k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

Analysis Mathematica - We introduce and study the k-Hankel Gabor transform. We investigate the localization operators for this transform. In particular, we study their trace class properties and we...     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Extraction-ability and -selectivity of tetra-aza-crown ethers for transition metal cations

In order to investigate the relative effects of the differences between the structures and lipophilicities of 1, 10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TA-18-crown-6) and the tetrabenzyl derivative of 1,10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TBTA-18-crown-6) on their extraction-abilities and -selectivities for transition metal cations, constants of the overall extraction (logK _ex) of 1:1 (M:L) complexes, the distribution (K _D) for two diluents (CH₂Cl₂ and CHCl₃) with different dielectric constants have been determined at 25 ± 0.1 °C. The magnitude of logK _ex is largely determined by that of K _D. The equilibrium constants of TA-18-crown-6 have been compared with those of TBTA-18-crown-6. It is found that:(i) logK _ex sequences of TA-18-crown-6 and TBTA-18-crown-6 for transition metals in CH₂Cl₂ lie in order: Fe³⁺ > Cu²⁺ > Mn²⁺ > Co²⁺ > Cd²⁺ > Ni²⁺ > Zn²⁺ and Fe³⁺ > Cu²⁺ > Co²⁺ > Mn²⁺ > Ni²⁺ > Cd²⁺ > Zn²⁺ respectively; (ii) the stability sequences of two types of tetra-aza-crown ethers with the transition metal cations in CHCl₃ are the same as follows: Fe³⁺ > Ni²⁺ > Cu²⁺ > Co²⁺ > Zn²⁺ > Cd²⁺ > Mn²⁺, and (iii) unusual selectivities are observed for transition metal-tetra-aza-crowns, e.g. the high Fe³⁺/M ⁿ⁺ selectivity factors (S_f) of TA-18-crown-6, except for the competitive-extractions for the special case in CHCl₃ of TBTA-18-crown-6, it was found that the Mn²⁺/M ⁿ⁺ values were relatively higher according to the other transition metal cations. A systematic sequence in these two types of solvents is not found for a given transition metal cation in terms of the variation of selectivity with the tetra-aza-crown ethers. The results provide alternatives for the rational design of other specific ligands on the transition metal cations.     

Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

The Transport Properties of the Cell Membrane Ion Channels in Electric Fields: Bethe Lattice Treatment

The interactive two-state model of cell membrane ion channels in an electric field is formulated on the Bethe lattice by means of the exact recursion relations. The probability of channel opening or maximum fractions of open potassium and sodium channels are obtained by solving a non-linear algebraic equation. Using known parameters for the conventional mean-field theory the model gives a good agreement with the experiment both at low and high trans-membrane potential values. For intermediate voltages, the numerical results imply that collective effects are introduced by trans-membrane voltage.