Non-locality and Gauge Freedom in Deutsch and Hayden’s Formulation of Quantum Mechanics

Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must be understood as having a form of ‘gauge freedom’ according to which mathematically distinct states are physically equivalent. Once this gauge freedom is taken into account, their formulation is no longer local.     

The minimal polynomial of a matrix

Let Rbe a finite dimensional central simple algebra over a field FA be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial q_A(λ) of A over F. By using q_A(λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.     

单位球面的三维紧致极小子流形

本文得到高维球面上三维紧致极小子流形的若干刚性定理．在一个整体拚挤条件下，数量曲率的拚挤常数被改进了，也对李奇曲率的拚挤问题进行了讨论．     

Active redundancy allocation for a k-out-of-n:F system of dependent components

We characterize active redundancy through compensator transform and use the reverse rule of order 2 (RR₂) property between compensator processes to investigate the problem of where to allocate a spare in a k-out-of-n:F system of dependent components through active redundancy.     

量子角动量理论新探

用完全初等的方法推导了量子力学角动量理论中Ｃｌｅｂｓｃ－Ｇｏｒｄａｎ系数，３ｊ系数，所用的 是一些初等排列的组合一量子力学基本知识；同时，在实际问题计算中，只需直接应用简单的推导方法本身是一种极为简捷的算法。     

The Lappo-Danilevskii method and trivial intersections of radicals in lower central series terms for certain fundamental groups

In this paper, it is proved that the intersection of the radicals of nilpotent residues for the generalized pure braid group corresponding to an irreducible finite Coxeter group or an irreducible imprimitive finite complex reflection group is always trivial. The proof uses the solvability of the Riemann—Hilbert problem for analytic families of faithful linear representations by the Lappo-Danilevskii method. Generalized Burau representations are defined for the generalized braid groups corresponding to finite complex reflection groups whose Dynkin—Cohen graphs are trees. The Fuchsian connections for which the monodromy representations are equivalent to the restrictions of generalized Burau representations to pure braid groups are described. The question about the faithfulness of generalized Burau representations and their restrictions to pure braid groups is posed.     

On classes of minimal circular-imperfect graphs

Circular-perfect graphs form a natural superclass of perfect graphs: on the one hand due to their definition by means of a more general coloring concept, on the other hand as an important class of χ-bound graphs with the smallest non-trivial χ-binding function χ(G)?ω(G)+1.The Strong Perfect Graph Conjecture, recently settled by Chudnovsky et al. [The strong perfect graph theorem, Ann. of Math. 164 (2006) 51-229], provides a characterization of perfect graphs by means of forbidden subgraphs. It is, therefore, natural to ask for an analogous conjecture for circular-perfect graphs, that is for a characterization of all minimal circular-imperfect graphs.At present, not many minimal circular-imperfect graphs are known. This paper studies the circular-(im)perfection of some families of graphs: normalized circular cliques, partitionable graphs, planar graphs, and complete joins. We thereby exhibit classes of minimal circular-imperfect graphs, namely, certain partitionable webs, a subclass of planar graphs, and odd wheels and odd antiwheels. As those classes appear to be very different from a structural point of view, we infer that formulating an appropriate conjecture for circular-perfect graphs, as analogue to the Strong Perfect Graph Theorem, seems to be difficult.     

Extreme behavior of multivariate phase-type distributions

This paper investigates the limiting distributions of the componentwise maxima and minima of suitably normalized iid multivariate phase-type random vectors. In the case of maxima, a large parametric class of multivariate extreme value (MEV) distributions is obtained. The flexibility of this new class is exemplified in the bivariate setup. For minima, it is shown that the dependence structure of the Marshall-Olkin class arises in the limit.     

Estimate of the L^p-Fourier Transform on Strong ＊-Regular Exponential Solvable Norm Lie Groups

We study the L^p-Fourier transform for a special class of exponential Lie groups, the strong ＊-regular exponential Lie groups. Moreover, we provide an estimate of its norm using the orbit method.