New oxazoline-containing phosphoramidite ligand for palladium-catalyzed asymmetric allylic sulfonylation

New chiral oxazoline-containing phosphoramidite was synthesized and its complex formation with rhodium(i) and palladium(ii) was examined. The new ligand is a highly efficient chiral inductor (ee up to 92%) in palladium-catalyzed asymmetric sulfonylation of 1,3-diphenylallyl acetate with sodium p-toluenesulfinate.     

Two-dimensional Fuchsian systems and the Chebyshev property

Let (x(t),y(t))^? be a solution of a Fuchsian system of order two with three singular points. The vector space of functions of the form P(t)x(t)+Q(t)y(t), where P,Q are real polynomials, has a natural filtration of vector spaces, according to the asymptotic behavior of the functions at infinity. We describe a two-parameter class of Fuchsian systems, for which the corresponding vector spaces obey the Chebyshev property (the maximal number of isolated zeros of each function is less than the dimension of the vector space). Up to now, only a few particular systems were known to possess such a non-oscillation property. It is remarkable that most of these systems are of the type studied in the present paper. We apply our results in estimating the number of limit cycles that appear after small polynomial perturbations of several quadratic or cubic Hamiltonian systems in the plane.     

Quantum computer elements based on coupled quantum waveguides

Possible applications of two weakly coupled quantum waveguides for quantum computation are considered. The approach is based on the resonance phenomena in the system. Two different qubits interpretations are described. Some single-qubit and two-qubits operations are realized in the framework of these interpretations. The text was submitted by the authors in English.     

The transmission and bistability of a nonlinear quasioptical resonator in ESR-conditions in ruby

Due to rapid progress of the nonlinear optics it has become real to observe and use the phenomenon of optics bistability in such passive structure as a Fabry-Perot resonator filled (completely or partially) with a substance having nonlinear adsorbtion and refraction. The problem of the optic bistability of such resonance structures were discussed in [1,2].     

Complex-exponential representation of time-domain response of a one-mode resonator

Time-domain response of a one-mode resonator is investigated by using a complex-exponential representation of the time-domain impulse response. The transient response of a resonator has calculated for a short incident pulse which has rectangular form and the radio frequency filling. The convolution integral has been analytically carried out and two solutions for the time histories of the transient response of the resonator have been found. They are the early-time and late-time portions of the signal. The behaviour of amplitude and frequency of the transient response of the electrodynamical structure under consideration is studied.     

The State of Copper Ions in Aqueous and Aqueous Ammonia Solutions of Copper Acetate

Stabilization of Cu²⁺ ions in aqueous and aqueous ammonia solutions of copper acetate was studied for a wide range of ammonia concentrations. The structure of copper acetate hydrate complexes was shown to markedly change upon dissolution in water. In aqueous solutions, copper is stabilized as strongly bound Cu²⁺ associates (dimers) in a distorted octahedral environment composed of water molecules and acetate groups oxygen atoms in equatorial positions with strong exchange interaction via acetate groups. In solutions of copper acetate in aqueous ammonia, the concentration of ammonia has a crucial effect on the ordering of Cu²⁺ ions in associates. At high ammonia concentration, disordered copper tetra-ammoniate associates with the \({d_{{x^2} - {y^2}}}\) ground state are formed, whereas at low ammonia concentration, bulky Cu²⁺ ion associate structures are generated, with the \({d_{{x^2} - {y^2}}}\) ground state, hydroxyl groups in the equatorial plane, and water molecules in the axial positions.