Asymptotic behavior of the potential and existence of a periodic solution for a second order differential equation

We establish the existence of a 2π-periodic solution for a second order semilinear equation in terms of the asymptotic behavior of the potential of the nonlinearity. Our condition includes the case in which the nonlinearity is asymptotically linear with slopes at infinity of the jumping nonlinearity between the positive axes and the first Fucik spectrum curve (see [S. Fucik (1976 Fucik, S. 1976. Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101: 69–87.  [Google Scholar]). Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101, 69–87.]). Our results extend those of [L. Fernandez and F. Zanolin (1988 Fernandez, L. and Zanolin, F. 1988. Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51: 151–163.  [Google Scholar]). Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51, 151–163.].     

Berberine cation: A fluorescent chemosensor for alkanes and other low-polarity compounds. An explanation of this phenomenon

Alkanes in the presence of berberine sulfate provide an enhancement of fluorescent signal, which depends on alkane concentration and structure, when the system is irradiated with monochromatic UV light. Computational analysis suggests that an ion-induced dipole between alkanes and berberine sulfate is responsible for this phenomenon. This interaction can properly model the experimentally obtained fluorescent response. The proposed explanation allows other interacting systems to be designed, which have been experimentally confirmed.     

Light-induced aminocarbene to imine dyotropic rearrangement in a chromium(0) center: an unprecedented reaction pathway

1,2-Dyotropic rearrangement can be induced by irradiation of properly functionalized Fischer carbenes. This novel reaction takes place by a stepwise mechanism and with double inversion of configuration at the static scaffold. Good yields are obtained with both cyclic and acyclic structures, thus suggesting that this unprecedented transformation can be extended to other organometallic systems.     

Packing Non-Returning <Emphasis Type="Italic">A</Emphasis>-Paths*

Chudnovsky et al. gave a min-max formula for the maximum number of node-disjoint nonzero A-paths in group-labeled graphs [1], which is a generalization of Mader's theorem on node-disjoint A-paths [3]. Here we present a further generalization with a shorter proof. The main feature of Theorem 2.1 is that parity is “hidden” inside , which is given by an oracle for non-bipartite matching. * Research is supported by OTKA grants T 037547 and TS 049788, by European MCRTN Adonet, Contract Grant No. 504438 and by the Egerváry Research Group of the Hungarian Academy of Sciences. † The author is a member of the Egerváry Research Group (EGRES).     

Solvent and Substituent Effects in the Periselectivity of the Staudinger Reaction between Ketenes and alpha,beta-Unsaturated Imines. A Theoretical and Experimental Study

The outcome of the cycloaddition between activated ketenes and alpha,beta-unsaturated imines has been investigated both experimentally and theoretically. Our results indicate that activated monosubstituted ketenes yield exclusively [2 + 2] cycloadducts. Disubstituted activated ketenes yield [2 + 2] and/or [4 + 2] cycloadducts. In one case, an unexpected piperidin-2-one has been obtained, although its relative abundance with respect to the corresponding [2 + 2] or [4 + 2] cycloadducts can be minimized by the proper choice of experimental conditions. The ability of different ab initio and semiempirical methods to account for these results has been tested. The best agreement between theory and experiment is achieved at the MP2/6-31G level of theory, with solvent effects taken into account. The semiempirical hamiltonian AM1, at the RHF level, tends to overestimate the stability of the transition structures leading to six-membered cycloadducts, whereas 3 x 3CI-HE/AM1 and CASSCF(2,2)/6-31G methods tend to overestimate the stability and the biradical character of the transition structures leading to [2 + 2] cycloadducts.     

Asymptotic behaviour and stability to linear non-autonomous neutral delay difference equations

This paper is concerned with the asymptotic behaviour and the stability of a class of linear neutral delay difference equations with variable coefficients and constant delays. Via an appropriate solution of the so-called generalized characteristic equation, an asymptotic criterion and a stability result are established.     

An alternative procedure for the determination of the optical band gap and thickness of amorphous carbon nitride thin films

In this work, we propose an alternative procedure to obtain the optical band gap and the thickness of amorphous carbon nitride thin films that requires only the measurement of the absorbance spectrum of the samples. The method is based on an absorbance spectrum fitting (ASF) procedure using the Tauc model, which is widely applied to the study of amorphous semiconductors. With the aim of evaluating the proposed method two sets of carbon nitride samples deposited on glass substrates were analyzed; one prepared by pulsed laser ablation (PLA) and the second by magnetron sputtering. The obtained results using different conventional methods were compared with the results of the ASF method and a good agreement between the values and the tendencies with the experimental conditions used to prepare the films were observed.