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41.
Pham Duy Khanh Tran Hong Mo Trinh T. T. Tran 《Numerical Functional Analysis & Optimization》2019,40(8):924-943
Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example. 相似文献
42.
Stevo Stevi&#x; Bratislav Iri
anin Witold Kosmala Zden k &#x;marda 《Mathematical Methods in the Applied Sciences》2019,42(5):1687-1701
Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal. 相似文献
43.
《Mathematische Nachrichten》2018,291(8-9):1240-1268
In this work we deal with solvability of first‐order differential equations in the form , where L is a planar complex vector field, elliptic everywhere except along a simple closed curve Σ on which it is tangent and vanishes of order . In contrast with the local solvability, it is shown that the zero order term p has influence in the solvability in a full neighborhood of Σ. 相似文献
44.
A. Shabanskaya 《代数通讯》2018,46(11):5006-5031
For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type ?2 introduced by Camacho, Gómez, González and Omirov, all possible right and left solvable indecomposable extensions over the field ? are constructed so that the algebra serves as the nilradical of the corresponding solvable Leibniz algebras we find in the paper. 相似文献
45.
Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result. 相似文献
46.
In this paper quasi-exact solvability(QES)of Dirac equation with some scalar potentials based on sl(2)Lie algebra is studied.According to the quasi-exact solvability theory,we construct the configuration of the classes II,IV,V,and X potentials in the Turbiner’s classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions. 相似文献
47.
Sandor Kristyan 《International journal of quantum chemistry》2013,113(10):1479-1492
The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a nonlinear, approximate density functional of a three spatial dimension one‐electron density for an N electron system which is tractable in practice, is a long‐desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital‐free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree–Fock (HF) and Kohn–Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi( r 1)gk( r 2)rd r 1d r 2, etc.) to estimate electron‐electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation. © 2012 Wiley Periodicals, Inc. 相似文献
48.
49.
Our purpose is to describe the properties of the class of n×n matrices such that some or all of the signs of the nonzero elements of the inverse matrix can be determined based only upon the knowledge of the signs of the matrix being inverted. Applications of such matrices can be found in the study of the testibility of economic theory, the stability of economic systems and the general ‘quality’ of solutions to large computer models. 相似文献
50.
当非线性项奇异和无穷远处的极限增长函数存在时,考察了一类二阶拟线性边值问题．通过引入非线性项在有界集合上的高度函数,并且考察高度函数的积分,证明了一个解的存在定理．该定理表明当极限增长函数的积分具有适当值时此问题有一个解． 相似文献