Stability radii of positive linear Volterra-Stieltjes equations

We study stability radii of linear Volterra-Stieltjes equations under multi-perturbations and affine perturbations. A lower and upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via the associated transfer functions. Then, the class of positive linear Volterra-Stieltjes equations is studied in detail. It is shown that for this class, complex, real and positive stability radius under multi-perturbations or multi-affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices. As direct consequences of the obtained results, we get some results on robust stability of positive linear integro-differential equations and of positive linear functional differential equations. To the best of our knowledge, most of the results of this paper are new.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

Renormalization Effects in the Spectrum of a Coherently Driven Exciton–Biexciton System

Starting from the total Hamiltonian of an excited exciton–biexciton system, nonresonant renormalizations in the electronic spectrum of a coherently driven direct semiconductor are considered. Stringent group-theoretical inclusion of the particle spin in the Hamiltonian allows one to account for the dependence of different renormalization effects on polarizations of the incident laser fields. On the example of circularly polarized driving and probing pulses it is shown that the kind of observed renormalization is defined by the pump-and-probe polarization geometry. Thus, the exciton optical Stark effect must appear in the case of co-circular pump-and-probe, whereas a mixing of the polariton and biexciton spectra is possible only in the case of counter-circular pump-and-probe. The polariton--biexciton dispersion renormalization may manifest itself as synchronous splittings of the exciton--polariton and biexciton spectra under resonant pumping at a frequency of the polariton--biexciton transition, or in their shifts in opposite directions under near-resonant pumping. The mechanisms of both kinds of renormalization effects are analyzed, and the dependence of their characteristics on the pump parameters and microscopic parameters of the exciton–biexciton–photon system is established. An evaluation of the characteristics shows that the effect of polariton–biexciton dispersion renormalization dominates in the spectra of semiconductors with stable biexciton formation. Results of the theoretical study provide an adequate explanation of available experimental data.     

Prediction of brand stories spreading on social networks

Advances in Data Analysis and Classification - Online social network is a major media for many types of information communication. Although the primary purpose of social networks is to connect...     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Dipole moments of selenophene analogs of the chalcones

The dipole moments of 24 selenophene analogs of the chalcones have been measured and have been compared with the data calculated by a vectorial additive scheme and also with their chemical structures. Considerations are expressed on the conformational state of the molecules of the compounds investigated. The existence of a correlation between the dipole moments the intramolecular distances, and the Hammett's -parameters has been shown. The applicability of Higashi's equation to the calculation of for , -unsaturated ketones is pointed out.     

n-Hexane dehydrocyclization over Pt?Ni supported on alumina catalysts

Pt–Ni/-Al₂O₃ catalysts have been prepared and studied in n-hexane dehydrocyclization. The selectivity for benzene and toluene, a chain lengthening product formation was improved by Ni and correlated with its content.

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Pt–Ni/-Al₂O₃ -. Ni . Ni , .

     

Fast determination of the tin content in cassiterite ores by photon activation method

Photon activation analysis has been success-fully applied to the fast and non-destructive analysis of tin in cassiterite ores based on the 159.7 keV gamma line of^123mSn produced in the¹²⁴Sn/γ, n/^123mSn reaction. In order to improve the accuracy of analytical results, corrections for self-absorption and pile-up effects were performed. Under typical conditions /15 μA electron beam current, 15 MeV bremsstrahlung energy, 5 min irradiation time and 10 min measurement/ the sensitivity of the analysis is 10 ppm. The proposed method can be used for routine analysis of tin in geological samples.