Symmetry of coupling coefficients for cubic and trigonal group under association

Relations between Racah matrices for products of irreducible representations of the double cubic and trigonal group are derived using the concept of association, i.e. multiplication by the representation A₂. Relations for the associated decomposition coefficients for O′ → D′₃ and the appropriate reduction coefficients are established.     

On the quantification of OH*, CH*, and C2* chemiluminescence in flames

Absolute concentrations of all important chemiluminescent species, OH–A, CH–A, CH–B, and C₂-d have been measured for the first time in methane-oxygen flames at low pressure. The optical detection system for chemiluminescence measurements has been calibrated with Rayleigh and Raman scattering of a cw laser, with the latter approach yielding superior results. The measured ratio between the concentration of CH–B and CH–A suggests that the electronically excited CH* is formed close to thermal equilibrium. Introduction of different rate constants for reactions leading to CH–A and CH–B were not necessary to explain the experimental results. Results are compared with a recent numerical model. Deviations in profile shape and peak positions are relatively small for stoichiometric flames, but become more pronounced in richer mixtures. Larger discrepancies are observed for the absolute concentrations, depending on the chemiluminescent species and the stoichiometry. In an attempt to find an alternative method for the quantification of chemiluminescent species, MIR-CRDS has been performed around 3.9 μm. While H₂O and OH–X could be measured, the sensitivity was not high enough to detect the low sub-ppb concentration of OH–A—in part due to the limited reflectivity of mirrors in the MIR, in part due to a significant background of hot H₂O lines.     

C*-algebras and automorphism groups

Let (A,G, α) be aC*-dynamical system withG a topological group. Let π be a representation ofA. We will show that there exists a quasiequivalent representation \(\hat \pi \) to π which is a covariant representation, if and only if the folium of π is invariant under the action ofG and this action is strongly continuous.     

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.     

Normal form coefficients for the nonresonant double Hopf bifurcation

Expressions are given for the coefficients in the normal form for the nondegenerate double Hopf bifurcation when the two frequencies are not in strong resonance.     

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.     

Chemiluminescent emission of CH*, C*<Subscript>2</Subscript>, OH*, and CO*<Subscript>2</Subscript> during the ignition of ethane behind reflected shock waves

The chemiluminescent emission from CH*, C*₂, OH*, and CO*₂ during the self-ignition of various mixtures of ethane with oxygen and argon behind reflected shock waves in the 1240–1790 K temperature range at a total concentration of the mixture М ₅ = (1 ± 0.2) × 10^?5 mol/cm³ is experimentally studied. It has been shown that the time-to-maximum in the emission intensity profiles is almost identical for all the emitters studied. How the pattern of the OH* emission profile changes with the temperature and mixture composition is examined. The CH* and C*₂ emission profiles demonstrate virtually symbatic behavior in the covered ranges of temperature, pressure, and equivalence ratio. It is established that the emission signals from OH* and CO*₂ appear earlier than the C*₂ and CH* emission signals. The numerical simulation predictions are found to be in close agreement with the experimental results.     

Method for determining the two-beam coupling gain coefficients of photorefractive crystals

A new method is proposed for determining the two-beam coupling gain coefficients of photorefractive crystals with both o- and e-polarized lights. This method enables one to determine simultaneously and precisely the gain coefficients of a crystal for o- and e-polarized lights while the fanning effect is diminished. Experimental demonstrations are presented.     

A method for calculating the character tables of double groups of products of groups

A method for calculating the character table of a double group from the character tables of two of its subgroups is presented. The procedure is applicable not only to spin double groups but also to the generation of the character tables of the torsional double groups.     

Note on influence of dipole-quadrupole coupling upon the C12(γ,n)C11 cross section

The cross section for the C¹² (γ, n) C¹¹ reaction has been measured from threshold to 25-MeV with a small energy bin (100 keV). The giant resonance was resolved into a very well defined triplet structure. It seems that the shape of the C¹² (γ, n) C¹¹ cross section is influenced by the dipole-quadrupole coupling.     

A double Paul trap system for the electronic coupling of ions

We report on the progress towards the implementation of a double trap system for the coupling of ion clouds stored in different traps through the charges they induce in a common electrode. The two traps have cylindrical symmetry and can be used either as Penning or Paul traps. The laser system for Doppler cooling of ⁴⁰Ca⁺ clouds is described. The cooling can be performed differentially in the two traps, aiming at the study of the coupling between two clouds of ions at different temperatures. This setup is the starting point for the realization of energy transfer between two Doppler-cooled ions stored in different traps. We report on the status of the experiment and evaluate the performance required for an efficient coupling.     

New Symmetry Reductions,Dromions—Like and Compacton Solutions for a 2D BS（m,n） Equations Hierarchy with Fully Nonlinear Dispersion

We have found two types of important exact solutions,compacton solutions,which are solitary waves with the property that after colliding with their own kind,they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction,in the (1 1)D,(1 2)D and even (1 3)D models,and dromion solutions (exponentially decaying solutions in all direction) in many (1 2)D and (1 3)D models.In this paper,symmetry reductions in (1 2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m,n) equation)ut b(u^m)xxy 4b(u^n δx^-1uy)x=0,which is a generalized model of (1 2)D break soliton equation ut buxxy 4buuy 4buxδx^-1uy=0,by using the extended direct reduction method.As a result,six types of symmetry reductions are obtained.Starting from the reduction equations and some simple transformations,we obtain the solitary wavke solutions of BS(1,n) equations,compacton solutions of BS(m,m-1) equations and the compacton-like solution of the potential form (called PBS(3,2)) ωxt b(ux^m)xxy 4b(ωx^nωy)x=0.In addition,we show that the variable ∫^x uy dx admits dromion solutions rather than the field u itself in BS(1,n) equation.     

The infinite coupling limit and the asymptotics of coefficients of the perturbation expansion

For some functions in quantum field theory and quantum mechanics, presented by the asymptotic expansion in coupling constant g, the method for finding the approximate asymptotics when g is proposed.Such an estimation requires the first exact terms of the perturbation theory, their high-order asymptotics and supposition on the Borel summability. This method for the Gell-Mann-Low function (g) in the (4²/3)g ₍₄₎ ⁴ model gives approximately (g) 1.8 g ².     

Calculation of the strong coupling constants for B s1 B*K and B s1 B*K*0 vertices

The structure of the B _s1(5830) meson has not yet been exactly known in the quark model. In this paper, the strong form factors and coupling constants of B _s1, as a conventional meson, are investigated. The coupling constants $ g_{B_{s1} B^* K} $ and $ g_{B_{s1} B^* K_0^* } $ are calculated in the framework of the three-point QCD sum rules. Our findings are compared with the results of the light-cone sum rules (LCSR) and heavy-chiral unitary approaches.