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161.
Jinlu Li 《Journal of Mathematical Analysis and Applications》2004,295(1):115-126
In this paper, we study the existence of the solution of the variational inequality 〈Tx−ξ,y−x〉?0 by applying the generalized projection operator , where B is a Banach space with dual space B∗ and by using the well-known FanKKM Theorem. 相似文献
162.
We derive the Bell–Clauser–Horne–Shimony–Holt inequalities for two-particle mixed spin states both in the conventional quantum mechanics and in the hidden-variables theory. We consider two cases for the vectors
, and
specifying the axes onto which the particle spins of a correlated pair are projected. In the first case, all four vectors lie in the same plane, and in the second case, they are oriented arbitrarily. We compare the obtained inequalities and show that the difference between the predictions of the two theories is less for mixed states than for pure states. We find that the inequalities obtained in quantum mechanics and the hidden-variables theory coincide for some special states, in particular, for the mixed states formed by pure factorable states. We discuss the points of similarity and difference between the uncertainty relations and Bell's inequalities. We list all the states for which the right-hand side of the Bell–Clauser–Horne–Shimony–Holt inequality is identically equal to zero. 相似文献
163.
Ming-baoSun Xiao-pingYang 《应用数学学报(英文版)》2004,20(1):123-132
For a Carnot group G,we establish the relationship between extended mean values and r-convexfunctions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convexfunction on G. 相似文献
164.
Gao Huijun; Lam James; Xu Shengyuan; Wang Changhong 《IMA Journal of Mathematical Control and Information》2004,21(4):377-392
This paper extends the results obtained for one-dimensionalMarkovian jump systems, to investigate the problems of stochasticstabilization and H control of two-dimensional (2D) systemswith Markovian jump parameters. The mathematical model of 2Djump systems is established upon the well-known Roesser model,and sufficient conditions are obtained for the existence ofdesired controllers in terms of linear matrix inequalities,which can be readily solved by available numerical software.These obtained results are further extended to more generalcases whose system matrices also contain parameter uncertaintiesrepresented by either polytopic or norm-bounded approaches.A numerical example is provided to show the applicability ofthe proposed theories. 相似文献
165.
Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems 总被引:1,自引:0,他引:1
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Czechoslovak Mathematical Journal》2004,54(2):347-371
In this paper we examine nonlinear periodic systems driven by the vectorial p-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the sublinear problem. For the semilinear problem (i.e. p = 2) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the superlinear problem. Our work generalizes some recent results of Tang (PAMS 126(1998)). 相似文献
166.
We study the problem of completely describing the domains that enjoy the generalized multiplicative inequalities of the embedding theorem type. We transfer the assertions for the Sobolev spaces L
p
1() to the function classes that result from the replacement of L
p
() with an ideal space of vector-functions. We prove equivalence of the functional and geometric inequalities between the norms of indicators and the capacities of closed subsets of . The most comprehensible results relate to the case of the rearrangement invariant ideal spaces. 相似文献
167.
Gangsong Leng Lin Si Qingsan Zhu 《Proceedings of the American Mathematical Society》2004,132(9):2655-2660
For let and denote the arithmetic mean and geometric mean of elements of , respectively. It is proved that if is an integer in , then
with equality if and only if . Furthermore, as a generalization of this inequality, a mixed power-mean inequality for subsets is established.
with equality if and only if . Furthermore, as a generalization of this inequality, a mixed power-mean inequality for subsets is established.
168.
Feng-Yu Wang 《Proceedings of the American Mathematical Society》2004,132(9):2629-2638
Let be a probability space, and a symmetric linear contraction operator on with and . We prove that is the optimal sufficient condition for to have a spectral gap. Moreover, the optimal sufficient conditions are obtained, respectively, for the defective log-Sobolev and for the defective Poincaré inequality to imply the existence of a spectral gap. Finally, we construct a symmetric, hyperbounded, ergodic contraction -semigroup without a spectral gap.
169.
Tavan T. Trent 《Proceedings of the American Mathematical Society》2004,132(8):2429-2432
We find the maximal invariant subspaces for on -valued Bergman-type spaces.
170.
Edoardo Ballico Changho Keem Seungsuk Park 《Proceedings of the American Mathematical Society》2004,132(11):3153-3158
Let be a smooth projective algebraic curve of genus and an integer with . For all integers we prove the existence of a double covering with a smooth curve of genus and the existence of a degree morphism that does not factor through . By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound ).