q-Weyl coefficients forU q (3) andq-Racah coefficients forSU q (2)

We show that theq-Weyl coefficients of the quantum algebraSU _q (3) are equal to theq-Racah coefficients of the quantum algebraSU _q (2) (up to a simple phase factor). Using aq-analog of the resummation procedure we obtain also theq-analogues of all known general analytical expressions for the 6j-symbols (or the Racah coefficients) of the quantum algebraSU _q (2) starting from one such formula.Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.The research described in this publication was supported in part by Grants No. MB1000 and No. NRC000 from International Science Foundation.     

2 1维5U(2)0￣( )胶球波函数的四级近似

利用截断本征方程方法计算胶球波函数参数比值，得到良好的标度行为。关键词     

The Clebsch-Gordan coefficients of SU(4)

A set of recurrence relations connecting the matrix elements of finite transformation belonging to the same irreducible representation of SU(4) is used to obtain a wide class of matrix elements. An expression for the Clebsch-Gordan coefficient is obtained by integrating the product of three matrix elements belonging to three different irreducible representations of the group. The symmetry properties of the matrix elements and the Clebsch-Gordan coefficients are discussed.The author is grateful to Professors S.Datta Majumdar and G.Bandyopadhyay of the Department of Physics, I.I.T., Kharagpur, for many helpful discussions. This work was supported by the C.S.I.R., Government of India.     

The Clebsch-Gordan coefficients ofsl(2,R) in the parabolic basis

We realize the Lie algebra sl(2,R) in terms of second-order differential operators defined on a dense common domain of square-integrable functions on a two-chart space, where the self-adjoint extension(s) (families) lead to all (and only) self-adjoint irreducible representations of the algebra, single- as well as multi-valued over the group. This allows for a rather straight-forward evaluation of the Clebsch-Gordan coefficients of sl(2,R) in the parabolic subalgebra basis.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.I would like to thank the hospitality of Prof. J. A. de Azcárraga, at the Instituto de Fí'sica Teórica, Universidad de Valencia, where this review was written.     

Drinfeld twist for two-parametric deformation of gl(2) and sl(1/2)

Drinfeld twist is applied to the Lie algebra gl(2) so that a two-parametric deformation of it is obtained, which is identical to the Jordanian deformation of the gl(2) obtained by Aneva et al. The same twist element is applied to deform the Lie superalgebra sl(1/2), since the gl(2) is embedded into the sl(1/2). By making use of the FRT-formalism, we construct a deformation of the Lie supergroup SL(1/2).     

Origin of regge symmetry for wigner coefficients ofLU(2)

Using general properties of the representations of unitary groups and their relations to representations of symmetric groups, the 3j symbol of the unitary unimodular group ?U(2) is written in terms of a 9j symbol of the unitary unimodular group ?U(J) withJ being the sum of the threej's. The result yields the Regge symmetry of the 3j symbol as a consequence of new relations between Wigner coefficients and special invariants of unitary groups on one hand and the association symmetry of the symmetric group on the other.     

New quantum deformation of OSp(1;2)

The complete set of formulas describing the new quantum deformation of the OSp(1;2) supergroup is provided. A general Ansatz is solved for the deformation of the Borel subalgebra of its dual quantum deformation of osp(1;2).     

Fourth Order Approximation of(2+1)-D Su(2)0++ Gluball Wavefunction

In this Paper, the Parameter ratio of (2+1)-D SU(2) 0⁺⁺ glueball wavefunctionis calculated using scheme of truncating eigenvalus equations ,The result shows agood scaling behavior.     

3nj coefficients of u q(2) and multiple basic hypergeometric series

Triple-sum formulas for 9j coefficients and multiple-sum expressions [with five or four separate sums of the _p+1 F _p(1) or _p+1 φ _p type, p=2, 3, 4] for the 12j coefficients of both kinds (with or without braiding) of the SU(2) group and the quantum algebra u _q(2) are derived, eliminating sums over the j type parameters [q generalizations of the very well poised (Dougall’s type) hypergeometric ₄ F ₃(?1), ₅ F ₄(1), and ₆ F ₅(?1) series] from their expansions in terms of q-6j coefficients. The rearrangements of the derived formulas for generic and stretched q-9j coefficients (related to the q versions of some Kampé de Fériet series) are discussed, as well as the different versions of stretched and doubly stretched q-12j coefficients.     

Behavior of lateral-deformation coefficients during elastoplastic deformation of metals

The results of investigations into variation of the coefficients of lateral deformation (the Poisson ratio) during single-axis tension of samples of steel 12Kh18N10T and St3, titanium VT1, the aluminum alloy D16AM, copper M1, and a magnesium alloy are considered. The technique developed on the basis of the optoacoustic effect and simultaneous measurements of the longitudinal and surface speeds of sound in metallic samples during the tension makes it possible to measure the rates at various stages of the deformation process. The data obtained make it possible to construct the dependences of variation of the lateral-deformation coefficients at all stages of the plastic flow. The correlation of these variations both with known processes of structural reconstructions at various stages of plastic flow and with the process of localization of plastic-shear bands in the aluminum alloy is noted.     

Discrete Series of Su(1, 1) and Gaussian Deformation

Starting from the holomorphic discrete series of SU(1, 1), we construct a hyperbolic analogue of a quantum mechanical harmonic oscillator with a Poincaré disc as nonlinear phase space. A Bargmann-type transform is established which interwines the real wave and complex wave representation. The probability distribution of the position observable in vacuum is calculated explicitly, it admits the Gaussian law of the ordinary harmonic oscillator as zero-curvature limit.     

The deformation producing tendency of (d 3/2−f 7/2) empirical effective interaction

The effective matrix elements in (d _3/2−f _7/2)² configuration have been recently defined by Erskineet al. and Sherret al. assuming shell clcsures for S³² and Ca⁴⁰. We have attempted to verify whether this empirically deduced (d _3/2−f _7/2)² interaction permits thed _3/2 shell to remain closed when nucleons are added to Ca⁴⁰. It is found that the Erskine interaction gives rise to ground states of thef _7/2 shell nuclei in which thed _3/2 orbit is completely filled. However that interaction over-binds Ca⁴⁰. If the centroid of the (d _3/2)² interaction is modified to fit the Ca⁴⁰ binding energy, the ground states of Cr⁴⁸ and Fe⁵² become deformed and thed _3/2 orbit is not completely filled.     

The representations and coupling coefficients of su(n); application to su(4)

Analytical expressions for the matrices and an explicit algorithm for computing Clebsch-Gordan coupling coefficients are given forsu(4) in au(3)-coupled basis as an example of the construction for anysu(n) in au(n−1) basis. The results areinduced from the known results foru(3) by means of the vector-coherent-state (VCS) theory of induced representations. The important recent result that makes this possible is the discovery that a complete set of shift tensors for the finitedimensional representations of reductive Lie algebras can be induced, by VCS methods, from those of suitably defined subalgebras.     

New integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations with constant and time-dependent coefficients

In this work, we mainly address two new integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations, which naturally appear in surface theory and fluid dynamics. The first equation includes constant coefficients, while the other is characterized with time-dependent coefficients. It is of further value to investigate the integrability of each model. This study puts forward a Painlevé test to reveal the Painlevé integrability. We show that the first equation passes the Painlevé test to confirm its integrability. However, the compatibility conditions of the second model with time-dependent coefficients provides the relation between these coefficients to ensure its integrability. We show that the dispersion relations of the two equations are distinct, whereas the phase shifts are identical. We apply the simplified Hirota's method where four sets of multiple soliton are derived for these equations.     

Sticking coefficients of CO,O2 and Xe on the (110) and (100) planes of tungsten

Sticking coefficients for oxygen, CO and Xe on the (110) and (100) planes of tungsten are presented as functions of absolute coverage, surface and gas temperature. Sticking coefficients for CO are in general higher and show simpler behavior than those for oxygen. Sticking coefficients for all gases studied are higher on (100) than on (110) under comparable conditions. It is concluded that simple Kisliuk models are applicable over much of the temperature range for CO on (110) and (100), but not for oxygen, where adsorption and reflection coefficients on first impact vary with coverage, and surface and gas temperatures in complicated fashion. For Xe, at low surface temperatures sticking coefficients are close to unity and increase with coverage, indicating better energy accomodation on Xe-covered than on clean tungsten.     

The nu(2) Band of Formaldehyde-d(2)

High-resolution Fourier transform infrared spectrum of the nu(2) band (1590-1780 cm(-1)) of deuterated formaldehyde D(2)CO has been recorded. More than 2500 rovibrational transitions have been assigned up to J(max) = 52 and K(max)(a) = 17. The upper state v(2) = 1 (A(1)) was found to be perturbed by a DeltaK(a) = 2 interaction with the v(4) = 2 (A(1)) state. To explain the resonance perturbation in the v(2) = 1 state, some lines of the 2nu(4) band (the band center at about 1868 cm(-1)) have also been assigned. Both bands were fitted simultaneously to the Watson-type rotational Hamiltonian using I(r) representation in A reduction, and the mutual interaction was taken into account. As a result, the rotational parameters of the v(2) = 1 state up to eighth order and the interaction parameter have been obtained. Copyright 2001 Academic Press.     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.     

The SU6 Clebsch-Gordan coefficients for the reduction of (35) ⊗ (35) to (35), and (56) ⊗ (35) to (56)

A convenient definition of the basis vectors of SU₆ representations is given. The most important Clebsch-Gordan coefficients are calculated.