Steiner's problem and fagnano's result on the sphere

This note describes the nature of optimal solutions for the spherical Steiner-Weber location problem for the case of unit weights and either 3 or 4 demand points (requireing 4 demand points to lie in an open hemisphere). Geometrically appealing results which are necessary conditions for optimum solutions and spherical analogs of known planar results are obtained.     

Numerical computation of optimal control problems with unknown final time

This paper presents a numerical computational method for the solution of optimal control problems with unknown final time. The method presented is based on a transformation and a modified quasilinearization technique. A numerical example is included for illustration.     

Interfacial energy and the law of corresponding states 2: associated fluids

A mesoscopic model for the liquid/vapor interface previously developed for nonpolar fluids [J. Phys. Chem. A 2003, 107, 875; 2003, 107, 883] is extended to the case of polar associated compounds. The interfacial energy is factorized in two terms: one corresponding to association depending on the hydrogen bonds density, the other corresponding to the nonpolar contribution. This last term is treated in the framework of the corresponding states formalism similar to the one used in the case of nonpolar fluids [J. Phys. Chem. B 2004, 108, 5951]. The model yields a generalized behavior of the association factor as a function of the dielectric constant for the treated fluids. The calculated surface tension shows a mean error of about 1% for seven compounds having different multivalent H-bond characters.     

Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line

The nonlinear evolution of the kink instability of a plasma with an elliptic magnetic stagnation line is studied by means of an amplitude expansion of the ideal magnetohydrodynamic equations. Wahlberg et al. [12] have shown that, near marginal stability, the nonlinear evolution of the stability can be described in terms of a two-dimensional potential U(X,Y), where X and Y represent the amplitudes of the perturbations with positive and negative helical polarization. The potential U(X,Y) is found to be nonlinearly stabilizing for all values of the polarization. In our paper a Lagrangian and an invariant variational principle for two coupled nonlinear ordinal differential equations describing the nonlinear evolution of the stagnation line instability with arbitrary polarization are given. Using a trial function in a rectangular box we find the functional integral. The general case for the two box potential can be obtained on the basis of a different ansatz where we approximate the Jost function by polynomials of order n instead of a piecewise linear function. An example for the second order is given to illustrate the general case. Some considerations concerning solar filaments and filament bands (circular or straight) are indicated as possible applications besides laboratory experiments with cusp geometry corresponding to quadripolar cusp geometries for some clouds and thunderstorms.     

Forward Variance Dynamics: Bergomi’s Model Revisited

Abstract

In this article, we propose an arbitrage-free modelling framework for the joint dynamics of forward variance along with the underlying index, which can be seen as a combination of the two approaches proposed by Bergomi. The difference between our modelling framework and the Bergomi (2008. Smile dynamics III. Risk, October, 90–96) models is mainly the ability to compute the prices of VIX futures and options by using semi-analytic formulas. Also, we can express the sensitivities of the prices of VIX futures and options with respect to the model parameters, which enables us to propose an efficient and easy calibration to the VIX futures and options. The calibrated model allows to Delta-hedge VIX options by trading in VIX futures, the corresponding hedge ratios can be computed analytically.     

Thermal stability and crystallization kinetics of Ge–Se–Cd glasses

The effect is reported of varying cadmium concentration on the glass transition, thermal stability and crystallization kinetics of Ge₂₀Se_{80? x} Cd _x (x = 2.5, 5, 7.5 and 10 at. %) glasses. Differential scanning calorimetry results under non-isothermal conditions for the studied glasses are reported and discussed. The values of the glass transition temperature (T_g ) and the peak temperature of crystallization (T_p ) were found to be dependent on heating rate and Cd content. From the heating rate dependence of T_g and T_p , the values of the activation energy for glass transition (E_g ) and the activation energy for crystallization (E_c ) were evaluated and their composition dependence discussed. The thermal stability of the glasses was evaluated using various thermal stability criteria such as ΔT, H_g and S. The stability calculations emphasize that the thermal stability decreases with increasing Cd content.     

Reactive intermediates in the reaction of hydrazinecarbothioamides with 2-(bis(methylthio)methylene)malononitrile and ethyl 2-cyano-3,3-bis(methylthio)acrylate

Research on Chemical Intermediates - The reaction of N-substituted hydrazinecarbothioamides with both 2-(bis(methylthio)methylene)malononitrile and ethyl 2-cyano-3,3-bis(methylthio)acrylate...     

Effect of heat treatment on the optical and electrical transport properties of Ge15Sb10Se75 and Ge25Sb10Se65 thin films

The effect of heat treatment on the optical and electrical properties of Ge₁₅Sb₁₀Se₇₅ and Ge₂₅Sb₁₀Se₆₅ thin films in the range of annealing temperature 373-723 K has been investigated. Analysis of the optical absorption data indicates that Tauc's relation for the allowed non-direct transition successfully describes the optical processes in these films. The optical band gap (E_g^opt.) as well as the activation energy for the electrical conduction (ΔE) increase with the increase of annealing temperature (T_a) up to the glass transition temperature (T_g). Then a remarkable decrease in both the E_g^opt. and ΔE values occurred with a further increase of the annealing temperature (T_a>T_g). The obtained results were explained in terms of the Mott and Davis model for amorphous materials and amorphous to crystalline structure transformations. Furthermore, the deduced value of E_g^opt. for the Ge₂₅Sb₁₀Se₆₅ thin film is higher than that observed for the Ge₁₅Sb₁₀Se₇₅ thin film. This behavior was discussed on the basis of the chemical ordered network model (CONM) and the average value for the overall mean bond energy 〈E〉 of the amorphous system Ge_xSb₁₀Se_90−x with x=15 and 25 at%. The annealing process at T_a>T_g results in the formation of some crystalline phases GeSe, GeSe₂ and Sb₂Se₃ as revealed in XRD patterns, which confirms our discussion of the obtained results.     

Transport Characteristics of Mesoscopic Radio-Frequency Single Electron Transistor

The transport property of a quantum dot under the influence of external time-dependent field is investigated. The mesoscopic device is modelled as semiconductor quantum dot coupled weakly to superconducting leads via asymmetric double tunnel barriers of different heights. An expression for the current is deduced by using the Landauer-Buttiker formula, taking into consideration of both the Coulomb blockade effect and the magnetic field. It is found that the periodic oscillation of the current with the magnetic field is controlled by the ratio of the frequency of the applied ac-field to the electron cyclotron frequency. Our results show that the present device operates as a radio-frequency single electron transistor.     

Peltier Coefficient and Photon-Assisted Tunnelling in Quantum Point Contact

We present the Peltier coefficient and thermal transport in quantum point contact (QPC), under the influence of external fields and different temperatures. Also we obtain the oscillations of the Peltier coefficient in external fields. Numerical calculations of the Peltier coefficient are performed at different applied voltages, amplitudes and temperatures. The obtained results are consistent with the experimental data in the literature.