u q(2,1) noncompact quantum algebra: Intermediate discrete series of unitary irreducible representations

The unitary irreducible representations of the u _q(2,1) quantum algebra that belong to the intermediate discrete series are considered. The q analog of the Mickelsson-Zhelobenko algebra is developed. Use is made of the U basis corresponding to the reduction u _q(2,1) ? u _q(2). Explicit formulas for the matrix elements of the generators are obtained in this basis. The projection operator that projects an arbitrary vector onto the extremal vector of the intermediate-series representation is found.     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

The quantum groups GLq(n) and Weyl-Heisenberg operators

It is shown that for deformation parameters q = 1, the bilinear product relations which define the quantum groups GL_q(n) can be recast as Weyl-Heisenberg relations, provided some invertibility conditions are met. Finite- and infinite-dimensional representations of GL_q(n) are then easily constructed, as shown in a few examples.     

q-Fuzzy Spheres and Quantum Differentials on Bq[SU2] and Uq(su2)

We provide a new unified construction of the two-parameter Podleś two-spheres as characterised by a projector e with trace _q (e) = 1 + λ. In our formulation the limit in which q → 1 with λ fixed is the fuzzy sphere, while the limit λ → 0 with q fixed is the standard q-deformed sphere. We show further that the non-standard Podleś spheres arise geometrically as ‘constant time slices’ of the unit hyperboloid in q-Minkowski space viewed as the braided group B _q [SU ₂]. Their localisations are then isomorphic to quotients of U _q (su ₂) at fixed values of the q-Casimir precisely q-deforming the fuzzy case. We also use transmutation and twisting theory to introduce a C_q[G_\mathbb C]{C_q[G_\mathbb {C}]} -covariant differential calculus on general B _q [G] and U _q (g), with Ω(B _q [SU ₂]) and Ω(U _q (su ₂) given in detail. To complete the picture, we show how the covariant calculus on the 3D bicrossproduct spacetime arises from Ω(C _q [SU ₂]) prior to twisting.     

Matrix elements for the representations of SO(n) and SO0(n, 1)

Matrix elements of the unitary irreducible representations of the group SO(n) of class higher then 1 (with respect to SO(n−1)) in Gel'fand-Zetlin basis are obtained in explicit form. They are represented as polynomials in cosθ and sinθ of the order equal to the first coordinate of the highest weight. Making use of them the representation matrix elements for the group SO₀(n, 1) in SO(n) basis are calculated.     

Analysis of irreducible representations of the group U (4) Up(2) × Un(2)

The general method of projection operators is used to construct the noncanonical nonorthogonal basis of arbitrary irreducible representation of the group U (4) in the reduction U (4) U_p(2) × U_n(2), where U_p(2)(U_n(2)) is the transformation group in the proton (neutron) spin space. The completeness of this basis is proved and the matrices of the U (4) group generators and of the Bargmann-Moshinsky operator Ω in this basis are obtained. The matrix Ω exhibits a nondegenerate spectrum of the eigenvalues which may be used as the missing quantum number.     

Critical String Wave Equations and the QCD(U(Nc)) String. (Some Comments)

We present a simple proof that self-avoiding fermionic strings solutions solve formally (in a Quantum Mechanical Framework) the QCD(U(N _c )) Loop Wave Equation written in terms of random loops.     

A classification of the unitary irreducible representations ofSU(N, 1)

All inequivalent continuous unitary irreducible representations ofS U(N, 1) (N2) have been determined and classified. The matrix elements of the infinitesimal generators realized on a certain Hilbert space have been derived. Representations of the groups ,S U(N, 1)/Z _N+1, andU(N, 1) are classified in a similar manner.     

Deformed traces and covariant quantum algebras for quantum groups GLqp(2) and GLqp (1¦1)

The q-deformed traces and orbits for the two parametric quantum groups GL_qp(2) and GL_qp(1¦1) are defined, they are subsequently used in the construction of q-orbit invariants for these groups. General qp-(super)oscillator commutation relations are obtained, which remain invariant under the coactions of groups GL_qp(2) and GL_qp(1¦1). The GL_qp(2)-covariant deformed algebra is deduced in terms of the bilinears of bosonic qp-oscillators, which turns out to be a central extension of the Witten-type deformation of sl(2) algebra. In the case of the supergroup GL_qp(1¦1), the corresponding covariant algebras contain the N = 2 supersymmetric quantum mechanical subalgebras.     

A classification of the unitary irreducible representations ofSO 0(N, 1)

All inequivalent continuous unitary irreducible representations of the groupSO ₀(N, 1),N3, and its universal covering group are classified.     

Constrained current algebras and g/u(1) conformal field theories

Operator quantization of the WZNW theory invariant with respect to an affine Lie algebra with a constrained subalgebra is performed using Dirac's procedure. Upon quantization the initial energy-momentum tensor is replaced by the g/u(1)^d coset construction. The WZNW theory with a constrained current is equivalent to the su(2)/u(1) conformal field theory.     

EPR study of quasi-one-dimensional complex oxides A3n + 3mA′nMn3m + nO9m + 6n (A-Sr, Ba; A′-Mg, Zn, Cu)

Exchange interactions in the quasi-one-dimensional complex oxides Sr₄MgMn₂O₉, Ba₆MgMn₄O₁₅, Ba₈MgMn₆O₂₁, and Ba₉ M ₂Mn₅O₂₁ (M-Cu, Zn, Mg) have been studied by electron paramagnetic resonance. The temperature dependence of the spectral parameters showed that the exchange interaction is antiferromagnetic and occurs mainly inside the manganese-containing groups and to a lesser extent between them.     

Structures and electronic properties of Mo2nNn（n=1-5）:a density functional study

The lowest-energy structures and the electronic properties of Mo2nNn(n=1-5) clusters have been studied by using the density functional theory(DFT) simulating package DMol 3 in the generalized gradient approximation(GGA).The resulting equilibrium geometries show that the lowest-energy structures are dominated by central cores which correspond to the ground states of Mo n(n = 2,4,6,8,10) clusters and nitrogen atoms which surround these cores.The average binding energy,the adiabatic electron affinity(AEA),the vertical electron affinity(VEA),the adiabatic ionization potential(AIP) and the vertical ionization potential(VIP) of Mo2nNn(n=1-5) clusters have been estimated.The HOMO-LUMO gaps reveal that the clusters have strong chemical activities.An analysis of Mulliken charge distribution shows that charge-transfer moves from Mo atoms to N atoms and increases with cluster size.     

Structures and electronic properties of AUn-1Cu and AUn （n ≤ 9） clusters

A systematic study on the structure and electronic properties of gold clusters doped each with one copper atom has been performed using the density functional theory. The average bond lengths in the Aun-1Cu （n ≤ 9） bimetallic clusters are shorter than those in the corresponding pure gold clusters. The ionization potentials of the bimetallic clusters Aun-1Cu （n 〈 9） are larger than those of the corresponding homoatomic gold clusters except for Aus. The energy gaps of the Au-Cu binary clusters are narrower than those of the Aun clusters except AuCu and Au3Cu. No obvious even-odd effect exists in the variations of the electron affinities and ionization potentials for the Aun-1Cu （n ≤ 9） clusters, which is in contrast to the case of gold clusters Aun.     

The A2 (n, 3px) Rydberg state of formaldehyde

Pairs of bands were observed in the absorption spectrum of H₂CO, HDCO, and D₂CO in the 1470-1430 Å region which were characterized by well-defined rotational band contours. A band contour synthesis of the observed band envelopes demonstrated that the bands are described by type C selection rules. From the observed intervals and their shifts on deuterium isotope substitution these bands were assigned to quantum additions of ν₅ and ν₆. The symmetry of the upper state was deduced to be ¹A₂ from the vibrational assignment of the bands and their polarizations, while the results from MO theory lead to the orbital assignment n → 3p_x. The electronic transition then is .     

Finite-dimensional irreducible representations of the quantum superalgebraU q [gl(n/1)]

It is shown that every finite-dimensional irreducible module over the general linear Lie superalgebragl(n/1) can be deformed to an irreducible module ofU _q [gl(n/1)], aq-analogue of the universal enveloping algebra ofgl(n/1). The results are extended also to all Kac modules, which in the atypical cases remain indecomposible. Within each module expressions for the transformations of the Gel'fand-Zetlin basis under the action of the algebra generators are written down. An analogoue of the Poincaré-Birkhoff-Witt theorem is formulated.     

Orbital responses to methyl sites in CnH2n+2 (n=1-6)

Orbital responses to methyl sites in C_nH_2n+2 (n=1-6) are studied by B3LYP/TZVP based on the most stable geometries using the B3LYP/aug-cc-pVTZ method. Vertical ionization energies are produced using the SAOP/et-pVQZ model for the complete valence space. The highest occupied molecular orbital (HOMO) investigations indicate the p-electron profiles in methane, ethane, propane, and n-butane. By increasing the number of carbon-carbon bonds in lower momentum regions, the s, p-hybridized orbitals are built and display strong exchange and correlation interactions in lower momentum space (P≤0.50 a.u.). Meanwhile, the relative intensities of the isomers in lower momentum space show the strong bonding number dependence of the carbon-carbon bonds, meaning that more electrons have contributed to orbital construction. The study of representative valence orbital momentum distribution further confirms that the structural changes lead to evident electronic rearrangement over the whole valence space. An analysis based on the isomers reveals that the valence orbitals are isomer-dependent and the valence ionization energy experiences an apparent shift in the inner valence space. However, such shifts are greatly reduced in the outer valence space. Meanwhile, the opposite energy shift trend is found in the intermediate valence space.     

宽带非均匀半径渐变TE0n-TE0(n+1)模式转换器的设计研究

基于耦合波理论,对两类半径渐变圆波导TE_0n-TE_0(n+1)模式转换器进行理论分析、数值计算和仿真模拟.均匀半径渐变波导高功率模式转换器,采用中心频率为17.14GHz、六周期TE₀₂-TE₀₃模式和中心频率为34.30GHz、六周期TE₀₁-TE₀₂模式两种设计参数.非均匀半径渐变波导高功率模式转换器,采用中心频率为34.30GHz、六周期TE 关键词： 模式转换器 耦合波理论 非均匀半径渐变 转换带宽     

PdnPbm(n+m≤5)混合团簇的结构与光谱性质

在相对论有效原子实势(RECP)近似下，用密度泛函中的B3LYP/LANL2DZ方法，对纯Pb_n(n=2—5)团簇、Pd_nPb_m(n+m≤5)混合团簇的各种可能几何构型进行全优化计算，得到它们的基态结构和光谱性质；从结构和振动光谱两个方面分析了其形成规律；最后计算了团簇的能级分布和最高占据轨道(HOMO)与最低空轨道(LUMO)之间的能级间隙(HLG)，分析了团簇的化学活性. 关键词： 团簇 有效原子实势 密度泛函     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters

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, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with

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as well as in an orthorhombic cell with lattice parameters

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.