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物理化学学报 2018年第6期34卷 650-655页

作者： FINZEL Kati BULTINCK Patrick Department of Inorganic and Physical Chemistry Ghent University 281 Krijgslaan 9000 Ghent Belgium.

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each *** aspect is first derived in an orbital-free *** is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each *** numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic *** numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few *** chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total ***,the effect on the bond dissociation curve was studied exemplarily for the carbon *** data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond ***,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.

关键词： The Influence of the Exchange-Correlation Functional the Non-Interacting Kinetic Energy Density Functional approximations

GENERAL FULL IMPLICIT STRONG TAYLOR approximations FOR STIFF STOCHASTIC DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2022年第4期40卷 541-569页

作者： Kai Liu Guiding Gu School of Mathematics Shanghai University of Finance and EconomicsShanghai 200433China College of Science Hunan University of Technology and BusinessChangsha 410205China

In this paper,we present the backward stochastic Taylor expansions for a Ito process,including backward Ito-Taylor expansions and backward Stratonovich-Taylor *** construct the general full implicit strong Taylor approximations(including Ito-Taylor and Stratonovich-Taylor schemes)with implicitness in both the deterministic and the stochastic terms for the stiff stochastic differential equations(SSDE)by employing truncations of backward stochastic Taylor *** demonstrate that these schemes will converge strongly with corresponding order 1,2,3,....Mean-square stability has been investigated for full implicit strong Stratonovich-Taylor scheme with order 2,and it has larger meansquare stability region than the explicit and the semi-implicit strong Stratonovich-Taylor schemes with order *** can improve the stability of simulations considerably without too much additional computational effort by using our full implicit *** full implicit strong Taylor schemes allow a larger range of time step sizes than other schemes and are suitable for SSDE with stiffness on both the drift and the diffusion *** numerical experiment show these points.

关键词： Stiff stochastic differential equations approximations Backward Stochastic Taylor expansions Full implicit Taylor methods

Improved Analytical approximations to the Scattering Solutions of the Schrdinger Equation with a Hyperbolical Potential

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Communications in Theoretical Physics 2014年第9期61卷 315-319页

作者：尤源陆法林孙东升陈昌远 School of Physics and Electronics Yancheng Teachers University

Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalized wavefunctions are presented. All data calculated by the above approximate analytical formula are compared with those obtained by using the numerical integration method in the scattering state cases. We find that this improved approximate formula is better than previous one since the calculated results are in good agreement with those exact ones.

关键词： hyperbolic potential scattering solutions analytical approximations

Rational and algebraic approximations of algebraic numbers and their application

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Science China Mathematics 1997年第10期40卷 1045-1051页

作者：袁平之 Department of Mathematics and Mechanics Changsha Railway InstituteChangsha 410075China Department of Mathematics Sichuan UniversityChengdu 610064China

Effective rational and algebraic approximations of a large class of algebraic numbers are obtained by Thue-Siegel's *** an application of this result,it is proved that; if D>0 is not a square,and ε=x0 +y0 D denotes the fundamental solution of x2-Dy2=-1,then x2+1=Dy4 is solvable if and only if y0=A2 where A is an ***,if ≥64,then x2+1=Dy4 has at most one positive integral solution (x,y).

关键词： hypergeometric functions diophantine approximations imaginary quadratic fields quartic equations.

Generalized multi-layered granulations and approximations based on neighborhood systems under incomplete information systems

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Journal of Harbin Institute of Technology(New Series) 2005年第2期12卷 205-208页

作者：何明冯博琴 Dept. of Computer Science and Technology Xian Jiaotong University Xian 710049 China

A generalized multi-layered granulation structure used by neighborhood systems is proposed. With granulated views, the concepts of approximations under incomplete information systems are studied, which are represented by covering of the universe. With respect to different levels of granulations, a pair of lower and upper approximations is defined and an approximation structure is investigated, which lead to a more general approximation structure. The generalized multi-layered granulation structure provides a basis of the proposed framework of granular computing. Using this framework, the interesting and useful results about information granulation and approximation reasoning can be obtained. This paper presents some useful explorations about the incomplete information systems from information views.

关键词： rough set approximations neighborhood systems granular computing

A Study of Weighted Polynomial approximations with Several Variables (II)

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Applied Mathematics 2017年第9期8卷 1239-1256页

作者： Ryozi Sakai Department of Mathematics Meijo University Tenpaku-ku Nagoya Japan

In this paper we investigate weighted polynomial approximations with several variables. Our study relates to the approximation for by weighted polynomial. Then we will give some results relating to the Lagrange interp... 详细信息

关键词： Weighted Polynomial approximations the Lagrange Interpolation the Best of Approximation Inequalities

Method of Successive approximations for a Fluid Structure Interaction Problem

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Applied Mathematics 2014年第15期5卷 2299-2304页

作者： Aliou Gueye Sow Ibrahima Mbaye Department of Mathematics University of Thies Thies Senegal

In this paper, we present a method for solving coupled problem. This method is mainly based on the successive approximations method. The external force acting on the structure is replaced by λ = p (x1, H + u (x1, λ)). Then we have a nonlinear equation of unknown?λ to solve by successive approximations method. By this method, we obtain easily the analytic expression of the displacement. In addition, good results are obtained with only a few iterations.

关键词： Beam Equation Stokes Equation Finite Elements Method Successive approximations Method

One Approach to Construction of Bilateral approximations Methods for Solution of Nonlinear Eigenvalue Problems

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American Journal of Computational Mathematics 2012年第2期2卷 118-124页

作者： Bohdan Mykhajlovych Podlevskyi Institute of Applied Problems of Mechanics & Mathematics National Academy of Sciences of Ukraine Lviv Ukraine

In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterat... 详细信息

关键词： Nonlinear Eigenvalue Problem Derivatives of Matrix Determinant Numerical Algorithm of Alternate approximations

γ and β approximations via General Ordered Topological Spaces

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Applied Mathematics 2016年第14期7卷 1580-1588页

作者： Mohamed Abo-Elhamayel Mathematics Department Faculty of Science Mansoura University Mansoura Egypt

In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ordered topological approximation spaces (GOTAS, for short). Some important properties of them were investigated. From this study, we can say that studying any properties of rough set concepts via GOTAS is a generalization of Pawlak approximation spaces and general approximation spaces.

关键词： Rough Sets approximations Ordered Topological Spaces

Anisotropy measurements and characterization of the Qingshankou shale

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APPLIED GEOPHYSICS 2024年第3期21卷 468-478页

作者： Li, Qing-feng Yan, Xue-hong Yan, Wei-lin Ren, Li Wang, Peng Han, Jian-qiang Xia, Xue Chen, Hao Daqing Oilfield Explorat Div Daqing 163000 Heilongjiang Peoples R China CNPC Logging Daqing Branch Co Daqing 163000 Heilongjiang Peoples R China Daqing Oilfield Co Ltd Explorat & Dev Res Inst Daqing 163712 Peoples R China Chinese Acad Sci Inst Acoust State Key Lab Acoust Beijing 100190 Peoples R China

Qingshankou shale (Gulong area, China) exhibits strong acoustic anisotropy characteristics, posing significant challenges to its exploration and development. In this study, the five full elastic constants and multipole response law of the Qingshankou shale were studied using experimental measurements. Analyses show that the anisotropy parameters & varepsilon; and gamma in the study region are greater than 0.4, whereas the anisotropy parameter delta is smaller, generally 0.1. Numerical simulations show that the longitudinal and transverse wave velocities of these strong anisotropic rocks vary significantly with inclination angle, and significant differences in group velocity and phase velocity are also present. Acoustic logging measures the group velocity in dipped boreholes; this differs from the phase velocity to some extent. As the dip angle increases, the longitudinal and SH wave velocities increase accordingly, while the qSV-wave velocity initially increases and then decreases, reaching its maximum value at a dip of approximately 40 degrees. These results provide an effective guide for the correction and modeling of acoustic logging time differences in the region.

关键词： Transverse isotropy anisotropy parameter sonic logging group velocity phase velocity WAVE-PROPAGATION INVERSION PARAMETERS approximations VELOCITIES FIELD