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Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the ql-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as ql-integrable f with q(|f|) < ∞, and of ql-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most
finitely additive integration theories. 相似文献
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A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities. 相似文献
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Germán A. Enciso Morris W. Hirsch Hal L. Smith 《Journal of Dynamics and Differential Equations》2008,20(1):115-132
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward
an equilibrium or toward the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results
in terms of the measure-theoretic notion of prevalence, developed in Christensen (Israel J. Math., 13, 255–260, 1972) and Hunt et al. (Bull. Am. Math. Soc., 27, 217–238, 1992). For monotone reaction–diffusion systems with Neumann boundary conditions on convex domains, we show the
prevalence of the set of continuous initial conditions corresponding to solutions that converge to a spatially homogeneous
equilibrium. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is
given to the measurability of the various sets involved. 相似文献
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N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1987,53(2):259-268
In the present paper, we generalize, within the family of convex-valued multifunctions, a selection theorem of Cole (Ref. 1). This then leads us to prove some new results concerning Cesari's property (Q) and to the introduction of the Cesari limit of sets, which is then compared to the Kuratowski-Mosco limit.This work was done while the author was a visiting professor at the University of Pavia, Pavia, Italy. Financial support was provided by CNR and by NSF Grant No. 84-03135. 相似文献
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The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive
applications was presented. Two methods were used to investigate the basic characteristics of the system: 1) transforming
the system in the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the
lumped parameter system. It is found that there are two critical values for the control variable: the larger one determines
whether or not the boundary would move, while the smaller one determines whether or not the boundary would stop automatically.
For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a
unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have
been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is
well posed, stable, measurable and controllable.
Foundation item: the National Natural Science Foundation of China (59936140)
Biographies:ZHOU Jian-jun (1953-); XU Yan-hou (1933-) 相似文献
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陈应天 《应用数学和力学(英文版)》1983,4(3):431-434
The general form of J-integral conservation law in three di-mensions has been derived from the principle of virtual work.The necessary conditions for J-integral conservation are alsogiven. 相似文献
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拟凸函数的若干充分条件 (英) 总被引:1,自引:1,他引:0
本文提出了中点拟凸函数的概念,在可测函数空间中,给出了中点拟凸函数拟凸的若干个充分条件. 相似文献
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Tie-xin GUO Department of Mathematics School of Science Beijing University of Aeronautics Astronautics Beijing China 《中国科学A辑(英文版)》2007,50(5):737-747
The central purpose of this paper is to illustrate that combining the recently developed theory of random conjugate spaces and the deep theory of Banach spaces can, indeed, solve some difficult measurability problems which occur in the recent study of the Lebesgue (or more general, Orlicz)-Bochner function spaces as well as in a slightly different way in the study of the random functional analysis but for which the measurable selection theorems currently available are not applicable. It is important that this paper provides a new method of studying a large class of the measurability problems, namely first converting the measurability problems to the abstract existence problems in the random metric theory and then combining the random metric theory and the relative theory of classical spaces so that the measurability problems can be eventually solved. The new method is based on the deep development of the random metric theory as well as on the subtle combination of the random metric theory with classical space theory. 相似文献