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141.
We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities
are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe
the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands
in this algebra. We prove that if a function from ℝ+ into ℝ+ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on
the set of positive self-adjoint operators affiliated with this algebra. 相似文献
142.
Phan Quoc Khanh Dinh Ngoc Quy 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2245-2259
We propose a definition of lower closed transitive relations and prove the existence of minimal elements for such a relation. This result is shown to contain probably a large part of existing versions of Ekeland’s variational principle (EVP). We introduce the notion of a weak τ-function p as a generalized distance and use it together with the above result on minimal elements to establish enhanced EVP for various settings, under relaxed lower semicontinuity assumptions. These principles conclude the existence not only of p-strict minimizers of p-perturbations of the considered vector function, but also p-sharp and p-strong minimizers. Our results are proved to be stronger than the classical EVP and many generalizations in the literature, even in the usual one-dimensional case, by numerous corollaries and examples. We include equivalent formulations of our enhanced EVP as well. 相似文献
143.
Thai Thuan Quang Lien Vuong Lam Nguyen Van Dai 《Complex Analysis and Operator Theory》2013,7(1):237-259
The aim of this paper is to give some criterions for holomorphy of F-valued σ(F, W)-holomorphic functions which are bounded on bounded sets in a domain D of Fréchet spaces E (resp. ${\mathbb{C}^n}$ ) where ${W \subset F'}$ defines the topology of Fréchet space F. Base on these results we consider the problem on holomorphic extension of F-valued σ(F, W)-holomorphic functions from non-rare subsets of D and from subsets of D which determines uniform convergence in H(D). As an application of the above, some theorems of Vitali-type for a locally bounded sequence ${\{f_i\}_{i \in \mathbb{N}}}$ of Fréchet-valued holomorphic functions are also proved. 相似文献
144.
Duc Quang Si 《Complex Analysis and Operator Theory》2013,7(4):1357-1370
In this article, we prove that two meromorphic functions $f$ and $g$ must be linked by a quasi-Möbius transformation if they share two pairs of small functions ignoring multiplicities and share other four small functions with multiplicities truncated by 2. We also show that two meromorphic functions which share seven pairs of small functions ignoring multiplicities are linked by a quasi-Möbius transformation. 相似文献
145.
In this article, necessary conditions of Fritz John type for weak efficient solutions of a nonsmooth vector equilibrium problem involving equilibrium constraints (VEPEC) in terms of the Clarke subdifferentials are established. Under constraint qualifications which are suitable for (VEPEC), necessary conditions of Kuhn-Tucker type for efficiency are derived. Under assumptions on generalized convexity of data, sufficient conditions for efficiency are developed. Some applications to vector variational inequalities and vector optimization problems with equilibrium constraints are also given. 相似文献
146.
147.
Tien-Cuong Dinh 《Journal of Geometric Analysis》2013,23(3):1189-1195
Let T be an exterior modular correspondence on an irreducible locally symmetric space X. We show that the isolated fixed points of the power T n are equidistributed with respect to the invariant measure on X as n tends to infinity. A similar statement is given for general sequences of modular correspondences. 相似文献
148.
We study Stanley–Reisner ideals of broken circuit complexes and characterize those ones admitting linear resolutions or being complete intersections. These results will then be used to characterize hyperplane arrangements whose Orlik–Terao ideal has the same properties. As an application, we improve a result of Wilf on upper bounds for the coefficients of the chromatic polynomial of a maximal planar graph. We also show that for a matroid with a complete intersection broken circuit complex, the supersolvability of the matroid is equivalent to the Koszulness of its Orlik–Solomon algebra. 相似文献
149.
Yang Liu Hsiangkuo Yuan Andrew M. Fales Tuan Vo‐Dinh 《Journal of Raman spectroscopy : JRS》2013,44(7):980-986
Local pH environment has been considered to be a potential biomarker for tumor diagnosis because solid tumors contain highly acidic environments. A pH‐sensing nanoprobe based on surface‐enhanced Raman scattering (SERS) using nanostars under near‐infrared excitation has been developed for potential biomedical applications. To theoretically investigate the effect of protonation state on SERS spectra of p‐mercaptobenzoic acid (pMBA), we used the density functional theory (DFT) with the B3LYP functional to calculate Raman vibrational spectra of pMBA‐Au/Ag complex in both protonated and deprotonated states. Vibrational spectral bands were assigned with DFT calculation and used to investigate SERS spectral changes observed from experiment when varying pH value between five and nine. The SERS peak position of pMBA at ~1580 cm−1 was identified to be a novel pH‐sensing index, which has small but noticeable downshift with pH increase. This phenomenon is confirmed and well‐explained with theoretical simulation. The study demonstrates that SERS is a sensitive tool to monitor minor structural changes due to local pH environment, and DFT calculations can be used to investigate Raman spectra changes associated with minor differences in molecular structure. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
150.