Plücker-type relations for orthogonal planes

We explore a Plücker-type relation which occurs naturally in the study of maximally supersymmetric solutions of certain supergravity theories. This relation generalises at the same time the classical Plücker relation and the Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity of a metric n-Lie algebra. In low dimension we present evidence for a geometric characterisation of the relation in terms of middle-dimensional orthogonal planes in Euclidean or Lorentzian inner product spaces.     

Baryon inhomogeneities due to cosmic string wakes at the quark-hadron transition

Baryon inhomogeneities generated during the quark-hadron transition may alter the abundances of light elements if they persist up to the time of nucleosynthesis. These inhomogeneities survive up to the nucleosynthesis epoch if they are separated by a distance of at least a few metres. In this work we present a model where large sheets of these inhomogeneities separated by a distance of a few km are formed by cosmic string wakes during the quark-hadron transition. The effect of these sheets on nucleosynthesis will also put constraints on the various cosmic string parameters.     

Fusion Operators and Cocycloids in Monoidal Categories

The Yang–Baxter equation has been studied extensively in the context of monoidal categories. The fusion equation, which appears to be the Yang–Baxter equation with a term missing, has been studied mainly in the context of Hilbert spaces. This paper endeavours to place the fusion equation in an appropriate categorical setting. Tricocycloids are defined; they are new mathematical structures closely related to Hopf algebras.     

Matrix models, complex geometry, and integrable systems: I

We consider the simplest gauge theories given by one-and two-matrix integrals and concentrate on their stringy and geometric properties. We recall the general integrable structure behind the matrix integrals and turn to the geometric properties of planar matrix models, demonstrating that they are universally described in terms of integrable systems directly related to the theory of complex curves. We study the main ingredients of this geometric picture, suggesting that it can be generalized beyond one complex dimension, and formulate them in terms of semiclassical integrable systems solved by constructing tau functions or prepotentials. We discuss the complex curves and tau functions of one-and two-matrix models in detail. [This article was written at the request of the Editorial Board. It is based on several lectures presented at schools of mathematical physics and talks at the conference “Complex Geometry and String Theory” and the Polivanov memorial seminar.] __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 163–228, May, 2006.     

Integrable structure of the field theory of open superstrings

We find asymptotic expansions in the “string mass” μ for μ-deformed Γ-functions and Neumann coefficients characterizing the three-string vertex in the light-cone gauge of the field theory of open superstrings on a maximally supersymmetric pp-wave background. Dedicated to the 80th birthday of Academician Anatolii Alekseevich Logunov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 381–385, December, 2006.     

Closed relativistic strings in geometrically nontrivial spaces

We find exact solutions of the equations of motion for a closed relativistic string that carries a point mass and moves in the space given by the direct product of Minkowski space and a compact manifold (multidimensional torus). We investigate physical characteristics of the system states described by these solutions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 72–82, January, 2005.     

电子小提琴与常规小提琴的无线载波传输演示

小提琴可分解成拉弦系统和共振箱系统．在拉弦系统中,弦的振动被变为电声信号,以电磁波的形式发射到空中．在共振箱系统中,由调频接收器接收信号,经电声转换后驱动共鸣箱发声．改装后的电子小提琴可用于物理实验演示教学及小提琴弦振动和共鸣箱的频谱分析．     

IR,Raman, and Surface‐enhanced Raman Spectroscopic Study on Triruthenium Dipyridylamide Diruthenium Nickel Dipyridylamide Family: Metal‐metal Bonding and Structures

We report the infrared, Raman, and surface‐enhanced Raman scattering (SERS) spectra of triruthenium dipyridylamido complexes and of diruthenium mixed nickel metal‐string complexes. From the results of analysis on the vibrational modes, we assigned their vibrational frequencies and structures. The infrared band at 323–326 cm^?1 is assigned to the Ru₃ asymmetric stretching mode for [Ru₃(dpa)₄Cl₂]^0–2+. In these complexes we observed no Raman band corresponding to the Ru₃ symmetric stretching mode although this mode is expected to have substantial Raman intensity. There is no frequency shift in the Ru₃ asymmetric stretching modes for the complexes with varied oxidational states. No splitting in Raman spectra for the pyridyl breathing line indicates similar bonding environment for both pyridyls in dpa^– , thus a delocalized structure in the [Ru₃]^6–8+ unit is proposed. For Ru₃(dpa)₄(CN)₂ complex series, we assign the infrared band at 302 cm^?1 to the Ru₃ asymmetric stretching mode and the weak Raman line at 285 cm^?1 to the Ru₃ symmetric stretching. Coordination to the strong axial ligand CN^– weakens the Ru‐Ru bonding. For the diruthenium nickel complex [Ru₂Ni(dpa)₄Cl₂]^0–1+, the diruthenium stretching mode ν_Ru‐Ru is assigned to the intense band at 327 and 333 cm^?1 in the Raman spectra for the neutral and oxidized forms, respectively. This implies a strong Ru‐Ru metal‐metal bonding.     

气体钻井钻柱轴扭耦合动态屈曲数学建模与求解

针对钻柱轴扭耦合动态屈曲的基本问题构造哈密顿体系,在辛几何空间中将临界屈曲载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛几何算法.方法较好的解决了钻柱轴扭耦合动态屈曲的复杂边界条件问题.在解决气体钻井钻柱动态屈曲问题的研究中具有良好的应用前景.