The purpose of this paper is to determine the b-functions of all the prehomogeneous vector spaces associated to nilpotent orbits in the Dynkin-Kostant theory for all the complex simple algebraic groups of exceptional ...
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The purpose of this paper is to determine the b-functions of all the prehomogeneous vector spaces associated to nilpotent orbits in the Dynkin-Kostant theory for all the complex simple algebraic groups of exceptional type. Our method to calculate b-functions is based on the structure theorem for b-functions of several variables and the functional equations for them.
The purpose of this paper is to compute the explicit form of the relative invariants and their b-functions of a certain important prehomogeneous vector space appearing in the study of a cuspidal character sheaf of the...
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The purpose of this paper is to compute the explicit form of the relative invariants and their b-functions of a certain important prehomogeneous vector space appearing in the study of a cuspidal character sheaf of the exceptional group E-7. For every simple algebraic group excepting the type E-7, the b-functions of this kind of prehomogeneous vector space have been determined. (C) 2001 Academic Press.
The evaluation of nuclear attraction integrals with certain exponential-type orbitals (ETO's), the bfunctions [E. Filter and E.O. Steinborn, Phys. Rev. A 18 (1978) 1] has been programmed. The programs are based o...
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The evaluation of nuclear attraction integrals with certain exponential-type orbitals (ETO's), the bfunctions [E. Filter and E.O. Steinborn, Phys. Rev. A 18 (1978) 1] has been programmed. The programs are based on a number of relatively compact general formulas for molecular integrals with bfunctions. These formulas can be derived using the Fourier transform method. bfunctions are particularly well suited for this method because they possess a very simple Fourier transform. Other ETO's like Slater-type orbitals (STO's) can be expressed as a finite linear combination of bfunctions. Hence, molecular integrals for other ETO's can be written as finite sums of integrals with bfunctions.
Recently, extensive calculations have been made on b-functions of prehomogeneous vector spaces with reducible representations. by examining the results of these calculations, we observe that b-functions of a large num...
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Recently, extensive calculations have been made on b-functions of prehomogeneous vector spaces with reducible representations. by examining the results of these calculations, we observe that b-functions of a large number of reducible prehomogeneous vector spaces have decompositions which seem to be correlated to the decomposition of representations. In the present;paper, we show that such phenomena can be ascribed to a certain multiplicity one property for group actions on polynomial rings. Furthermore, we give some criteria for the multiplicity one property. Our method can be applied equally to non-regular prehomogeneous vector spaces.
In this paper we evaluate a new Estimation of Distribution Algorithm (EDA) constructed on top of a very successful bayesian network learning procedure, Max-Min Hill-Climbing (MMHC). The aim of this paper is to check w...
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ISBN:
(纸本)9783030011321;9783030011314
In this paper we evaluate a new Estimation of Distribution Algorithm (EDA) constructed on top of a very successful bayesian network learning procedure, Max-Min Hill-Climbing (MMHC). The aim of this paper is to check whether the excellent properties reported for this algorithm in machine learning papers, have some impact on the efficiency and efficacy of EDA based optimization. Our experiments show that the proposed algorithm outperform wellknown state of the art EDA like bOA and EbNA in a test bed based on b-functions. On the basis of these results we conclude that the proposed scheme is a promising candidate for challenging real-world applications, specifically, problems related to the areas of Data Mining, Patter Recognition and Artificial Intelligence.
An algorithm for computing comprehensive Grobner systems (CGS) is introduced in rings of linear partial differential operators. Their applications to b-functions are considered. The resulting algorithm designed for a ...
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ISBN:
(纸本)9781450343800
An algorithm for computing comprehensive Grobner systems (CGS) is introduced in rings of linear partial differential operators. Their applications to b-functions are considered. The resulting algorithm designed for a wide use of computing comprehensive Grobner systems can be used to compute all the roots of b-functions and relevant holonomic D-modules. Furthermore, with our implementation, effective methods are illustrated for computing holonomic D-modules associated with hypersurface singularities. It is shown that the proposed algorithm is full of versatility.
We consider dual coordinate ascent methods for minimizing a strictly convex (possibly nondifferentiable) function subject to linear constraints. Such methods are useful in large-scale applications (e.g., entropy maxim...
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We consider dual coordinate ascent methods for minimizing a strictly convex (possibly nondifferentiable) function subject to linear constraints. Such methods are useful in large-scale applications (e.g., entropy maximization, quadratic programming, network flow), because they are simply, can exploit sparsity and in certain cases are highly parallelizable. We establish their global convergence under weak conditions and a free-steering order of relaxation. Previous comparable results were restricted to special problems with separable costs and equality constraints. Our convergence framework unifies to a certain extent the approaches of bregman. Censor and Lent, De Pierro and lusem, and Luo and Tseng, and complements that of bertsekas and Tseng.
We present a method for finding common points of finitely many closed convex sets in Euclidean space. The bregman extension of the classical method of cyclic orthogonal projections employs nonorthogonal projections in...
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We present a method for finding common points of finitely many closed convex sets in Euclidean space. The bregman extension of the classical method of cyclic orthogonal projections employs nonorthogonal projections induced by a convex bregman function, whereas the bauschke and borvein method uses bregman/Legendre functions. Our method works with generalized bregman functions (b-functions) and inexact projections, which are easier to compute than the exact ones employed in other methods. We also discuss subgradient algorithms with bregman projections.
We apply a recent extension of the bregman proximal method for convex programming to LP relaxations of 0-1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successive...
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We apply a recent extension of the bregman proximal method for convex programming to LP relaxations of 0-1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successively to retain global convergence. Our framework is applied to relaxations of large-scale set covering problems that arise in airline crew scheduling. Approximate relaxed solutions are used to construct primal feasible solutions via a randomized heuristic. Encouraging preliminary experience is reported.
We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that oc...
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We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of b-functions (generalized bregman functions).
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