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41.
Chang-jian Zhao 《中国科学A辑(英文版)》2007,50(9):1347-1360
In this paper, we first introduce a concept of L
p
-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar
projection Aleksandrov-Fenchel inequality for L
p
-dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L
p
-Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results.
This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial
Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of
China (Grant No. 20050392) 相似文献
42.
The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications. 相似文献
43.
We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures
multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which
three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions
of the spectrum.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007. 相似文献
44.
New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values 总被引:1,自引:1,他引:0
N. A. Sokolov 《Computational Mathematics and Mathematical Physics》2007,47(12):1952-1969
New variants of the generalized level method for minimization of convex Lipschitz functions on a compact set with a nonempty interior are proposed. These variants include the well-known generalized and classical level methods. For the new variants, an estimate of the convergence rate is found, including the variants in which the auxiliary problems are solved approximately. 相似文献
45.
Xin Tao YE Chong LI 《数学学报(英文版)》2007,23(1):65-76
The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided. 相似文献
46.
47.
48.
Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search. 相似文献
49.
In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings. 相似文献
50.
C. Zălinescu 《Mathematical Methods of Operations Research》1991,35(4):291-298
In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems. 相似文献