Periodicity of Y-Systems and Flat Connections

We give a proof of the periodicity of Zamolodchikov’s Y-system in the AxA case using an interpretation of the system as a condition of flatness of a certain graph connection. In our approach, the periodicity property appears as an identity among representations of a matrix as products of two-diagonal matrices.     

Connections on Naturally Reductive Spaces,Their Dirac Operator and Homogeneous Models in String Theory

 Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇ ^t joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D ^t corresponding to t=1/3 is the so-called ``cubic' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first eigenvalue of D <sup>1/3</sup>. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor with respect to some metric connection ∇ whose torsion T≠ 0 is a 3-form, the geometric model for the common sector of string theories. We present some results about solutions to the string equations and a detailed discussion of a 5-dimensional example. Received: 19 February 2002 / Accepted: 26 August 2002 Published online: 22 November 2002 RID="*" ID="*" This work was supported by the SFB 288 ``Differential geometry and quantum physics' of the Deutsche Forschungsgemeinschaft and the Max-Planck Society.     

On the Periodicity Conjecture for Y-systems

The conjecture in question (due ultimately to Alexei Zamolodchikov) asserts the periodicity of all the solutions to the so-called Y-systems. Those systems are naturally associated to pairs of indecomposable Cartan matrices of finite type, and the conjectured period is equal to twice the sum of the respective Coxeter numbers. This conjecture has so far been proven only if one of the ranks equals one, in which case the Y-systems are intrinsically related to Fomin-Zelevinsky’s cluster algebras. In this paper, I use elementary projective geometry to prove the case when the two Cartan matrices involved are of type A with both ranks arbitrary.     

Periodicity measures for repeated random auditory patterns

Random auditory patterns were repliated according to defined rules, converted toauditory pulse trains, and presented to listeners. Three ined: the threshold fraction of repeated elements necessary for a fixed level of discrimination from a nonrepeated pattern; the accuracy of periodicity matching; and periodicity magnitude ratings. A short-term periodicity analysis over successive replications appears to be more representative of the behavioral measures than a long-term periodicity analysis. Of the signal measures of periodicity examined, the maximum autocorrelation, irrespective of delay, most closely reflects behavioral measures of periodicity strength.     

An Energy Gap for Yang-Mills Connections

Consider a Yang-Mills connection over a Riemann manifold M = M ⁿ , n ≥ 3, where M may be compact or complete. Then its energy must be bounded from below by some positive constant, if M satisfies certain conditions, unless the connection is flat.     

Formal Connections for Families of Star Products

We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection, which was introduced by the first author. We establish a necessary and sufficient condition that guarantees the existence of a formal connection, and we describe the space of formal connections for a family as an affine space modelled on the formal symplectic vector fields. Moreover, we showthat if the parameter space has trivial first cohomology group, any two flat formal connections are related by an automorphism of the family of star products.     

Periodicity Characteristic of TOAD's Switching Window

1 IntroductionThere are a variety of all-optical demultiplexing schemes for OPtical time divisionmultiplexing (OvuM) system, such as nonlinear optical loop horror (NOLM)[IJ,terahertz optical asyrnxnetric demultiplexer (TOAD)[2], four wave ndking (aaM) offiber or semiconductor optical amplifier (~)[3'4), etc. Axnong them, the terahertzoptical asymmetric demultiplexer (TOAD) has advantages of requirement for shorterlength of fiber and lOWer energy of control pulse, no dispersion and walk…     

Periodicity Characteristic of TOAD's Switching Window

The periodicity characteristic of switching window of a terahertz optical asymmetric demultiplexer (TOAD) using numerical simulation was investigated. The results show that the switching window width of TOAD changes periodically with the time asymmetry of TOAD and the period is one half of the period of control pulses. The theoretical results agree with the experimental results very well.     

On the Gribov Problem for Generalized Connections

 The bundle structure of the space of Ashtekar's generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space . However, for a certain class of non-abelian gauge theories – e.g., all SU(N) theories – the generic stratum is nontrivial. This means, there are no global gauge fixings – the so-called Gribov problem. Nevertheless, for many physical measures there is a covering of the generic stratum by trivializations each having total measure 1. Finally, possible physical consequences and the relation between fundamental modular domains and Gribov horizons are discussed. Received: 4 March 2002 / Accepted: 20 August 2002 Published online: 30 January 2003 Communicated by H. Nicolai     

Periodicity and area spectrum of black holes

The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon areas of a Schwarzschild black hole and a Kerr black hole. It is shown that the equally spaced area spectrum for both cases takes the same form and the spacing is the same as that obtained through the quasinormal mode frequencies. Particularly, for a Kerr black hole, the small angular momentum assumption, which is necessary from the perspective of quasinormal mode, is not employed as the general area spacing is reproduced.     

均匀炸药冲击起爆和起爆后的行为

 介绍并分析了Campbell等人研究均匀炸药冲击起爆和起爆后行为所获得的实验结果,但不涉及其冲击起爆条件。Campbell等人的实验表明,足够强的冲击波进入硝基甲烷后,经过若干微秒的感应时间,爆轰发生在隔板与炸药间的界面处。这就是说,在均匀炸药中,足够强的冲击虽非瞬时但直接（指不经过其它过程,如爆燃）引发了爆轰。重新处理后的实验数据表明：硝基甲烷起爆后,爆轰波的净爆速小于正常爆速;当进入硝基甲烷的初始冲击波的有效压力p_eff由8.82 GPa升至12.14 GPa时,感应时间t_ind的实验值由3.06 μs降至0.705 μs。以两相的排平（A,m）物态方程描述爆轰产物,较为严格地重新推导了基于热起爆理论的估算感应时间t_ind的公式。在上述p_eff的变化范围内,t_ind的理论值则由248 μs降至0.99 μs,明显地高于实验值。这表明,热起爆理论不适于描述硝基甲烷的冲击起爆行为。从本质上讲,热起爆理论对均匀炸药的冲击起爆行为的描述,不符合物质运动的微观图像,因此,它不适于描述均匀炸药的上述行为。     

Homogeneous cosmological model for a Kaluza-Klein-type metric

Cosmological solutions are obtained for a homogeneous, spatially isotropic five-dimensional (5D) Kaluza-Klein-type metric with variable rest mass. The dynamical behavior of the model is studied and a comparison made with the corresponding solution in Einstein's 4D theory. Some important Cosmological parameters are also calculated for this model.     

Homogeneous sound-absorbing structures for aircraft engine ducts

As applied to the ducts of aircraft engines, a new method is studied for extending the frequency range of sound absorption by using special homogeneous materials of a rigid structure. A through- or blind-hole perforation of such a homogeneous material is for the first time suggested with a view to substantially extend its capabilities. A theory is developed for sound-absorbing structures of perforated homogeneous material that allows for computing their wave parameters and impedance on the basis of those of the starting material. Based on this theory, one can calculate the impedance of any, no matter how complex a structure built up of several layers differing in thickness and perforation percentage and diameter. The results of calculations made for the impedance and sound absorption coefficient of single and multiple layer samples show good agreement with experimental data.     

Integrability Conditions for Complex Homogeneous Kukles Systems

In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ? = x + P_n(x, y), ? = ?y, where P_n(x, y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous Kukles systems of degree n that belong to the Sibirsky ideal. Finally, we provide necessary and sufficient conditions when n = 2,?. . .?, 7 in order that the complex homogeneous Kukles system has a local analytic first integral computing the saddle constants and using Gröbner bases to find the decomposition of the algebraic variety into its irreducible components.     

二维各向同性谐振子的双波描述

二维各同性谐振子体系除哈密顿量外还有三个独立的守恒量。本文给出了对这些不同描术宾比较。     

Periodicity and chaos in strongly perturbed classical orbitals for Coulomb interactions

Within the framework of classical mechanics two prototypes of strongly perturbed orbitals, the diamagnetism in hydrogen and electronic double excitation, are analyzed near critical phase space points (fixed points). The motion of the hydrogen electron under the joint influence of the Coulomb field and the magnetic field is periodic for any field strengths. For a two-electron atom however we find a chaotic time evolution of the electron pair correlation, causing presumably irregular spectral patterns.     

Homogeneous nucleation of dislocations

The mechanism and stochastic properties of the homogeneous nucleation of dislocations have been studied. An approach has been proposed for determining the nucleation rate based on consideration of the lifetimes of a metastable state. Primary data have been obtained using the molecular dynamics method. The dependences of the nucleation rate on the shear stresses have been determined for several temperatures. An approximation of the obtained results in terms of the Arrhenius equation has been proposed. The regions of shear stresses and temperatures in which the mechanism of homogeneous dislocation nucleation can be realized have been estimated.     

The Periodicity of Persistent Currents in Mesoscopic Rings

In a tight-binding model, we find that the equation of the Green's function in a onedimensional mesoscopic ring threaded by a Aharonov-Bohm (AB) flux can be exactly solved. From the poles of the Green's function, the eigenvalues are obtained and are periodic in the AB flux with period h/e. However, the periodicity of the persistent currents is determined by the number of electrons in the ring.