High-Q whispering gallery modes in a spherical shell dielectric resonator: Characterization at microwave frequencies

We present a numerical and experimental characterization of high-Q whispering gallery resonant modes excited in a fused quartz spherical shell operated in the 18-26.5 GHz band; easy coupling and selection of modes is a most advantageous feature of the proposed structure with respect to ordinary bulk resonators. The numerical results, based on a finite element algorithm, well match experimental data, which also show the capability of our device to perform gaseous spectroscopy measurements. Received 25 October 2002 Published online 4 February 2003     

On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P ₀ and Q ₀.     

Discrete limit theorems for general Dirichlet series. III

Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given. Partially supported by Lithuanian Foundation of Studies and Science     

On zeta-functions associated to certain cusp forms. I

In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained. Partially supported by Lithuanian Foundation of Studies and Science     

Equations of Advanced–Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems

In the paper we study infinite-dimensional dynamic systems with the Frenkel–Kontorova potentials. For such systems we describe their traveling-wave-type solutions, which are solutions for the corresponding boundary-value problem with nonlocal conditions. Describing the mentioned solutions is equivalent to describing the space of solutions for a functional differential equation that can be canonically derived from the original dynamic system. The stability of traveling-wave-type solutions is also investigated.     

Solubility parameter determination of cationic surfactants by inverse GC

Summary The solubility parameters of cationic surfactants were obtained using the inverse gas chromatographic technique. The surfactants didodecyl dimethyl ammonium bromide, dioctadecyl dimethyl ammonium bromide and dodecyl pyridinium chloride were used as stationary phase and retention data of different probe solutes were measured at different temperatures. The results were analysed by the combination of Flory-Huggins and Hildebrand theories, and the solubility parameters of the surfactants were obtained in a range of temperatures between 80–120°C.     

Heuristic Rejection in Interval Global Optimization

Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach.     

Luminescence enhancement by hydrogenation of Si:Er,O

Erbium (Er)- and oxygen (O)-doped Cz–Si was additionally doped with hydrogen, using plasma enhanced chemical vapour deposition. Photoluminescence (PL) spectra show a large enhancement especially for samples treated with solid phase epitaxy before hydrogenation and annealing at 900°C later. Secondary ion mass spectroscopy measurements give evidence for an enhanced diffusion of O and Er at this temperature towards the surface. Etching shows that the PL does not stem from the heavily doped surface layer but from a deeper region with lower Er concentration. This conclusion is supported by the appearance of the so-called “cubic” centre with low solubility. Comparing the PL yield of the hydrogenated samples to that of samples with similar Er volume concentration but without hydrogenation still gives a large enhancement. We thus conclude that hydrogen can enhance the solubility of the cubic centre in Si:Er,O.