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An example in Ref. 1 is corrected to show that indeed a strongly pseudoconvex function, which is only once but not twice differentiable, does not necessarily have a strongly pseudoconvex gradient. 相似文献
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A previous critique of the relevance of Piron's questions-propositions system as a generator of quantum mechanics by interpretation is reinforced and brought to a close by further investigation. 相似文献
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N. Hadjisavvas 《Letters in Mathematical Physics》1981,5(4):327-332
We study the density operators expressed as mixtures of non-orthogonal pure states in quantum mechanics. The general mathematical law of formation of such mixtures is found. Applications are given concerning the entropy properties of density operators etc. 相似文献
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Nicolas Hadjisavvas 《TOP》2005,13(2):279-283
Discussion
Aris Daniilidis Universitat Autònoma de Barcelona, Spain 相似文献6.
Suliman Al-Homidan Nicolas Hadjisavvas Loai Shaalan 《Journal of Optimization Theory and Applications》2018,177(1):93-105
Quasiconvex functions present some difficulties in global optimization, because their graph contains “flat parts”; thus, a local minimum is not necessarily the global minimum. In this paper, we show that any lower semicontinuous quasiconvex function may be written as a composition of two functions, one of which is nondecreasing, and the other is quasiconvex with the property that every local minimum is global minimum. Thus, finding the global minimum of any lower semicontinuous quasiconvex function is equivalent to finding the minimum of a quasiconvex function, which has no local minima other than its global minimum. The construction of the decomposition is based on the notion of “adjusted sublevel set.” In particular, we study the structure of the class of sublevel sets, and the continuity properties of the sublevel set operator and its corresponding normal operator. 相似文献
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Nicolas Hadjisavvas Flávia M. O. Jacinto Juan E. Martínez-Legaz 《Set-Valued and Variational Analysis》2016,24(2):323-332
We present necessary and sufficient conditions for a monotone bifunction to be maximally monotone, based on a recent characterization of maximally monotone operators. These conditions state the existence of solutions to equilibrium problems obtained by perturbing the defining bifunction in a suitable way. 相似文献
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Coercivity conditions and variational inequalities 总被引:9,自引:0,他引:9
Received November 17, 1997 / Revised version received August 6, 1998?Published online March 16, 1999 相似文献
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The present paper deals with the possibility of existence of best approximation elements, simultaneously with respect to two norms ·i,i=1,2, for all the elements of a class of subspaces. In case this class in any of the following: (a) All n-dimensional subspaces, (b) All ·1-or ·||2-closed, n-codimensional subspaces, (c) All ·1-or ·2-closed subspaces with infinite dimension and codimension, we prove that the two norms differ at most by a constant factor. 相似文献