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排序方式: 共有1865条查询结果,搜索用时 31 毫秒
31.
32.
Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x
n)}, where {x
n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper. 相似文献
33.
R. L. Dobrushin A. Pellegrinotti Yu. M. Suhov L. Triolo 《Journal of statistical physics》1988,52(1-2):423-439
The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived. 相似文献
34.
New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras
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Yan Han & Shaoyuan Xu 《分析论及其应用》2022,38(3):335-350
In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the
mappings should be continuous. Furthermore, the existence and the uniqueness of the
fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples
and an application are given to support our new results. 相似文献
35.
T. Iwaniec M. Mitrea C. Scott 《Proceedings of the American Mathematical Society》1996,124(5):1467-1471
We prove a bound for the -norm of harmonic forms in terms of certain -norms of their normal and tangential components. In turn, this is used to show the -norm equivalence of the normal and tangential components of harmonic forms on manifolds.
36.
R. A. Poliquin R. T. Rockafellar 《Transactions of the American Mathematical Society》1996,348(5):1805-1838
The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.
37.
C. S. Hsu 《Journal of Optimization Theory and Applications》1985,46(4):547-569
A discrete method of optimal control is proposed in this paper. The continuum state space of a system is discretized into a cell state space, and the cost function is discretized in a similar manner. Assuming intervalwise constant controls and using a finite set of admissible control levels (u) and a finite set of admissible time intervals (), the motion of the system under all possible interval controls (u, ) can then be expressed in terms of a family of cell-to-cell mappings. The proposed method extracts the optimal control results from these mappings by a systematic search, culminating in the construction of a discrete optimal control table.The possibility of expressing the optimal control results in the form of a control table seems to give this method a means to make systems real-time controllable.Dedicated to G. LeitmannThe material is based upon work supported by the National Science Foundation under Grant No. MEA-82-17471. The author is also indebted to Professor G. Leitmann for his many helpful comments. 相似文献
38.
Dieter H. Mayer 《Journal of statistical physics》1985,38(3-4):785-803
We derive universal scaling properties for k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered. 相似文献
39.
C. Le Van 《Journal of Optimization Theory and Applications》1980,30(1):33-44
We define the degree of a family of convex functionsf
x, wherex
, and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points. 相似文献
40.
Teobald Kupka Roman Wrzalik Gra
yna Pasterna Karol Pasterny 《Journal of Molecular Structure》2002,616(1-3):17-32
The results of extended MO calculations using density functional theory (DFT) approximation supported by experimental Raman, 1H and 13C NMR studies on thiophene are reported. Raman spectra of liquid thiophene were re-examined and the performance of a hybrid B3PW91 density functional was compared with the ab initio restricted Hartree–Fock (RHF) method. With the basis sets of the 6-311++G** quality, the DFT calculated bond lengths, dipole moments and harmonic vibrations were predicted in a very good agreement with available experimental data.
Additionally, the results on thiophene were extended by calculations on 3-methylthiophene and selenophene. In this case, a significant change in geometry and charge distribution in thiophene ring due to a methyl group substituent or replacement of sulphur by selene atom was observed.
A linear correlation between the predicted harmonic vibrational frequencies (scaled using SQM method) and experimental ones for thiophene, selenophene and 3-methylthiophene was shown. The theoretically calculated spectra have satisfactorily reproduced the available experimental spectra for thiophene and selenophene. 相似文献