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31.
32.
In the present paper, we deal with the complex Szász-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found. 相似文献
33.
Nikolay K. Vitanov Zlatinka I. Dimitrova Kaloyan N. Vitanov 《Entropy (Basel, Switzerland)》2021,23(1)
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of to solution for arbitrary finite values of . Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM. 相似文献
34.
Yu Liu 《数学学报(英文版)》2019,35(8):1334-1356
In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394, 245–284 (2013)”, we introduced the notion o 相似文献
35.
Qiong-Tao Xie 《理论物理通讯》2020,72(6):65105-64
An analytical method is developed to study the two-mode quantum Rabi model. For certain specific parameter conditions, especially for the resonant conditions, we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies. It is shown that there exist new types of the exact energies which do not correspond to the level-crossings. Our analytical method may find applications in some related models. 相似文献
36.
We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely. 相似文献
37.
By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large. 相似文献
38.
39.
Abundant explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law nonlinearities
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This paper is concerned with the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law. Abundant explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
40.
Kinetics of radical‐molecule reactions in aqueous solution: A benchmark study of the performance of density functional methods
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The performance of 18 density functional approximations has been tested for a very challenging task, the calculations of rate constants for radical‐molecule reactions in aqueous solution. Despite of the many difficulties involved in such an enterprise, six of them provide high quality results, and are recommended to that purpose. They are LC‐ωPBE, M06‐2X, BMK, B2PLYP, M05‐2X, and MN12SX, in that order. This trend was obtained using experimental data as reference. The other relevant aspects used in this benchmark are: (i) the SMD model for mimicking the solvent; (ii) the conventional transition state, the zero‐curvature tunneling correction, and the limit imposed by diffusion for the calculation of the rate constants. Even though changing any of these aspects might alter the trend in performance, at least, when using them, the aforementioned functionals can be successfully used to obtain high quality kinetic data for the kind of reactions investigated in this work. © 2014 Wiley Periodicals, Inc. 相似文献