格的弱奇异元

引入了弱奇异元的概念，得到了若干重要性质和相关结果：1．L的每个非零元是弱奇异元当且仅当L∈A；2．L∈Fs，则L的一个非零元g是弱奇异元当且仅当g是有限个基元素的并。     

Tensor products of Hilbert space effect algebras

A definition of a tensor product in the category of Hilbert space effect algebras is introduced such that the tensor product reflects as much as possible of the physically important properties of the components. It is shown that in the complex case, there are two candidates to the tensor product, which are not equivalent. The situation is similar to the tensor product in the category of projection lattices, but also the two dimensional case is included. The case of tensor product of two classical systems is also investigated.     

Nuclear Spin Alignment and Alignment Correlation Terms in Mass A = 8 System

The pure nuclear spin alignments of ⁸Li and ⁸B were produced from the nuclear spin polarization applying the β-NMR method. The alignment correlation terms in the β-ray angular distribution were observed to test the G parity conservation in the nuclear β decay.     

关于积和式差的一点注记

It is shown that for any two n×n complex valued matrices A, B the inequality |perA-perB|≤n‖A-B‖Fmax(‖A‖F,‖B‖F)n-1 or |perA-perB|≤‖A‖Fn ‖B‖Fn holds for where AH denotes the conjuagte transpose of the matrix A=(aij)n×n.     

Natural orbital functional approach: Calculation of dielectric properties in molecules

Recently, we proposed a new natural orbital functional for taking into account the electronic correlation in molecular systems. Calculation of dipole moments and polarizabilities of eight selected molecules are presented. By comparison with other correlated methods, it is shown that the method has predictive capabilities for these properties. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Evaporating Black Holes and Long Range Scaling

For an effective treatment of the evaporation process of a large black hole the problem concerning the role played by the fluctuations of the (vacuum) stress tensor close to the horizon is addressed. We present arguments which establish a principal relationship between the outwards fluctuations of the stress tensor close to the horizon and quantities describing the onset of the evaporation process. This suggest that the evaporation process may be described by a fluctuation-dissipation theorem relating the noise of the horizon to the black hole evaporation rate.     

Separability of Pure and Mixed States of the Quantum Network of Four Nodes

This article discusses the separability of the pure and mixed states of the quantum network of four nodesby means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.     

Letter: String Cosmology in Brane World Scenarios

We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I & V geometry and string dust as the matter source. We assume the Weyl tensor in the bulk has vanishing projection on the brane and examine the different equations of state, for the string dust system. Exact analytic solutions are possible only in few cases.     

Geometric Proof of Lie's Linearization Theorem

In 1883, S. Lie found the general form of all second-order ordinary differential equations transformable to the linear equation by a change of variables and proved that their solution reduces to integration of a linear third-order ordinary differential equation. He showed that the linearizable equations are at most cubic in the first-order derivative and described a general procedure for constructing linearizing transformations by using an over-determined system of four equations. We present here a simple geometric proof of the theorem, known as Lie's linearization test, stating that the compatibility of Lie's four auxiliary equations furnishes a necessary and sufficient condition for linearization.     

Perron–Frobenius theorem for hypermatrices in the max algebra

Recently, there have been many intriguing new developments in the study of hypermatrices and their associated eigenvalue problems. In particular, results coming from the matrix setting when studying the max algebra have shown especially attractive combinatorial features. We now extend this max algebra setting into the realm of hypermatrices. Considering that the max algebra has shown particular significance in optimization problems for the matrix setting, we look to examine and extend these results in the higher order conditions. Furthermore, we establish some algebraic properties for hypermatrices and then proceed to extend the Perron–Frobenius Theorem for this setting and prove the existence of a unique eigenvalue. We continue by stating a result from Nussbaum, that the Min–Max theorem holds, and provide a proof for completeness. For strongly increasing hypermatrices, an iterative algorithm which converges to our unique eigenvalue is given. Finally, we conclude with an analysis of our results in the hypergraph setting.