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101.
We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. Ideal nondegeneracy at a local minimizer is taken to mean satisfaction of second order sufficient conditions, linear independence and strict complimentary slackness. Following a brief exploration of the relationship of these conditions with the classical definition of nondegeneracy in linear programming, we recall a number of optimality and regularity conditions used to attempt to resolve degeneracy and survey results of Fiacco, McCormick, Robinson, Kojima, Gauvin and Janin, Shapiro, Kyparisis and Liu. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.Research supported by National Science Foundation Grant ECS 90-00560 and Grant N00014-89-J-1537 Office of Naval Research 相似文献
102.
The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed.
After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations
of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion
of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations
of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total
trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding
Heisenberg equations.
Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph.
D. Directing Programme of Chinese University, and the Chinese Academy of Sciences. 相似文献
103.
We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy. 相似文献
104.
Tom Kennedy 《Journal of statistical physics》1990,59(1-2):195-220
A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for0.77
critical. 相似文献
105.
We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation. 相似文献
106.
107.
The oscillating conditions for a series piezoelectric quartz crystal (SPQC) are proposed and verified experimentally. The influence of the cell constant and oscillator phase on the oscillational ability of the SPQC was investigated. It is shown that the SPQC possesses excellent oscillational ability in low or high conductivity solutions, but in solution of intermediate conductivity, the oscillational ability decreases with increasing oscillator phase or decreasing cell constant, sometimes resulting in a cease-to-oscillate zone. The SPQC was applied to determine the urease activity in plant seeds with a detection limit of 0.004 U ml−1, based on the change in conductivity. 相似文献
108.
Bao Gia Nguyen 《Journal of statistical physics》1987,49(1-2):235-243
A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by
t
=2 fort=2, 3,. Scaling theory predicts thatP
p
(¦C
0¦S(p))–(p
c
–p) andE
p
(1/¦C
0¦; ¦C
0¦S(p))–(p
c
–p)3, whereS(p) is the typical cluster size. It is found that (p
c
–p)P
p
(|C
0S(p)
1–)(p
c
–p)1–2 and (p
c
–p)3E
p
(1/|C
0|;|C
0|S(p)
1–))(p
c
–p)3–4. 相似文献
109.
Microgel-like poly(allyl methacrylate) (PAMA nanosphere) was prepared by the emulsion polymerization of AMA as the reactive crosslinked polymer nanosphere with abundant pendant allyl groups. The terpolymerization of PAMA nanosphere with allyl benzoate (ABz) and vinyl benzoate (VBz) was conducted in bulk using benzoyl peroxide as initiator at 80 °C. The gelation depended on the feed ABz/VBz molar ratio since the molecular weights of resulting poly(ABz-co-VBz)s that act as the bridges increased with an increase in the mole fraction of VBz in the feed monomer. Beyond the gel point, the sol was rapidly incorporated into the gel and the increasing tendency of the gel fraction became steeper from 70 to 95 mol% of VBz as a reflection of increased chain length of bridge between PAMA nanospheres. Moreover, the swelling ratio became lower with increasing the mole percentage of VBz in the feed monomer. These results would support the preferential incorporation of PAMA nanosphere into the gel and the longer bridge can capture more nanospheres to give a much shrunken gel. 相似文献
110.