On exponential stability of second order delay differential equations

We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method works not only for autonomous equations but also for equations with variable coefficients and delays.     

Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.     

Simple one‐pot conversion of organic compounds by hydrogen peroxide activated by ruthenium(III) chloride: organic conversions by hydrogen peroxide in the presence of ruthenium(III)

The aromatic compounds p‐nitrobenzaldehyde, p‐hydroxybenzaldehyde, naphthalene, toluene, catechol, quinol, aniline and toluidine dissolved in aqueous acetic acid or aqueous medium were oxidized in quantitative to good yields by 50% H₂O₂ in the presence of traces of RuCl₃ (～10^?8 mol; substrate/catalyst ratio 1488:1 to 341 250:1). Conditions for highest yields, in the most economical way, were obtained. Higher catalyst concentrations decrease the yield. Oxidation in aromatic aldehydes is selective at the aldehydic group only. In the case of hydrocarbons, oxidation results in the introduction of a hydroxyl group with >85% (in the case of toluene) selectivity for the ortho position. Formation of low‐molecular‐weight polyaniline was reduced to 10%, along with 90% formation of higher molecular weight polyaniline. In this new, simple and economical method, which is environmentally safe and requires less time, oxo‐centered carboxylate species of ruthenium(III) in acetic acid medium and hydrated ruthenium(III) chloride in aqueous medium probably catalyze the oxidation. Copyright © 2005 John Wiley & Sons, Ltd.     

Fixed-point theorems for S-KKM maps

A number of new fixed-point results are presented for S-KKM self maps. Also the notion of essentiality for S-KKM maps is introduced.     

Electrical conduction and optical properties of amorphous (Sb2Se3)100−xSnx thin films

The variation of DC electrical conductivity and the optical properties of thermally evaporated a- (Sb₂Se₃)_100−xSn_x thin films with temperature have been studied. It is found that the thermal activation energy decreases, while the optical gap first increases (up to x=1) and then decreases, with the increase in Sn content. These results have been explained by taking into consideration the structural modifications induced by the incorporation of Sn into the parent alloy. The variation in the conductivity prefactor (σ_o) with Sn addition indicates a change in the dominant conduction transport mechanism from extended states to localized states. An experimental correlation between the activation energy and the pre-exponential factor has been observed, indicating the validity of Meyer–Neldel rule in the studied samples.     

Dead cores of singular Dirichlet boundary value problems with ϕ-Laplacian

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable. This work was supported by grant no. A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic and by the Council of Czech Government MSM 6198959214.     

The influence of the entrance channel mass asymmetry on the reaction mechanism

We have tried to investigate the influence of the entrance channel mass asymmetry on the reaction mechanisms associated with heavy ion collisions. Two systems, one very much asymmetric (O+Mo) and the other one almost symmetric (Cr+Fe), were studied in detail by measuring evaporation residues, deep inelastic collision products and fission fragments. An important fraction of the fragments observed in the Cr+Fe system exhibits all the characteristics of fission fragments. The analysis of these data seems to indicate that these fission like products are most likely emitted by a long lived composite system having not reached full statistical equilibrium for all the degrees of freedom. As a consequence, the fusion cross section for this symmetric system is too low as compared to predictions based on a critical distance approach for fusion, whereas the asymmetric system (O+Mo) is well understood in term of the same model.     

Electronic properties of tin dichalcogenides (SnS2 and SnSe2)

Using Phillips and Van Vechten's theory the homopolar gap (E_h), ionic gap (E_c) and Penn gap (E_p) have been derived for the layered compound semiconductors SnS₂ and SnSe₂. The values of E_p so derived have been found to be in agreement with the values obtained from the Grimes-Cowley modification of the Penn model, and also with the reflectance spectra of the respective materials. Using the above data the Phillips ionicity has been calculated and the octahedral coordination of SnS₂ and SnSe₂ has been discussed on the basis of the calculated value of ionicity. The bond electronic polarizability has been evaluated using Chemla's approach and the values so obtained have been found in agreement with the values obtained from the Clausius-Mossottirelation. The Varshni formula has been shown to explain fairly well the temperature dependence of energy gap and the constants involved have been derived. The calculated isobaric temperature gradient of E_g[($\text{?E}{}_{\mathrm{g}}\text{?T)}{}_{\mathrm{p}}$] has been found to be in accordance with the reported values, and the electron lattice interaction has been evaluated.