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61.
This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R0-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically. 相似文献
62.
Masahiro Kubo 《Journal of Evolution Equations》2007,7(4):701-717
We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex
functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions
on the convex functions and other data, we prove the existence and uniqueness of a strong solution, and give some applications
of the abstract theorem to hyperbolic variational inequalities with time-dependent constraints.
相似文献
63.
In the introduction of the Arithmetica Diophantus says that in order to solve arithmetical problems one has to “follow the way he (Diophantus) will show.” The present paper has a threefold objective. Firstly, the meaning of this sentence is discussed, the conclusion being that Diophantus had elaborated a program for handling various arithmetical problems. Secondly, it is claimed that what is analyzed in the introduction is definitions of several terms, the exhibition of their symbolism, the way one may operate with them, but, most significantly, the main stages of the program itself. And thirdly, it is argued that Diophantus' intention in the Arithmetica is to show the way the stages of his program should be practically applied in various arithmetical problems. 相似文献
64.
We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs. 相似文献
65.
Christian Wolf 《Journal of statistical physics》2006,122(6):1111-1138
In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical
physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform
a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete
theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification
for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss
possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence
of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques
from smooth ergodic theory including the thermodynamic formalism.
2000
Mathematics Subject Classification. Primary: 37C45, 37D20, 37D35, Secondary: 37A35, 37E30 相似文献
66.
The steel ASTM A213 P22 is used for superheater outlet header in power plants. During duty cycles lasting over tens of years the temperature is of the order of 545°C and the pressure 125 atm. The microscopic changes in these steels are hard to analyze under working conditions, but they are believed to be responsible for the appearance of creeps in such devices. Investigation of the microscopic modifications will help to predict future failures due to creeps, increasing the reliability and saving a lot of money.We report the investigation of such changes in ASTM A213 P22 steel in use for 30 years as a Superheater header at Haifa power station. The analysis has been carried out using Mössbauer Spectroscopy, X-ray diffraction and optical microscopy. As a result it seems that the morphology and phase change of the carbide phases M3C/M7C3 and M23C6 are the most prominent changes leading to the material failures. 相似文献
67.
Z.X. Cheng S.J. ZhangF. Song H.C. GuoJ.R. Han H.C. Chen 《Journal of Physics and Chemistry of Solids》2002,63(11):2011-2017
Erbium and ytterbium codoped double tungstates NaY(WO4)2 crystals were prepared by using Czochralski (CZ) pulling method. The absorption spectra in the region 290-2000 nm have been recorded at room temperature. The Judd-Ofelt theory was applied to the measured values of absorption line strengths to evaluate the spontaneous emission probabilities and stimulated emission cross sections of Er3+ ions in NaY(WO4)2 crystals. Intensive green and red lights were measured when the sample were pumped by a 974 nm laser diode (LD), especially, the intensities of green upconversion luminescence are very strong. The mechanism of energy transfer from Yb3+ to Er3+ ions was analyzed. Energy transfer and nonradiative relaxation played an important role in the upconversion process. Photoexcited luminescence experiments are also fulfilled to help analyzing the transit processes of the energy levels. 相似文献
68.
Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr2O3 using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr2O3). A second phase, namely θ-(Al,Cr)2O3, was revealed by XRD in the sample containing 9.60 wt% Cr2O3. The structure of mullites was refined by the Rietveld method, location of Cr3+ was performed by the EPR spectroscopy. At low chromium doping level (Cr2O3 content less than ∼5 wt%) Cr3+ ions were substituted for Al3+ in the AlO6 octahedra of the mullite structure (M1 site). For higher doping level, Cr3+ ions were additionally substituted for Al3+ in the AlO6 octahedra of the second phase [θ-(Al,Cr)2O3 at 1400 °C, or α-(Al,Cr)2O3 at 1600 °C] which segregated in the system. Substitution of Cr3+ for Al3+ on M1 site in the mullite structure resulted in increase of average distances in (M1)O6 octahedron and decrease of average distances in T*O4 tetrahedron, while average distances in TO4 tetrahedron stayed almost constant. 相似文献
69.
A simple microscopic model of charge ordering in the NaxCoO2 system is presented. The model takes into account the interplane interactions between the ordered Na ions and d electrons from the CoO2 layers as well as the nearest-neighbor intraplane Coulomb interactions between d electrons. It is shown that a driving force of charge ordering in the CoO2 layers is the interplane interaction that alone is able to describe various types of inhomogeneous charge ordering (e.g., the striped phases) as well as to predict correctly the conducting properties of the system. 相似文献
70.