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61.
The notions of exhausters were introduced in (Demyanov, Exhauster of a positively homogeneous function, Optimization 45, 13–29
(1999)). These dual tools (upper and lower exhausters) can be employed to describe optimality conditions and to find directions
of steepest ascent and descent for a very wide range of nonsmooth functions. What is also important, exhausters enjoy a very
good calculus (in the form of equalities). In the present paper we review the constrained and unconstrained optimality conditions
in terms of exhausters, introduce necessary and sufficient conditions for the Lipschitzivity and Quasidifferentiability, and
also present some new results on relationships between exhausters and other nonsmooth tools (such as the Clarke, Michel-Penot
and Fréchet subdifferentials). 相似文献
62.
Chun-fa Li Xue Yang En-min Feng 《应用数学学报(英文版)》2008,24(1):29-40
In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified. 相似文献
63.
Jianxun Hu 《Compositio Mathematica》2001,125(3):345-352
In this paper, using the gluing formula of Gromov–Witten invariants for symplectic cutting developed by Li and Ruan, we established some relations between Gromov–Witten invariants of a semipositive symplectic manifold M and its blow-ups along a smooth surface. 相似文献
64.
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems.
We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems
which involve the Chern and Lagrange class. Our approach, which uses simple ideas from differential geometry and algebraic
topology, reveals the fundamental role of the integer affine structure on the base space of these bundles. We provide a geometric
proof of the classification of Lagrangian bundles with fixed integer affine structure by their Lagrange class.
相似文献
65.
将摄动配置方法应用到含时薛定谔方程,在计算实现的基础上结合摄动配置的特征提出了一类新的数值积分方法,并给出了一个2级2阶和一个3级4阶的辛摄动配置方法对含时薛定谔方程的数值算例.为了检验新的数值积分方法,我们还给出了与两个辛摄动配置格式在理论上等价的辛龙格-库塔方法以及同阶的非辛方法的数值模拟.展示了一些数值结果,并给出了一些分析. 相似文献
66.
L. Chierchia 《Regular and Chaotic Dynamics》2008,13(2):130-139
Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of
integrable Hamiltonian systems by including few “straightforward” estimates.
相似文献
67.
Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single
individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic
GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
68.
We continue the study of G. Castelnuovo on the group of birational transformations of the complex plane that fix each point
of a curve of genus > 1 ; we use adjoint linear system of the curve as Castelnuovo does. We prove that these groups are abelian,
and that these are either finite, of order 2 or 3, or conjuguate to a subgroup of the de Jonquières group. We show also that
these results do not generalise to curves of genus ≤ 1.
*Partiellement soutenu par le CNPq-Brasil et la Section de Mathématiques de l'Université de Genève. 相似文献
69.
本文给出四阶整数辛群中扭元的全部共轭等价类.总共有55个不同的扭元等价类,它们的阶数分别是2, 3, 4, 5, 6, 8, 10, 12.没有其它阶的扭元. 相似文献
70.
This paper is concerned with a second-order numerical method for shape optimization problems. The first variation and the second variation of the objective functional are derived. These variations are discretized by introducing a set of boundary-value problems in order to derive the second-order numerical method. The boundary-value problems are solved by the conventional finite-element method.The authors would like to express their thanks to Mr. T. Masanao, who was an undergraduate student, for his cooperation and comments. They also thank Professor Y. Sakawa of Osaka University for his encouragement.A part of this paper was presented at the IFIP Conference on Control of Boundaries and Stabilization, Clermont-Ferrand, France, 1988. 相似文献