共查询到20条相似文献,搜索用时 15 毫秒
1.
Bidyut Guha Thakurta 《Proceedings Mathematical Sciences》1986,95(1):53-59
In this paper, Weisner’s group-theoretic method of obtaining generating functions is utilized in the study of Jacobi polynomialsP> n (a,ß)(x) by giving suitable interpretations to the index (n) and the parameter (β) to find out the elements for constructing a six-dimensional Lie algebra. 相似文献
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A class of bent functions which contains bent functions with various properties like regular, weakly regular and not weakly regular bent functions in even and in odd dimension, is analyzed. It is shown that this class includes the Maiorana–McFarland class as a special case. Known classes and examples of bent functions in odd characteristic are examined for their relation to this class. In the second part, normality for bent functions in odd characteristic is analyzed. It turns out that differently to Boolean bent functions, many – also quadratic – bent functions in odd characteristic and even dimension are not normal. It is shown that regular Coulter–Matthews bent functions are normal. 相似文献
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This paper provides a new approach to study the solutions of a class of generalized Jacobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n + 1.A new class of generalized differential operators is defined.We investigate the kernel of the corresponding maximal operators by applying operator theory.It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic,in which there are n dimension solutions with exponential... 相似文献
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It is shown that parametric linear programming algorithms work efficiently for a class of nonconvex quadratic programming problems called generalized linear multiplicative programming problems, whose objective function is the sum of a linear function and a product of two linear functions. Also, it is shown that the global minimum of the sum of the two linear fractional functions over a polytope can be obtained by a similar algorithm. Our numerical experiments reveal that these problems can be solved in much the same computational time as that of solving associated linear programs. Furthermore, we will show that the same approach can be extended to a more general class of nonconvex quadratic programming problems. 相似文献
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In this paper, the reproduction of trigonometric polynomials with two-overlapping local cosine bases is investigated. This study is motivated by the need to represent most effectively a Fourier series in the form of a localized cosine series for the purpose of local analysis, thus providing a vehicle for the transition from classical harmonic analysis to analysis by Wilson-type wavelets. It is shown that there is one and only one class, which is a one-parameter family, of window functions that allows pointwise reproduction of all global harmonics, where the parameter is the order of smoothness of the window functions. It turns out that this class of window functions is also optimal in the sense that all global harmonics are reproduced by using a minimal number of the local trigonometric basis functions. 相似文献
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A class of penalty functions for solving convex programming problems with general constraint sets is considered. Convergence theorems for penalty methods are established by utilizing the concept of infimal convergence of a sequence of functions. It is shown that most existing penalty functions are included in our class of penalty functions. 相似文献
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This paper is concerned with obtaining the approximate solution of a class of semi-explicit Integral Algebraic Equations (IAEs) of index-2. A Jacobi collocation method including the matrix-vector multiplication representation is proposed for the IAEs of index-2. A rigorous analysis of error bound in weighted L2 norm is also provided which theoretically justifies the spectral rate of convergence while the kernels and the source functions are sufficiently smooth. Results of several numerical experiments are presented which support the theoretical results. 相似文献
11.
Oleg Khamisov 《Journal of Global Optimization》1999,14(1):79-101
We give a definition of the class of functions with a concave minorant and compare these functions with other classes of functions often used in global optimization, e.g. weakly convex functions, d.c. functions, Lipschitzian functions, continuous and lower semicontinuous functions. It is shown that the class of functions with a concave minorant is closed under operations mainly used in optimization and how a concave minorant can be constructed for a given function. 相似文献
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Nonconvex functions and variational inequalities 总被引:8,自引:0,他引:8
M. A. Noor 《Journal of Optimization Theory and Applications》1995,87(3):615-630
In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and arc-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm. 相似文献
14.
John A. Ewell 《Proceedings of the American Mathematical Society》1998,126(2):421-423
An identity involving eight-fold infinite products, first derived by Jacobi in his theory of theta functions, is the subject of this note. Three similar identities, including one that implies Jacobi's identity, are presented.
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We continue the study of the regularity of electronic wave functions in Hilbert spaces of mixed derivatives. It is shown that the eigenfunctions of electronic Schr?dinger operators and their exponentially weighted counterparts possess, roughly speaking, square integrable mixed weak derivatives of fractional order ${\vartheta}$ for ${\vartheta < 3/4}$ . The bound 3/4 is best possible and can neither be reached nor surpassed. Such results are important for the study of sparse grid-like expansions of the wave functions and show that their asymptotic convergence rate measured in terms of the number of ansatz functions involved does not deteriorate with the number of electrons. 相似文献
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This paper analyzes portfolio diversification for nonlinear transformations of heavy-tailed risks. It is shown that diversification of a portfolio of convex functions of heavy-tailed risks increases the portfolio’s riskiness if expectations of these risks are infinite. In contrast, for concave functions of heavy-tailed risks with finite expectations, the stylized fact that diversification is preferable continues to hold. The framework of transformations of heavy-tailed risks includes many models with Pareto-type distributions that exhibit local or moderate deviations from power tails in the form of additional slowly varying or exponential factors. The class of distributions under study is therefore extended beyond the stable class. 相似文献
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给出一类有理幂函数其积分为对数函数的判别式和计算方法,使得此类看上去其计算十分复杂的函数的积分变得容易.方法本身也具有可操作性,可在微积分的教学中引入. 相似文献
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Sándor Komlósi 《Mathematical Programming》1983,26(2):232-237
It is shown that certain theorems concerning differentiable pseudoconvex functions can be extended to a class of nondifferentiable pseudoconvex functions that was defined with help of the Dini-derivative by Diewert recently. 相似文献
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Symmetries and solutions to the thin film equations 总被引:1,自引:0,他引:1
Changzheng Qu 《Journal of Mathematical Analysis and Applications》2006,317(2):381-397
We study symmetries and solutions of the generalized fourth-order nonlinear partial differential equations which arise from studies of thin liquid films. It is shown that the equations admit extended scaling and rotation symmetries and a class of generalized conditional symmetries for certain coefficient functions. Exact solutions associated to the symmetries are obtained. 相似文献
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In this paper, we give a new definition for the space of non-holomorphic Jacobi Maaß forms (denoted by J k,m nh ) of weight k∈? and index m∈? as eigenfunctions of a degree three differential operator \(\mathcal{C}^{k,m}\). We show that the three main examples of Jacobi forms known in the literature: holomorphic, skew-holomorphic and real-analytic Eisenstein series, are contained in J k,m nh . We construct new examples of cuspidal Jacobi Maaß forms F f of weight k∈2? and index 1 from weight k?1/2 Maaß forms f with respect to Γ0(4) and show that the map f ? F f is Hecke equivariant. We also show that the above map is compatible with the well-known representation theory of the Jacobi group. In addition, we show that all of J k,m nh can be “essentially” obtained from scalar or vector valued half integer weight Maaß forms. 相似文献