Nonlinear Maxwell Equations in Inhomogeneous Media

We study the basic properties of the Maxwell equations for nonlinear inhomogeneous media. Assuming the classical nonlinear optics representation for the nonlinear polarization as a power series, we show that the solution exists and is unique in an appropriate space if the excitation current is not too large. The solution to the nonlinear Maxwell equations is represented as a power series in terms of the solution of the corresponding linear Maxwell equations. This representation holds at least for the time period inversely proportional to the appropriate norm of the solution to the linear Maxwell equation. We derive recursive formulas for the terms of the power series for the solution including an explicit formula for the first significant term attributed to the nonlinearity.     

Study of the thermal stages of the photoinitiated cyclization of diarylamines with polyhalogenated methanes

On the basis of a study of the kinetics of the dark stages of the photoinitiated formation of acridines from substituted diphenylamines and bromoform the ionic nature of these stages was confirmed. Quantum chemical calculations confirmed the assumption of the dependence of the efficiency of cyclization on the charge state of the reacting molecules.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 564–569, March, 1991.     

Anisotropic quantum spin fluid and quantum spin glass in La cuprate-based catalyst

Evidence of quantum spin fluid and of quantum spin glass behaviour has been detected by extended EPR analysis in some La-cuprate catalysts of general formula La_2−xEu_xCuO_{4 + δ}. Some features of the EPR spectrum, appearing in a few cases, are also discussed and attributed to a pseudo Jahn-Teller effect due to a particular coordination of up to five oxygen ions around surface copper ions at low temperature.     

Comparative nonempirical study and isodesmic calculations of heats of formation of HNCO and HPCO isomers

The structural, electronic, and energetic characteristics of CHNO and CHOP isomers, and also of several related compounds, were calculated by a nonempirical method. Enthalpies of these isomers, obtained using the method of isodesmic reactions, are given.V. I. Lenin Moscow Pedagogical State University, 117913 Moscow. Institute of Physiologically Active Compounds, Russian Academy of Sciences, 142432 Chernogolovka. Institute of New Chemical Problems, Russian Academy of Sciences, 142432 Chernogolovka. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 7, pp. 1585–1590, July, 1992.     

The aromatic diboracyclopropenyl (diboriranyl) anion; CB2H3 −: An ab initio study

The most stable structure of CB₂H₃ ^–, as established computationally, is the aromatic diboracyclopropenyl (diboriranyl) anion (5), while open-chainC _2v, isomer H₂BCBH (7) is only 3 kcal/mol higher in energy at the QCISD(T)/6-311 +G^**//MP2/6-31+G^*+ZPE (HF/6-31 +G^*). The 47-kcal/mol barrier between cyclic,5, and open-chain,7, structures suggests that both of them may be observed. The aromatic stabilization energy of the diboriranyl anion (18 kcal/mol) is half the value in the isoelectronic cyclopropenium ion, C₃H₃ ⁺. The computed, by IGLO method (5a), and experimental (6a) chemical shifts,(¹³C) and(¹¹B), agree within 4 ppm range. The theoretical vibrational frequencies of the most stable isomers,5 and7, are presented for experimental verification of these species.     

Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

Polysila analogs of aromatic hydrocarbon ions: Structures and energies of Si3H3+, Si4H,and Si5H5−

Silicon analogs of aromatic monocyclic ions, (SiH) ( 4 ), (SiH) ( 5 ), and (SiH) ( 6 ) have been studied ab initio at MP 2(full)/6-31G *. The D_3h structure of Si₃H₃⁺ is the global minimum, whereas other two ions are nonplanar. The D_2d structure of (SiH) is less folded than the carbon analog and possesses a higher stabilization energy. Stabilization energies for the monocharged ions are diminished with respect to the corresponding carbons © 1993 John Wiley & Sons, Inc.     

Global stabilization in nonlinear discrete systems with time-delay

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.     

1,3,2,4-Oxaazaphosphatitanetidine. Structure and Properties

The interaction of 1,3,2,4 -oxaazaphosphatitanetidines with chlorides of aluminium and zirconium, alcohols, piperidine and R₂NBr (R=SiMe₃) has been studied. The reaction routes have been determined with NMR spectra and X-ray structure analyses.