BRST cohomology and highest weight vectors. I

We initiate a program to study certain recent problems in non-compact coset CFT by the BRST approach. We derive a reduction formula for the BRST cohomology by making use of a twisting by highest weight modules. As illustrations, we apply the formula to the bosonic string model and a rank one non-compact coset model [DPL]. Our formula provides a completely new approach to non-compact coset construction.Partially supported by NSF Grant DMS-8703581     

Fibrations of bigroupoids

Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given.     

Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.     

Linear and nonlinear optical susceptibilities of orthorhombic rare earth molybdates RE2(MoO4)3

The dielectric responses (i.e. the refractive indices and the second order nonlinear susceptibilities) of all orthorhombic rare earth molybdates have been studied on the basis of the relationship between dielectric responses and the average atomic number of constituent atoms of crystals. Both the linear and second order nonlinear optical responses at 1.064 μm decrease with increasing atomic number from La to Lu.     

Frequency dependence of ionic conductivity and dielectric relaxation studies in Na3H(SO4)2 single crystal

Electrical impedance measurements of Na₃H(SO₄)₂ were performed as a function of both temperature and frequency. The electrical conductivity and dielectric relaxation have been evaluated. The temperature dependence of electrical conductivity reveals that the sample crystals transformed to the fast ionic state in the high temperature phase. The dynamical disordering of hydrogen and sodium atoms and the orientation of SO₄ tetrahedra results in fast ionic conductivity. In addition to the proton conduction, the possibility of a Na⁺ contribution to the conductivity in the high temperature phase is proposed. The frequency dependence of AC conductivity is proportional to ω^s. The value of the exponent, s, lies between 0.85 and 0.46 in the room temperature phase, whereas it remains almost constant, 0.6, in the high-temperature phase. The dielectric dispersion is examined using the modulus formalism. An Arrhenius-type behavior is observed when the crystal undergoes the structural phase transition.     

ANALYSIS OF A PIEZOELECTRIC MULTIMORPH IN EXTENSIONAL AND FLEXURAL MOTIONS

Impedance and admittance matrices are presented for the analysis of the beam-type piezoelectric multimorph (PM). Each piezoelectric layer is polarized in the thickness direction. The stacking sequence can be arbitrary, and both the extensional and flexural motions are considered. The variational principle is used for deriving the lumped conjugate parameters: two mechanical ports for the extensional motion, four mechanical ports for the flexural motion, and m electrical ports for the m piezoelectric layers. The resonance and antiresonance frequencies are then easily calculated from the admittance matrices. For the case of all the piezoelectric layers either in series or parallel connection, them +6 ports reduce to the seven ports, and its impedance and admittance matrices are presented. The present methods are applied to the cantilevered PM and their electromechanical behavior is studied. The tip trajectory of the cantilevered piezomotor is also investigated using the presented matrices. It is found that the present methods are very effective in analyzing the multilayer piezoelectric transducers.     

Laser induced copper electroless plating on polyimide with Q-switch Nd:YAG laser

The results of laser induced deposition of copper on polyimide substrate from copper electrolyte solution are reported. Unlike most work reported in the literatures where CW Ar⁺ lasers were used, a second harmonic (532 nm wavelength) Q-switch Nd:YAG laser was used for our experiments. The deposition process was conducted by laser-catalyzing of the polyimide surface and subsequent photothermal-accelerated reduction of copper-complex ions in an alkaline reducing environment. The characteristics of the deposited copper line were investigated in terms of laser beam scanning speed, and the number of scans. The surface morphology and chemical composition of the deposited copper were analyzed using field emission scanning electron microscope (FESEM) and energy dispersive spectrometer (EDX). The optimum processing conditions have been identified. The copper deposit was found to adhere well to the substrate.     

A Modified Quasi-Newton Method for Structured Optimization with Partial Information on the Hessian

This paper develops a modified quasi-Newton method for structured unconstrained optimization with partial information on the Hessian, based on a better approximation to the Hessian in current search direction. The new approximation is decided by both function values and gradients at the last two iterations unlike the original one which only uses the gradients at the last two iterations. The modified method owns local and superlinear convergence. Numerical experiments show that the proposed method is encouraging comparing with the methods proposed in [4] for structured unconstrained optimization Presented at the 6th International Conference on Optimization: Techniques and Applications, Ballarat, Australia, December 9–11, 2004     

Time delay as a key to apoptosis induction in the p53 network

A feedback mechanism that involves the proteins p53 and mdm2, induces cell death as a controlled response to severe DNA damage. A minimal model for this mechanism demonstrates that the response may be dynamic and connected with the time needed to translate the mdm2 protein. The response takes place if the dissociation constant k between p53 and mdm2 varies from its normal value. Although it is widely believed that it is an increase in k that triggers the response, we show that the experimental behaviour is better described by a decrease in the dissociation constant. The response is quite robust upon changes in the parameters of the system, as required by any control mechanism, except for few weak points, which could be connected with the onset of cancer. Received 8 May 2002 / Received in final form 9 July 2002 Published online 17 September 2002