On Korovkin Type Theorem in the Space of Locally Integrable Functions

It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space L _p,w (loc) does not hold in all this space and is satisfied only on some subspace.     

Synthesis of Novel Chiral C 2-symmetric Diaza-18-crown-6 Ether Derivatives and their Enantioselective Recognition of Amino Acid Derivatives

New chiral diaza-18-crown-6 ether derivatives, 5 and 6 were synthesized from (R)-(-)-2-amino-1-bütanol. These chiral artificial receptors exhibit pronounced chiral recognition toward the enantiomers of l- and d- amino acid derivatives. The highest enantioselectivity was observed in the case of Trp-OMe·HCl (K_D/K_L=12.5).     

Dynamics of Ginzburg‐Landau Vortices

(Accepted August 19, 1996)     

Propagation factors of Hermite–Gaussian beams in turbulent atmosphere

Based on the extended Huygens–Fresnel integral and the second-order moments of the Wigner distribution function, an analytical formulae for the propagation factors (M²-factors) of coherent and partially coherent one-dimensional Hermite–Gaussian beams in a turbulent atmosphere are derived. Evolution properties of the M²-factor of the Hermite–Gaussian beam in a turbulent atmosphere are studied numerically in detail. Our results show that the M²-factor of the Hermite–Gaussian beam increases upon propagation in a turbulent atmosphere. The M²-factor of the Hermite–Gaussian beam with larger beam order (or lower coherence) increases slower that of the Hermite–Gaussian beam with smaller beam order (or higher coherence) in a turbulent atmosphere, which means that the Hermite–Gaussian beam with a larger beam order and lower coherence is less affected by a turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.     

Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

The differential quadrature method based on cosine expansion is applied to obtain numerical solutions of the RLW equation. The propagation of single solitary wave is studied to validate the efficiency of the algorithm. Then, test problems including interaction of two and three solitary waves, undulation, and evolution of solitary waves are implemented. Solutions are compared with earlier results. Discrete conservation quantities are computed for test experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Incipient separation over wall irregularities in transonic flow

Incipient separation over wall irregularities in a steady two dimensional flow field of a perfect fluid which has transonic speed characteristics has been investigated considering viscous-inviscid interactions at high Reynolds number. The aim of this work is to investigate dependence of the critical hump height (when a well attached flow over rigid body surface turns into a separated one) on the Karman–Guderley parameter which characterizes of the local flow field. The analysis of the flow field starts with the so-called inspection analysis of the flow properties and then the interaction problem has been constructed using the asymptotic analysis of triple-deck structure of interaction region. Finally, a method based on a semi-direct solution of governing equations of the transonic interaction problem has been used to obtain the numerical solution of the problem.     

Molecular structure, spectroscopic properties and DFT calculations of 2-(methylthio)nicotinic acid

The analyses of possible conformations, molecular structures, vibrational and electronic properties of 2-(methylthio)nicotinic acid molecule, C₇H₇NO₂S, with the synonym 2-(methylsulfanyl)nicotinic acid have been first presented theoretically. At the same time, FT-IR and micro-Raman spectra of 2-(methylthio)nicotinic acid were recorded in the regions 400–4000 cm^?1 and 100–4000 cm^?1, respectively. In our calculations, the DFTB3LYP method with 6–311G(d, p) basis set was used to have the structural and spectroscopic data about the mentioned molecule in the ground state and the results obtained were compared with experimental values. Furthermore, gauge invariant atomic orbital (GIAO) ¹H and ¹³C NMR chemical shifts in different solvents, UV-vis TD-DFT calculations, the highest occupied molecular orbitals (HOMO-2, HOMO-1, HOMO), lowest unoccupied molecular orbital (LUMO), molecular electrostatic potantial (MEP) surface, atomic charges and thermodynamic properties of molecule have been theoretically verified and simulated at the mentioned level. The energetic behavior of title molecule in different solvent media was investigated by using DFT/B3LYP method with 6–311G(d, p) basis set in terms of integral equation formalism polarizable continuum model (IEFPCM). In addition, the calculated infrared intensities, Raman activities, reduce masses and force constants of the compound under study have been also reported.     

Kaluza–Klein reduction of a quadratic curvature model

Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations, which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza–Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor are obtained in the actual four dimensional spacetime. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force density naturally emerges from the reduced field equations and the equations of the standard Kaluza–Klein theory are demonstrated to be intrinsically contained in this model.