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1.
本文研究了数值求解非自治随机微分方程的正则Euler-Maruyama分裂(CEMS)方法,该方程的漂移项系数带有刚性且允许超线性增长,扩散项系数满足全局Lipschitz条件.首先,证明了CEMS方法的强收敛性及收敛速度.其次,证明了在适当条件下CEMS方法是均方稳定的.进一步,利用离散半鞅收敛定理,研究了CEMS方法的几乎必然指数稳定性.结果表明,CEMS方法在漂移系数的刚性部分满足单边Lipschitz条件下可保持几乎必然指数稳定性.最后通过数值实验,检验了CEMS方法的有效性并证实了我们的理论结果. 相似文献
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AbstractWe present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed ensemble size. We will build on recent results on the convergence in the noise-free case and generalise them to the case of noisy observational data, in particular the influence of the noise on the convergence will be investigated, both theoretically and numerically. We focus on linear inverse problems where a very complete theoretical analysis is possible. 相似文献
4.
An experimentally feasible strong coupling system between a spin ensemble and a superconducting qubit is studied. The coupling strength can be exponentially enhanced by applying the squeezing transformations to the system. By means of the two spin ensembles commonly coupled to a superconducting qubit, a set of universal nonadiabatic holonomic single‐qubit quantum gates can be realized in a decoherence‐free subspace. Furthermore, this proposal is robust with respect to decay of the system parameters, and it is experimentally feasible with currently available technology. 相似文献
5.
Qing MENG 《数学年刊B辑(英文版)》2019,40(3):429-438
In this paper, the author first introduces the concept of
generalized algebraic cone metric spaces and some elementary results
concerning generalized algebraic cone metric spaces. Next, by using
these results, some new fixed point theorems on generalized
(complete) algebraic cone metric spaces are proved and an example is
given. As a consequence, the main results generalize the
corresponding results in complete algebraic cone metric spaces and
generalized complete metric spaces. 相似文献
6.
In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献
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Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials 下载免费PDF全文
José Juan Peña Jesús García‐Martínez Jesus García‐Ravelo Jesus Morales 《International journal of quantum chemistry》2015,115(3):158-164
In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term . © 2014 Wiley Periodicals, Inc. 相似文献
9.
《Wave Motion》2020
Three problems for a discrete analog of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: (1) the problem with a point source on an entire plane; (2) the problem of diffraction by a Dirichlet half-line; (3) the problem of diffraction by a Dirichlet right angle. It is shown that the total field can be represented as an integral of an algebraic function over a contour drawn on some manifold. The latter is a torus. As a result, explicit solutions are obtained in terms of recursive relations (for the Green’s function), algebraic functions (for the half-line problem), or elliptic functions (for the right angle problem). 相似文献
10.
沸点(BP)是有机分子液体的基本物理化学量, 也是化学工业生产中的重要参数. 有机分子的沸点由分子结构决定, 呈现复杂的结构-沸点关系, 函数法(Function Method)、基团贡献法(Group Contribution Method)等传统方法无法应对复杂多样有机分子结构的预测, 应用范围狭窄, 预测精度低. 本研究中, 我们利用基于人工神经网络(ANN)和支持向量机(SVM)的多组件学习器实现有机分子沸点的精准预测. 我们构建了基于可解释性描述符的ANN、基于相关性描述符的ANN及基于复合分子指纹的SVM三个异质模型, 并通过包含4550个各种类别的有机分子沸点的数据集进行训练得到了三个异质性学习器, 最后集成三个学习器对有机分子沸点进行预测. 相比于传统方法和此前的定量结构性质关系(QSPR)模型, 多组件模型结合了三种模型的优点, 展现出很好的预测精度和泛化能力以及低的过拟合, 实现了对多种类型有机分子的沸点的有效预测. 相似文献