Effective excitation of quasi-optical resonator in millimeter wave

It is described effective excitation of quasi-optical resonator (Q. O. R) in millimeter wave (M. M. W) in this article in which some useful results are obtained.This research work was supported by National Natural Science Foundation of China. (No. 69171027)     

Modifications to the lidar equation due to nonlinear propagation in air

We study how the well-known lidar equation is affected by the use of ultra-short, high-power laser pulses. Because of the self-focusing and self-guiding, the overlap function ξ, representing the reduction fraction of the signal resulting from geometrical effects inside the experimental system, needs to be reconsidered. The losses due to multi-photon ionisation in the filament entail a heavy weakening of the return signal. We also investigate the contribution of the white-light components generated by self-phase modulation. Received: 2 January 2001 / Revised version: 8 June 2001 / Published online: 18 July 2001     

Performance of a fuel cell optimized for in situ X‐ray absorption experiments

A commercial fuel cell has been successfully modified to carry out X‐ray absorption spectroscopy (XAS) measurements under optimized in operando conditions. The design is conceived for the performance of XAS experiments in transmission mode over a wide range of X‐ray energies above 6 keV, owing to the reduced absorption of the cell. The wide angular aperture allows the collection of XAS in fluorescence mode and of X‐ray diffraction patterns when needed. Details of the design of the cell and its performances are given. The quality of the extended X‐ray absorption fine‐structure spectra under working conditions has been verified at the ESRF and ELETTRA synchrotron radiation facilities, showing that relatively fast and low‐noise transmission measurements on electrodes over a wide range of catalyst concentrations and energies are feasible.     

Orbifolds,Hopf algebras,and the Moonshine

We describe the modular properties and fusion rules of holomorphic orbifold models by Hopf algebraic techniques, using the representation theory of the orbifold quantum group. We apply this theory to the construction of generalized Thompson series, and discuss its connections with Moonshine.     

Reality in the differential calculus on q-Euclidean spaces

The nonlinear reality structure of the derivatives and the differentials for the Euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-85-15857.     

Inhomogeneous quantum groups and their quantized universal enveloping algebras

The quantum group IGL _q (N), the inhomogenization of GL _q (N), is formulated with -matrices. Theq-deformed universal enveloping algebra is constructed as the algebra of regular functionals in this formulation and contains the partial derivatives of the covariant differential calculus on the quantum space.     

A borel-weil-bott approach to representations of sl q (2, ℂ)

We use a quite concrete and simple realization of sl _q (2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme ¹ II ^1* as the counterpart of the standard ¹ = Sl(2, )/B.     

SU q (2) covariant\hat R-matrices for reducible representations

We consider SU _q (2) covariant -matrices for the reducible3 1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known -matrices for SO _q (3) and SO _q (3, 1). Also, they are the three -matrices which can be constructed by using four different SU _q (2) doublets. Only two of the three -matrices allow a differential structure on the reducible four-dimensional quantum space.     

The hopf algebra of vector fields on complex quantum groups

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A _n , B _n , C _n , and D _n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.Humboldt Fellow.     

The quantum bialgebra associated with the eight-vertexR-matrix

The quantum bialgebra related to the Baxter's eight-vertexR-matrix is found as a quantum deformation of the Lie algebra of sl(2)-valued automorphic functions on a complex torus.     

Six generatorq-deformed Lorentz algebra

The six generator deformation of the Lorentz algebra is presented. The Hopf algebra structure and the reality conditions are found. The chiral decomposition of SL(2, C) is generalized to theq-case. Casimir operators for theq-Lorentz algebra are given.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-85-15857.     

Differential operators on quantum spaces for GL q (n) and SO q (n)

We prove that the rings of q-differential operators on quantum planes of the GL _q (n) and SO _q (n) types are isomorphic to the rings of classical differential operators. Also, we construct decompositions of the rings of q-differential operators into tensor products of the rings of q-differential operators with less variables.     

C-V Technique on Schottky contacts — Limitation of implanted profiles

Some limiting effects for the application of theC-V technique on Schottky contacts for measuring ion-implanted impurity distributions in semiconductors are studied. The basic demand for this technique lies in the possibility to measure the profile with sufficient accuracy within a wide range of depths. The depth of the space charge region for zero bias determines the minimum measurable distance. In greater depths the avalanche breakdown of the metal-semiconductor junction is a limiting factor. The region of applicable implanted doses and energies, in which it is possible to measure the profile within the vicinity of the maximum concentration, is determined by a numerical computation. At the same time the errors resulting from the application of the assumption of a Debye lenght equal to zero (depletion approximation) are examined. The regions in which it is possible to measure the impurity profile in the vicinity of the maximum with an error less than 5% are shown by the dose vs. implanted energy dependence. The computations are performed for As, B, P ions implanted into Si, and for Si, Te, Se ions implanted into GaAs with energies ranging from 0 to 200 keV.     

Deformation of the Poisson-Lie structure in the SU(2) WZW model

A Lie bialgebra structure in the WZW model is considered. By the deformation of the Poisson structure in the SU(2) WZW model, a commutative noncocommutative Hopf algebra with nonlinear Poisson structure is obtained.     

Left regular representation and contraction of sl q (2) to e q (2)

The left regular representation of the quantum algebras sl _q (2) and e _q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.     

Reflection equations andq-Minkowski space algebras

We express the defining relations of theq-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties with respect to the quantum Lorentz group action in a straightforward way. Different equivalences ofq-Minkowski algebras are pointed out.On leave of absence from the St. Petersburg's Branch of the Steklov Mathematical Institute of the Russian Academy of Sciences, Spain.     

Construction of a new quantum double and new solutions to the Yang-Baxter equation

A new quantum double is established from a new Hopf algebra and a new kind of quantum R-matrix is obtained.     

A natural and rigid model of quantum groups

We introduce a natural (Fréchet-Hopf) algebra A containing all generic Jimbo algebras U _t (sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U _t (sl(2)). The Universal R-matrices converge in A A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.     

Casimir invariants for quantized affine Lie algebras

Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.