BPS states on non-commutative tori and duality

We study gauge theories on non-commutative tori. It has been proved that Morita equivalence of non-commutative tori leads to a physical equivalence ( ) of the corresponding gauge theories [Nucl. Phys. B 534 (1998) 720]. We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the . The relation of our results with those of recent calculations is discussed.     

一般退化时滞差分系统解的存在性及通解

本文研究退化时滞差分系统Ex(k+ 1)= Ax(k)+ ∑li= 1Bix(k- i)+ f(k) (k= 0,1,2,…),x(k)= φ(k) (k= 0,- 1,- 2,…,- l),其中E、A、Bi∈Rm ×n,x(k)∈Rn,f(k)∈Rm ,rank(E)< n.给出了上述系统解的存在性条件及通解表达式.     

On the Matrix Equations of Higher Degrees

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Introduction to M(atrix) theory and noncommutative geometry

Noncommutative geometry is based on an idea that an associative algebra can be regarded as “an algebra of functions on a noncommutative space”. The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang–Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was found recently that Yang–Mills theories on noncommutative spaces appear naturally in string/M-theory; the notions and results of noncommutative geometry were applied very successfully to the problems of physics.

In this paper we give a mostly self-contained review of some aspects of M(atrix) theory, of Connes’ noncommutative geometry and of applications of noncommutative geometry to M(atrix) theory. The topics include introduction to BFSS and IKKT matrix models, compactifications on noncommutative tori, a review of basic notions of noncommutative geometry with a detailed discussion of noncommutative tori, Morita equivalence and -duality, an elementary discussion of noncommutative orbifolds, noncommutative solitons and instantons. The review is primarily intended for physicists who would like to learn some basic techniques of noncommutative geometry and how they can be applied in string theory and to mathematicians who would like to learn about some new problems arising in theoretical physics.

The second part of the review (Sections 10–12) devoted to solitons and instantons on noncommutative Euclidean space is almost independent of the first part.     

Thermoanalytical investigations of extended and annealed keratins

DSC investigations have been used to characterize the microfibril-matrix complex of keratin consisting of helical low-sulfur microfibrils in a nonhelical high-sulfur matrix. The corresponding DSC curves display one or two endothermic peaks in the temperature range 230°–255°C. The first peak is a microfibrillar peak and the second one a matrix peak (cystine decomposition peak). DSC investigations of extended keratins have shown that the microfibrillar peak is a helix peak. DSC investigations of annealed keratins confirm our earlier assumption that the helix peak is no helix melting peak but an irreversible helix unfolding, superimposed by various decomposition reactions. The matrix peak of the above described keratin samples is less reproducible than the corresponding helix peak and cannot be used for further characterization studies of keratins.Dedicated to Professor E. G. Klesper on the occasion of his 60th birthday.     

一类特殊模糊矩阵方程的简便求解

给出了一类特殊模糊矩阵方程的简便且实用的求解方法.     

Large deformation in filled networks of different architecture and its interpretation in terms of the van der Waals network model

The first quasi-static stretch of the two limiting systems of filler loaded rubber have been investigated. One of them is found by filler to matrix contacts only, the other by crosslinking permanently the matrix. In this case filler-matrix contacts are made by adhesion. The experimental results were described in terms of an extended van der Waals approach. It is illuminated that different filler to matrix contact (permanent bonds or adhesion) lead to different deformation mechanism, substantially affecting the reinforcement. Moreover, filler induced local field-modifications due to the boundary value problem can be understood with the Einstein-Smallwood approach independent of the kind of the filler to matrix contacts.     

KrF准分子激光空间相干性测量

设计制作了一套反转剪切干涉仪,测量了ＫｒＦ准分子激光的空间相干性。用这种方法能够一次测量激光的空间相干度,并且在不同条纹相机的条件下能够实时测量相干度随时间的变化过程,在有注入、无注入锁定及百非稳腔中经过不同路程条件下对激光的空间相干性进行测量,并且和利用变换矩阵分析了相干度在非稳腔中的传播及其演变过程,计算了激光在不同往返次数的相干带宽度。