Compact involutions of semisimple quantum groups

It is proved that a complex cosemisimple Hopf algebra has at most one compact involution modulo automorphisms.     

On the tensor product of representations of semisimple Lie groups

All topologically irreducible representations involved in the tensor product of finite and infinite dimensional representations of the Principal nonunitary series (including the unitary series) of a semisimple Lie group are defined.     

On the Gravitization of Quantum Mechanics 1: Quantum State Reduction

This paper argues that the case for “gravitizing” quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change, the very formalism of quantum mechanics. Most particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.     

Reduction of intensities of paramagnetic resonance lines by lattice vibrations

Using a simple model of spin-phonon interaction we find that the intensities of paramagnetic resonance lines are reduced by lattice vibrations in solids. The intensity missing from the paramagnetic resonance line goes into phonon sidebands. If the phonon spectrum is a continuum, which it is in the frequency region of interest, the sidebands appear as a broad background.     

1:2内共振及主共振情况下高架索的面内振动分析

考虑了由货物自重引起高架索静态构型的分段特性、高架索的倾斜角以及发送端水平运动等多种因素的影响, 建立了海上航行干货补给高架索系统面内振动的三自由度分段动力学模型. 将惯性项解耦后, 得到了1:2内共振与主共振同时作用时的常微分方程, 并利用多尺度法对其进行了摄动分析和数值分析, 为后续开展相关的非线性动力学研究奠定了一定的理论基础.     

The concept of a quantum semisimple group

We explore the possibility of introducing the concept of a quantum semisimple group by exhibiting a class of deformations of classical groups whose Dynkin diagrams are disconnected at the classical level, but become connected at the quantum level. The possibility of applications to the quantization of Lorentz and Poincaré groups are mentioned.     

Embedding of the Galilei algebra into complex semisimple lie algebras

The following result is proven: Complex simple Lie algebras L? have subalgebras ε(?) isomorphic to the complex Galilei algebra ? if and only if L? ∈ {A_r (r ? 5); B_r (r ? 3); C_r, D_r (r ? 4); F₄; E₆; E₇; E₈}.The set of subalgebras ε(?) in A₅ decomposes intoconjugacy classes labelled by a complex number; there is only one conjugacy class in B?₃ and in C₄.     

The Gell-Mann formula for representations of semisimple groups

A method for constructing representations of non-compact semisimple groups from representations of semidirect product groups is presented. Necessary and sufficient algebraic conditions for the method to work are given, and these are applied to cases of possible interest for the classification of elementary particles.This work was supported by the Office of Naval Research, # NONR 3656 (09).     

Deformations of semisimple bihamiltonian structures of hydrodynamic type

We classify in this paper infinitesimal quasitrivial deformations of semisimple bihamiltonian structures of hydrodynamic type.     

Remark on the integrability of some representations of the semisimple Lie algebras

It is discussed how boundedness of the quadratic Casimir operator in skew-symmetric representation τ of semisimple Lie algebra can simplify the proof of integrability of τ.     

1H magnetic resonance spectroscopy of the normal testis: preliminary findings

PURPOSE: The purpose of this study was to determine the pre- and postpubertal 1H magnetic resonance spectroscopic characteristics of the normal testis to establish baseline values for further clinical studies. MATERIALS AND METHODS: The subjects consisted of male volunteers, of whom 19 were prepubertal with ages between 7 and 13 years and 24 were postpubertal with ages between 19 and 39 years. Their testes were evaluated at 1.5 T with magnetic resonance spectroscopy; in addition, testis volumes were measured. Major metabolite peaks were identified and their ratios were calculated. Metabolite differences of testis between pre- and postpubertal age were analyzed. RESULTS: Major constituents of spectra were 3.21 ppm choline and 0.9-1.3 ppm lipid peaks. At the echo time (TE) spectrum of 31 ms, choline/lipid ratios ranged from 0.35 to 8.30 (mean=1.87) in postpubertal males and from 0.06 to 5.45 (mean=0.88) in prepubertal males (P<.013). At the TE spectrum of 136 ms, choline/lipid ratios ranged from 0.66 to 15.42 (mean=4.09) in postpubertal males and from 0.05 to 4.91 (mean=0.9) in prepubertal males (P<.016). CONCLUSIONS: Choline/lipid ratio was higher in the postpubertal period. The existence of higher choline peak in that age group should be due to the initiation of spermatogenesis. The decrease in the lipid peak may represent the effect of testosterone on testicular tissue or may be due to histochemical changes initiated by puberty. The significant decrease in choline/lipid ratio noted after puberty could represent the presence of spermatogenesis. This hypothesis should be evaluated by further studies on postpubertal subjects with impaired spermatogenesis.     

On the genus two free energies for semisimple Frobenius manifolds

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as the sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called ??genus two G-function.?? Conjecturally, the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities, as well as for ?¹-orbifolds with positive Euler characteristics. We explain the reasons for the conjecture and prove it in particular cases.     

Observation of the M1 giant resonance by resonance averaging in 106Pd

An investigation of capture of 2 keV and 24 keV neutrons in a ¹⁰⁵Pd target resulted in resonance-averaged intensities of primary gamma rays with energies between 5.2 and 9.5 MeV. From these intensities the gamma ray strength functions have been evaluated for E1, M1 and E2 radiation and compared with predictions of the giant resonance theory. The inclusion of an energy dependent spreading width for the E1 giant resonance is necessary. The energy distribution of M1 reduced strength is consistent with an interpretation of a broad resonance around 8.8 MeV. E2 data agrees satisfactorily with the giant resonance extrapolation.     

Hamiltonian systems with detuned 1:1:2 resonance: Manifestation of bidromy

We consider a generalization of the 1:1:2 resonant swing-spring [see H. Dullin, A. Giacobbe, R.H. Cushman, Physica D 190 (2004) 15] which is suggested both by the symmetries of this system and by its physical and in particular molecular realizations [see R.H. Cushman, H.R. Dullin, A. Giacobbe, D.D. Holm, M. Joyeux, P. Lynch, D.A. Sadovskií, B.I. Zhilinskií, Phys. Rev. Lett. 93 (2004) 024302-1-024302-4]. Our generic integrable system is detuned off the exact Fermi resonance 1:2. The three-dimensional (3D) image of its energy-momentum map EM consists either of two or three qualitatively different non-intersecting 3D regions: a regular region at low vibrational excitation, a region with monodromy similar to that studied for the exact resonance, and in some cases—an intermediate region in which the 3D set of regular values of EM is partially self-overlapping while remaining connected. In the presence of this latter region, the system has an interesting property which we called bidromy. We analyze monodromy and bidromy for a concrete integrable classical Hamiltonian system of three coupled oscillators and for its quantum analog. We also show that the bifurcation involved in the transition from the regular region to the region with monodromy can be regarded as a special resonant equivariant analog of the Hamiltonian Hopf bifurcation.