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121.
O. Naselli 《Journal of Optimization Theory and Applications》1996,91(1):81-90
In this paper, we present a class of functions:f:X such that inf
xX
f(x)=
, whereX is a nonempty, finitely compact and convex set in a vector space andB
x
={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1). 相似文献
122.
123.
(磁)流体波动力学问题的近似求解─参数微分法 总被引:1,自引:1,他引:0
针对非线性物理如等离子体物理、流体力学、大气科学等领域中信受人们关注的两类摄动问题(Ⅰ)、(Ⅱ),引进"参数微分法"得到其近似解,其结果可用于研讨摄动对原物理问题解的影响。类似的问题在许多动力学问题物理解的数值定性分析及其应用WKB方法处理时也会经常遇到。这里的方法仅对两个特例给出,无疑可用于其它类似问题的处理。 相似文献
124.
A smooth method for the finite minimax problem 总被引:2,自引:0,他引:2
We consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions. We prove that, under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values. On this basis, we can define implementable algorithms for the solution of the minimax problem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported.This research was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy. 相似文献
125.
Shigeru Arimoto 《Journal of mathematical chemistry》2007,41(3):231-269
The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes
and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial
investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied
and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise
Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons.
The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube
(a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply.
Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem
(ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate
in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical
formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series.
The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via
resolution of singularities and related methods’ published in the JOMC. 相似文献
126.
Shigeru?ArimotoEmail author Mark?Spivakovsky Keith?F.?Taylor Paul?G.?Mezey 《Journal of mathematical chemistry》2005,37(2):171-189
The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism.
Dedicated to the memory of Prof. Kenichi Fukui (1918–1998). 相似文献
127.
O. Cârja 《Journal of Optimization Theory and Applications》1984,44(3):397-406
In this paper, it is shown that the minimal time function is locally Lipschitz continuous for the control systemx=Ax+u in a Banach spadeE, under either of two conditions:A is linear and generates aC
0-semigroup of bounded linear operators; orA is nonlinear, possibly multivalued, and dissipative. The main tool used for the nonlinear case is a result of Barbu concerning the null controllability of the system. 相似文献
128.
This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383. 相似文献
129.
L. G. Chalmet R. L. Francis J. F. Lawrence 《Journal of Optimization Theory and Applications》1980,32(2):135-149
An example of design might be a warehouse floor (represented by a setS) of areaA, with unspecified shape. Givenm warehouse users, we suppose that useri has a known disutility functionf
isuch thatH
i(S), the integral off
iover the setS (for example, total travel distance), defines the disutility of the designS to useri. For the vectorH(S) with entriesH
i(S), we study the vector minimization problem over the set {H(S) :S a design} and call a design efficient if and only if it solves this problem. Assuming a mild regularity condition, we give necessary and sufficient conditions for a design to be efficient, as well as verifiable conditions for the regularity condition to hold. For the case wheref
iis thel
p-distance from warehouse docki, with 1<p<, a design is efficient if and only if it is essentially the same as a contour set of some Steiner-Weber functionf
=1
f
1++
m
f
m
,when the
i
are nonnegative constants, not all zero.This research was supported in part by the Interuniversity College for PhD Studies in Management Sciences (CIM), Brussels, Belgium; by the Army Research Office, Triangle Park, North Carolina; by a National Academy of Sciences-National Research Council Postdoctorate Associateship; and by the Operations Research Division, National Bureau of Standards, Washington, D.C. The authors would like to thank R. E. Wendell for calling Ref. 16 to their attention. 相似文献
130.
L. Pandolfi 《Journal of Optimization Theory and Applications》1981,33(2):241-254
In this paper, we study the finite-time regulator problem for linear, autonomous, degenerate systems, i.e., systems described by the differential equation
with det(K)=0. Two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.This work was performed under the auspices of the National Research Council of Italy, Gruppo Nazionale per l'Analisi Funzionale e le Sue Applicazioni, Rome, Italy. 相似文献