Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials with the weight exp tr (X Ω Y Ω ^† ) are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat–Heckman’s theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.     

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D _N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D _N , N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \mathbb CP^l_q{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0⁺-dimensional equivariant even spectral triples. If ℓ is odd and N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8.     

Continuously tunable 1 byte delay in coupled-resonator optical waveguides

A reconfigurable coupled-resonator optical waveguide made of a few directly coupled ring resonators is employed to control the delay of data streams modulated at tens of gigabits per second. A delay of 8 bit lengths (1 optical byte) with a small pulse broadening and 1 dB/bit fractional loss is achieved by using only eight rings. The limiting role of waveguide loss and spurious backreflections is experimentally investigated. The high storage efficiency (1 bit/ring) of the device enables an easy, reliable, hitless, and relatively low-power-consuming management of the delay. A higher storage efficiency is demonstrated to be associated to an unavoidable higher pulse distortion.     

Modular forms and three-loop superstring amplitudes

We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.     

Stabilitätsverhalten der Stösselstange in geradgeführten Kurvengetrieben

Übersicht In diesem Beitrag wird die Stößelstange in geradgeführten Kurvengetrieben als ein gedämpfter Euler-Bernoulli-Stab aufgefaßt. Nach dem Aufstellen der Differentialgleichung für die Querschwingungen mittels des Hamiltonschen Prinzips wird diese mit Hilfe des Galerkinschen Verfahrens auf ein System von Hillschen Differentialgleichungen reduziert. Dann werden für ein allgemeines Kurvenbewegungsgesetz Näherungsformeln für die Grenzkurven der Instabilitätsbereiche hergeleitet, wobei der (bezogene) Stößelhub in Abhängigkeit der Kurvenwinkelgeschwindigkeit dargestellt wird. Die Ergebnisse werden durch ein Beispiel veranschaulicht.

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On the stability behaviour of the reciprocating follower in cam mechanisms

Summary This paper is concerned with the simulation of the reciprocating follower in cam mechanisms as a damped Euler-Bernoulli beam. The governing partial differential equation of the transversal vibrations of the follower is derived, using Hamilton's principle. Then it is reduced to a system of Hill-equations by the Galerkin method. For the case of a general motion of the follower the approximate formulas of the boundaries between the stable and unstable regions are derived, represented in the plane of strok depending on the angular velocity. The obtained results are illustrated by an example.

     

An iterative method of evaluation of elastic-plastic deflections of hyperstatic framed structures

Summary The concept of substitutive concentrated elastic-plastic rotations, replacing actual elasticplastic zones is used, together with an iterative method of determination of the bending moment distribution to simplify the evaluation of elastic-plastic deflections of hyperstatic beams and frames.

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Eine iterative Methode der Auswertung von elastisch-plastischen Verschiebungen für statisch unbestimmte Rahmen

Übersicht Die Idee von fiktiven Ersatzrotationen, welche die tatsächlichen elastisch-plastischen Zonen modelliert, wird mit einer iterativen Methode kombiniert, um eine relativ einfache Bestimmung von Biegemomentenfeldern in statisch unbestimmten Balken und Rahmen zu ermöglichen. Die resultierenden Verschiebungen, ergeben sich mit ausreichender Genauigkeit.

     

Projectile-like fragments excitation and gamma-rays emission after the deep inelastic reaction of32S on58Ni

The deep-inelastic reaction induced by 143 MeV³²S on⁵⁸Ni have been studied detecting projectile-like fragments (PLF) in coincidence withγ-rays in NaI(TI) scintillators. γ-ray multiplicity and anisotropy have been derived for Z_plf=14, 15 as a function of energy loss and/or γ-energy. The information obtained are compared with a discrete γ-line study of the same reaction. The effect of the exit channel selection (ejectileZ, energy loss,E _γ) on the γ-observables is discussed in connection with the evidence of a strong PLF γ-emission.     

An expression for transient thermal stress in a nonhomogeneous plate with temperature variation through thickness

Summary An expression for nonzero thermal stress in a nonhomogeneous flat plate with arbitrary variation in mechanical properties is presented under a transient temperature distribution. Especially an equation for nonzero thermal stress and its numerical calculation showing the effect of nonhomogeneous thermal and mechanical properties on temperature and thermal stress distribution, is given for the case of an exponentially varying thermal conductivity and Young's modulus, but for a homogeneous Poisson's ratio and coefficient of linear thermal expansion.

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Formeln für transiente Wärmespannungen in einer nichthomogenen Platte mit einer über die Dicke veränderlichen Temperatur

Übersicht Es werden Ausdrücke für nichtverschwindende Wärmespannungen in einer inhomogenen ebenen Platte bei beliebiger Ortsabhängigkeit der mechanischen Eigenschaften entwickelt, und zwar für eine transiente Temperaturverteilung. Insbesondere wird eine Gleichung für nichtverschwindende Wärmespannungen angegeben und numerisch ausgewertet, die den Einfluß nichthomogener thermischer und mechanischer Eigenschaften auf die Verteilung von Temperatur und Wärmespannung bei exponentieller Ortsabhängigkeit der Wärmeleitfähigkeit und des E-Moduls darstellt, wobei jedoch die Poissonzahl und der lineare Wärmeausdehnungskoeffizient konstant sind.