Metabolites of Artemisia juncea and their Effect on Regulation of Thymocyte Volume

Chemistry of Natural Compounds -     

Triterpene glycosides and their genins fromThalictrum foetidum. V. Structure of cyclofoetoside B

A new glycoside (cyclofoetoside B) (I) has been isolated from the epigeal part of the plantThalictrum foetidum L. (Ranunculaceae). On the basis of chemical transformations and with the aid of physicochemical characteristics it has been established that cyclofoetoside B is 24S-cycloartane-3, 16, 24, 25, 29-pentaol 3-O--L-arabinopyranoside 16-O-[O--L-rhamnopyranoside-(1 6)--D-glucopyranoside], C₄₇-H₈₀O₁₇, mp 194–197°C (methanol); [] _D ²⁴ +15.7 ± 2° (c 0.88; pyridine). The enzymatic hydrolysis of (I) has yielded cyclofoetigenin B (III), 24S-cycloartane-3,16,24,25,29-pentaol 16-O--D-glucopyranoside, (IV), C₃₆H₆₂O₁₀, mp 223–225°C (acetone), [] _D ²⁴ +37 ± 2° (c 0.97; methanol) and 24S-cycloartane-3,16,24,25,29-pentaol 16-O-[O--L-rhamnopyranosyl-(1 6)--D-glucopyranoside, C₄₂H₇₂O₁₄, mp 229–231°C (methanol), [] _D ³⁰ +41 ± 2° (c 0.7; methanol). Details of the IR and¹H and¹³C NMR spectra of the compounds are given.Irkutsk Institute of Organic Chemistry, Academy of Sciences of the USSR. Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Trashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 341–345, May–June, 1986.     

On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator

A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.     

Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice

For a three-particle operator on a lattice, we study the properties of its spectrum that depend on pairwise interactions and are determined by a parameter characterizing the intensity of interaction.     

Bound states of a system of two fermions on a one-dimensional lattice

We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of bound states N(k) is a nondecreasing function of the total quasimomentum of the system k ∈ [0, π]. We describe the set of discontinuity points of N(k) and evaluate the jump N(k +0) − N(k) at the discontinuity points. We establish that the bound-state energy z _n (k) increases as the total quasimomentum k ∈ [0, π] increases. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 47–57, April, 2006.     

An algorithm for reconstructing the Dirac operator with a spectral parameter in the boundary condition

The problem of reconstructing the Dirac operator with nonseparated boundary conditions of which one includes a spectral parameter is considered. A uniqueness theorem is proved, and an algorithm for solving the inverse problem is proposed.     

On the solution of boundary value problems with nonseparated multipoint and integral conditions

We suggest a numerical method for solving systems of linear nonautonomous ordinary differential equations with nonseparated multipoint and integral conditions. By using this method, which is based on the operation of convolution of integral conditions into local ones, one can reduce the solution of the original problem to the solution of a Cauchy problem for systems of ordinary differential equations and linear algebraic equations. We establish bounded linear growth of the error of the suggested numerical schemes. Numerical experiments were carried out for specially constructed test problems.     

Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations

A numerical method is suggested for solving systems of nonautonomous loaded linear ordinary differential equations with nonseparated multipoint and integral conditions. The method is based on the convolution of integral conditions into local ones. As a result, the original problem is reduced to an initial value (Cauchy) problem for systems of ordinary differential equations and linear algebraic equations. The approach proposed is used in combination with the linearization method to solve systems of loaded nonlinear ordinary differential equations with nonlocal conditions. An example of a loaded parabolic equation with nonlocal initial and boundary conditions is used to show that the approach can be applied to partial differential equations. Numerous numerical experiments on test problems were performed with the use of the numerical formulas and schemes proposed.     

Thermal conductivity of GaS and GaSe layered semiconductors

This paper reports on the results of experimental investigations into the thermal conductivity of GaS and GaSe layered semiconductor crystals in directions parallel and perpendicular to the crystal layers in the temperature range 5–300 K. Specific features of the thermal conductivity of these crystals are analyzed.