Character and determinant formulae of quasifinite representation of theW 1+∞ algebra

We diagonalize the Hilbert space of some subclass of the quasifinite module of theW ₁₊ algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials.     

Quasifinite highest weight modules over the superW 1+∞algebra

We study quasifinite highest weight modules over the supersymmetric extension of theW ₁₊ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by polynomials, and obtain the differential equations for highest weights. The spectral flow, free field realization over the (B, C)-system, and the embedding into (|) are also presented.Address after April 1, 1994: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, JapanAddress after April 1, 1994: Uji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University, Uji 611, Japan     

D=2 and D=4 realization of κ-conformal algebra

We describe the generators of-conformal transformations leaving invariant the-deformed d'Alembert equation. For the case D=4 the algebraic structure of the conformal extension of the off-shell spin zero realization of-Poincaré algebra is discussed. Then the D=2 off-shell realization of-conformal algebra for arbitrary spin and its commutation relations are studied.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2P 302 087 06.     

Fock space resolutions of the Virasoro highest weight modules withc ≤ 1

We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules withc1. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.Supported by the NSF Grant #PHY-88-04561.Supported in part by the Department of Energy Contract #DE-FG03-84ER-40168 and by the USC Faculty Research and Innovation Fund.     

Rotational character of sound intensity and surface sound intensity

By using the concept of complex sound intensity,the rotationalcharacter of the active sound intensity which is the real component of thecomplex sound intensity is descussed in this paper.It is shown that it isthe irrotational component of the active sound intensity that transferssound energy in sound field.When sound power is measured with thetwo-microphone technique,the rotation of the active sound intensity hasan effect on it.Because the irrotational component of the active sound in-tensity depends only on the surface sound intensity,measuring the surfacesound intensity can avoid the effect of the rotation.Based on atuo-powerspectra,formulas about the surface sound intensity are given in thispaper,providing a theoretical basis for measuring the surface soundintensity.     

The theoretical character of the X^1∑^＋ and A^1∑^＋ states of ScN

This paper calculates the potential energy curves (PECs) of the ground state (X 1 Σ + ) and excited state (A 1 Σ + ) of ScN molecule by multireference configuration interaction method. The correct character of the PECs has been gripped while they had been improperly reported in the literature. Based on the PECs, the spectroscopic parameters and vibrational energy levels are determined, and compared with experimental data and other theoretical works available at the present.     

Charm physics — A field full of challenges and opportunities

In this review, we discuss some interesting issues in charm physics, which is full of puzzles and challenges. So far in this field, there exist many problems which have not obtained satisfactory answers yet as more unexpected phenomena Continue to be observed at the current facilities of high energy physics. Charm physics may become an ideal place for searching new resonances and studying non-perturbative QCD effects, moreover it is probably an area for exploring new physics beyond the Standard Model. More data will be available at the BE-SIII, B-factories, LHC and even the future ILC, which may open a wide window to a better understanding of its nature.      

Hochschild cohomology of the Weyl algebra and Vasiliev’s equations

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as well as for the smash products of the Weyl algebra and a finite group of linear symplectic transformations. A relationship with the higher-spin field theory is briefly discussed.     

A 9 × 9 matrix representation of Temperleyben-Lieb algebra and corresponding entanglement

We present the matrix U. The 9 × 9 U matrix is a representation of specialized Temperley-Lieb algebra. Based on which, a unitary Ř matrix is generated via the Yang-Baxterization approach. The 9 × 9 Ř matrix, a solution of the Yang-Baxter equation, is universal for quantum entanglement.     

A 9 ? 9 matrix representation of Temperleyben-Lieb algebra and corresponding entanglement

We present the matrix U. The 9 ? 9 U matrix is a representation of specialized Temperley-Lieb algebra. Based on which, a unitary Ř matrix is generated via the Yang-Baxterization approach. The 9 ? 9 Ř matrix, a solution of the Yang-Baxter equation, is universal for quantum entanglement.     

A subalgebra of loop algebra A2^～ and its applications

A subalgebra of loop algebra A2^～ and its expanding loop algebra G^- are constructed. It follows that both resulting integrable Hamiltonian hierarchies are obtained. As a reduction case of the first hierarchy, a generalized nonlinear coupled Schroedinger equation, the standard heat-conduction and a formalism of the well known Ablowitz, Kaup, Newell and Segur hierarchy are given, respectively. As a reduction case of the second hierarchy, the nonlinear Schroedinger and modified Korteweg de Vries hierarchy and a new integrable system are presented. Especially, a coupled generalized Burgers equation is generated.     

Inversion of the Penrose transform and the Cauchy–Fantappie formula

We discuss the construction of an explicit inversion of the Penrose transform with the focus on connections with the Radon transform, multi-dimensional residues and the Cauchy–Fantappie integral formula following to results [1], [2]. The focus is on the new representation (M) of the inverse Penrose transform as a residue. The proof of this formula can be extracted from [1]. This proof includes an explicit computation of this residue (D). In this formula not the exact values of all coefficients but the existence of a differential operator, inverting the Penrose transform (we call this Leibnitz–Newton’s phenomenon) is important. It is similar to local inversion formulas in integral geometry.     

A 9 × 9 matrix representation of Temperley-Lieb algebra and corresponding entanglement

We present the matrix U.The 9×9 U matrix is a representation of specialized Temperley-Lieb algebra.Based on which,a unitary R matrix is generated via the Yang-Baxterization approach.The 9×9 R matrix,a solution of the Yang-Baxter equation,is universal for quantum entanglement.     

Structural and electronic properties of InNxP1-x alloy in full range (0 ≤ x ≤1)

We have performed first-principles method to investigate structural and electronic properties of InN_xP_1?x ternary semiconductor alloy in full range (0 ≤ x ≤ 1) using density functional theory. We have used modified Becke–Johnson potential to obtain accurate band gap results. From the electronic band structure calculation we have found that InN_xP_1?x become metal between 47 and 80% of nitrogen concentration. Additional to our band gap calculations, we have also used the band anticrossing model. The band anticrossing model supplies a simple, analytical expression to calculate the physical properties, such as the electronic and optical properties, of III-N_xV_1?x alloys. The knowledge of the electron density of states is required to understand and clarify some properties of materials such as the band structures, bonding character and dielectric function. In order to have a deeper understanding of these properties of the studied materials, the total and partial density of states has been calculated. Finally, we have calculated the total bowing parameter b of studied alloys, together with three contributions b_VD, b_CE, and b_SR due to volume deformation, different atomic electron negativities and structural relaxation, respectively.     

The mass formula of the spherically symmetric solution of the five-dimensional vacuum equationsR μυ=0

Within the concept of extended elementary particles proposed by the author in some previous papers the mass formula of the general stationary spherically symmetric and purely electrical solution of the 5-dimensional vacuum equationsR =0 is calculated. The problem of how to establish a discrete mass spectrum is discussed in detail.     

Analytical formula of rectangular surface mobility of an infinite plate and the parameters influences

This paper investigates the characteristics of surface mobility when power transmission over the contact area between sub-structures is considered.An analytical formula of the surface mobility of an infinite homogeneous plate over a rectangular contact area subject to a uniform,conpklase force excitation is derived by using complex power method and the concept of structural intensity.This formula provides a theoretical tool for investigating power transmission over the contact area between sub-structures.The influences of the size.the dimension and the aspect ratio of the cotact area on power transmission are analyzed and described according to the results calculated.That provides an effectively theoretical method for investigation of vibration isolation.     

Kirillov’s character formula,the holomorphic Peter–Weyl theorem,and the Blattner–Kostant–Sternberg pairing

By means of the orbit method we show that, for a compact Lie group, the Blattner–Kostant–Sternberg pairing map, with the constants being appropriately fixed, is unitary. Along the way we establish a holomorphic Peter–Weyl theorem for the complexification of a compact Lie group. Among our crucial tools is Kirillov’s character formula. The basic observation is that the Weyl vector is lurking behind the Kirillov character formula, as well as behind the requisite half-form correction on which the Blatter–Kostant–Sternberg-pairing for the compact Lie group relies, and thus produces the appropriate shift which, in turn, controls the unitarity of the BKS-pairing map. Our methods are independent of heat kernel harmonic analysis, which is used by B. C. Hall to obtain a number of these results [B.C. Hall, The Segal–Bargmann Coherent State Transform for compact Lie groups, J. Funct. Anal. 122 (1994) 103–151; B.C. Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type, Comm. Math. Phys. 226 (2002) 233–268, quant.ph/0012015].