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121.
The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm
must be isomorphic toW(m,n, 1) if the dimension ofG
i satisfies a certain condition.
Project supported by the National Natural Science Foundation of China and the Science of the University Doctoral Program of
CNEC. 相似文献
122.
Hayato Nawa 《Journal of statistical physics》1998,91(1-2):439-458
We consider the blow-up problem for the nonlinear Schrödinger equation with quartic self-interacting potential on
. We exhibit a class of initial data leading to the blow-up solutions which have at least two L
2-concentration points. 相似文献
123.
Given a finitely generated restricted Lie algebra L over the finite field \(\mathbb{F}_q \), and n ≥ 0, denote by a n (L) the number of restricted subalgebras H ? L with \(\dim _{\mathbb{F} _q} \) L/H = n. Denote by ã n (L) the number of the subalgebras satisfying the maximality condition as well. Considering the free restricted Lie algebra L = F d of rank d ≥ 2, we find the asymptotics of ã n (F d ) and show that it coincides with the asymptotics of a n (F d ) which was found previously by the first author. Our approach is based on studying the actions of restricted algebras by derivations on the truncated polynomial rings. We establish that the maximal subalgebras correspond to the so-called primitive actions. This means that “almost all” restricted subalgebras H ? F d of finite codimension are maximal, which is analogous to the corresponding results for free groups and free associative algebras. 相似文献
124.
125.
Edmund I. Zverovich 《Complex Analysis and Operator Theory》2008,2(4):709-732
In this paper, we present a general solution of the scalar Riemann problem on a closed Riemann surface in the case of a compound
contour in the class of piecewise meromorphic functions multiple of a given divisor. All the results are known and belong
to the author [15–17], except for the existence theorems and properties of basic functionals and also properties of a θ-function.
The solution of the problem in a ‘special case’ has been announced by the author but not published [15]. Similar problems
and some applications are considered in [1, 2, 12].
The main results of the paper were obtained by the author during his collaboration with Professor G. S. Litvinchuk, and this
paper is devoted to his cherished memory.
Received: April 13, 2007. Accepted: June 13, 2008. 相似文献
126.
A new two‐phase structure‐preserving doubling algorithm for critically singular M‐matrix algebraic Riccati equations 下载免费PDF全文
Tsung‐Ming Huang Wei‐Qiang Huang Ren‐Cang Li Wen‐Wei Lin 《Numerical Linear Algebra with Applications》2016,23(2):291-313
Among numerous iterative methods for solving the minimal nonnegative solution of an M‐matrix algebraic Riccati equation, the structure‐preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank‐one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank‐one component can be accurately recovered. We then propose an efficient hybrid method, called the two‐phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two‐phase SDA saves those SDA iterative steps that previously have to have for the rank‐one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two‐phase SDA. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
127.
Simplified Box Orbitals (SBO) for H To Ar atoms: Exact expressions,SBO‐3G approximations,and relations with the ZDO approximation 下载免费PDF全文
Victor García David Zorrilla Jesús Sánchez‐Márquez Manuel Fernández‐Núñez 《International journal of quantum chemistry》2016,116(17):1303-1312
Simplified Box Orbitals (SBO) are a kind of spatially restricted basis functions. SBOs have a similar use and value to Slater functions but, because they fulfill a version of the zero‐differential overlap approximation, they allow for a drastic reduction in the number of two‐electron integrals to be calculated when dealing with huge systems, and they seem to be specially adapted to study confined systems such as molecules in solution. In a previous study, the mathematical shape of SBOs was discussed and the necessary parameters were obtained by means of the variational method. In the present study, the parameters of each SBO were obtained by applying the condition that it is as similar as possible to the STO that would be used in a basis set without spatial restrictions. We have developed a method to achieve this likeness and deduced simple formulas to describe all the SBOs of any atom. We also present the SBO‐3G expansions of the SBOs obtained, making it possible to use these SBOs with standard quantum chemistry calculation software. Simple formulas were also deduced to directly write the SBOs and SBO‐3G corresponding to the atoms with a Z value of between 1 and 18. Finally, as a first example of the usefulness of this kind of functions, an optimized SBO‐3G basis set is proposed for atoms from H to Cl in molecules. © 2016 Wiley Periodicals, Inc. 相似文献
128.
In this article, the topic of "chemical principles in warmer pad" is used as an example to illustrate how problem-based learning (PBL) and case learning (CL) are used in the teaching of general chemistry. We take the advantages of PBL to arouse the studying interests of students in the casing learning atmosphere. Moreover, the teacher leads the discussion. By using these two teaching methods properly, students' active learning ability, the skills of analyzing and solving problems, as well as the comprehensive practical ability can be improved. 相似文献
129.
130.
Yuji Liu 《Journal of Mathematical Analysis and Applications》2007,327(2):801-815
Sufficient conditions for the existence of at least one T-periodic solution of nonlinear functional difference equation
Δx(n)+a(n)x(n)=f(n,u(n)), 相似文献