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.     

Determination of the Lipophilicity of Xanthines by Reversed-Phase Liquid Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

Hydrogen‐bonded supramolecule of N,N′‐bis(4‐pyridylmethyl)oxalamide and a zigzag chain structure of catena‐poly[[[dichloridocobalt(II)]‐μ‐N,N′‐bis(4‐pyridylmethyl)oxalamide‐κ2N4:N4′] hemihydrate]

N,N′‐Bis(4‐pyridylmethyl)oxalamide, C₁₄H₁₄N₄O₂, exists as a dimer which is extended into a two‐dimensional network with other dimers through pyridine–amide hydrogen bonds. The crystal structure of the title coordination polymer, {[CoCl₂(C₁₄H₁₄N₄O₂)]·0.5H₂O}_n, features a one‐dimensional zigzag chain, in which the cobalt ion sits at a twofold symmetry position and adopts a tetrahedral geometry, and the bridging ligand lies on an inversion center and connects to Co^II ions in a bis‐monodentate mode. Furthermore, two interwoven chains create a cavity of ca 8.6 × 8.6 Å, which produces a three‐dimensional channel. Water molecules are held in the channel by hydrogen bonds.     

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.     

Nouvelle méthode de détermination des taux de réativité des copolymères par résonance magnétique nucléaire: Application aux poly(méthacrylate de méthyle–chlorure de vinylidène)

Constant-composition copolymers of methyl methacrylate and vinylidene chloride produced by radical copolymerization are studied by ¹H-NMR at 60 and 250 MHz. The different methods of the literature for the derivation of reactivity ratios from either the copolymer composition or the sequence average lengths, or even the diad distribution, are applied but lead to rather dispersed results. A new graphical method is proposed, based on the use of peculiar values of the triad distribution functions. It allows us to detect a penultimate effect for the vinylidene chloride-rich region. In the same range, a change in tacticity of the diads and triads on the methylmethacrylate sequences, as compared with homopolymers, is observed; it suggests that the anomaly is caused by the competition of the depropagation reaction.