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271.
Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25. 相似文献
272.
LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt0, we define theiterated Brownian motion (IBM),Z, by setting
. In this paper we determine the exact uniform modulus of continuity of the process Z.Research supported by NSF grant DMS-9122242. 相似文献
273.
Bosko Zivaljevic 《Transactions of the American Mathematical Society》1996,348(5):1921-1938
We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.
274.
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.
275.
LetM be a compact minimal surface inS
3. Y. J. Hsu[5] proved that if S222, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·2 denotes theL
2-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS
3 with constant mean curvature.Supported by NSFH. 相似文献
276.
Jorge A. León 《Applied Mathematics and Optimization》1993,27(3):313-327
Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Yx,x X, of the anticipating integral of(x) such that the integral x Yx(dx) is a version of the anticipating integral of X
(x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space. 相似文献
277.
We consider a certain combinatorial game on a digraph for two cases of the price function. For one case the game in question extends the cyclical game studied in Ehrenfeucht and Mycielski (1979) and Gurvitch, Karzanov and Khachiyan (1988) which, in its turn, is a generalization of the well-known problem of finding a minimum mean cycle in an edge-weighted digraph. We prove the existence of optimal uniform stationary strategies for both cases and give algorithms to find such strategies.This work was partially supported by Chaire municipale, Mairie de Grenoble. 相似文献
278.
For benzenoid hydrocarbons the distribution of pi-electrons amongst rings is characterized in the context of Randis mode of assignment attending to the different Kekulé structures. In particular the mean and mean deviation from the mean are considered, and the benzenoids which achieve maximum deviation are identified. 相似文献
279.
The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies
electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation
and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed
that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The
possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations,
or even exact expressions, for the Fukui function for electron attachment. 相似文献
280.
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