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.     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

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.     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

On non-stationary Navier-Stokes flows with vanishing viscosity associated with a variational inequality

Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with K_ε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established.     

Graph bisection algorithms with good average case behavior

In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n ^{1?1/[(d+1)/2]}), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n ^2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:

1. the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
2. whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
3. the algorithm works well both theoretically and experimentally,
4. the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
5. the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).

     

1,4-Addition of benzene to a dihydrocyclopent[a]indene diradical: synthesis and DFT study

Photochemical cyclization of compound 1, a homoenediyne (-CCC=CCH2CC-) bearing two ethynylanthracene chromophores, yields two isomeric dihydrocyclopent[a]indene ring systems, spiro-fused to the 9-position of a 9,10-dihydroanthracene moiety. Evidence of a photochemically initiated diradical cyclization pathway is proposed on the basis of (i) hydrogen abstraction from reaction with 1,4-cyclohexadiene (1,4-CHD) and (ii) the observation of 1,4-addition of benzene (solvent). The reaction was further analyzed by a complete density functional theory (DFT) study, using an unrestricted approach (UBLYP) with a 6-31G* basis set for the open-shell triplet states of the reactants, products, and diradical intermediates to model the photochemical nature of observed transformation. A mechanism detailing the observed cyclization/addition reaction is proposed.     

Selective reduction of aldehydes by a formic acid- trialkylamine- RuCl2(PPh3)3 system

In the presence of trialkylamine and formic acid RuCl₂(PPh₃)₃ selectively reduces aldehydes to the corresponding alcohols at room temperature. Other reducible groups are unaffected.     

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...