反向Dresher不等式

配合使用 Holder不等式和 Minkowski不等式 ,得到一个反向 Dresher不等式 .

Classification of Crystallographic Groups in the Hyperbolic 5-Dimensional Indefinite Space

Let V be a hyperbolic 5-dimensional indefinite space. W is the infinite Weyl group of an irreducible root system. The principal aim of this paper is to classify all crystallgraphic groups associated with W up to conjugation in the affine group A(V).

Schmidt Decomposition of Quaternion Matrix and the Orthonormalization of Vectors in a Generalized Unitary Space

In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.

Torsion Axial-Vector in an Alternative Kerr Tetrad Field

In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation approximation, we obtain that the torsion axial-vector possesses the dipole-like structure. Furthermore, the effect of massive neutrino spin precession in this field is mentioned.

A Criterion of Decomposable Elements in V^(2)

In this paper, a criterion of decomposable element in V(2) is obtained , i. e.,Z = p(i, j)eij is decomposable if and only if its adjacent coordinate matrices are all "row 1≤i≤j≤ncommute" equivalent.

Summability results for operator matrices on topological vector spaces

Basic summability results are established for matrices of linear and some nonlinear mappings between topological vector spaces.

Augmented Spinor Space

In this paper, based on the Pauli matrices, a notion of augmented spinor space is introduced, and a uniqueness of such augmented spinor space of rank n is proved. It may be expected that this new notion of spaces can be used in mathematical physics and geometry.

Approximately unital operator systems

The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theorem for these systems,to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit,to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital operator system that is also an approximately unital matrix ordered *-algebra.

M-Theory in the Gaugeon Formalism

In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.

Strong representation of weak convergence

Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable.

THERMAL EQUILIBRIUM AND KMS CONDITION AT THE PLANCK SCALE

Considering the expected thermal equilibrium characterizing the physics at the Planck scale, it is here stated, for the first time, that, as a system, the space-time at the Planck scale must be considered as subject to the Kubo-Martin-Schwinger (KMS) condition. Consequently, in the interior of the KMS strip, i.e. from the scale B = 0 to the scale B = lplanck, the fourth coordinate g44 must be considered as complex, the two real poles being 6 = 0 and B = lplanck. This means that within the limits of the KMS strip, the Lorentzian and the Euclidean metric are in a 'quantum superposition state' (or coupled), this entailing a 'unification' (or coupling) between the topological (Euclidean) and the physical (Lorentzian) states of space-time.

A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONAL WAVE-VECTOR SPACE AND ITS DIFFUSION LIMIT

The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.