
Films of piezoelectric PVDF and P(VDF‐TrFE) were exposed to vacuum UV (115–300 nm VUV) and γ‐radiation to investigate how these two forms of radiation affect the chemical, morphological, and piezoelectric properties of the polymers. The extent of crosslinking was almost identical in both polymers after γ‐irradiation, but surprisingly, was significantly higher for the TrFE copolymer after VUV‐irradiation. Changes in the melting behavior were also more significant in the TrFE copolymer after VUV‐irradiation due to both surface and bulk crosslinking, compared with only surface crosslinking for the PVDF films. The piezoelectric properties (measured using d33 piezoelectric coefficients and D‐E hysteresis loops) were unchanged in the PVDF homopolymer, while the TrFE copolymer exhibited more narrow D‐E loops after exposure to either γ‐ or VUV‐radiation. The more severe damage to the TrFE copolymer in comparison with the PVDF homopolymer after VUV‐irradiation is explained by different energy deposition characteristics. The short wavelength, highly energetic photons are undoubtedly absorbed in the surface layers of both polymers, and we propose that while the longer wavelength components of the VUV‐radiation are absorbed by the bulk of the TrFE copolymer causing crosslinking, they are transmitted harmlessly in the PVDF homopolymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3253–3264, 2006 相似文献
60.
V. M. Murzina 《Algebra and Logic》2007,46(6):409-418
We study into the question whether calculi associated with Ershov topological spaces possess Craig’s interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 6, pp. 745–762, November–December, 2007. 相似文献