Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II

Consider a projective algebraic variety W which is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than d in n + 1 variables over a field of zero characteristic. Consider a dominant rational morphism from W to W′ given by homogeneous polynomials of degree d′. We suggest algorithms for constructing objects in general position related to this morphism. They generalize some algorithms from the first part of the paper to the case dim W > dim W′. These algorithms are deterministic and polynomial in (dd′)n and the size of the input. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 181–224.     

Estimates for the Second Order Derivatives of Eigenvectors in Thin Anisotropic Plates with Variable Thickness

For the second order derivatives of eigenvectors in a thin anisotropic heterogeneous plate Ω_h, we derive estimates of their weighted L₂-norms with majorants whose dependence on the plate thickness h and on the eigenvalue number is expressed explicitly. These estimates maintain the asymptotic sharpness throughout the entire spectrum, whereas inside its low-frequency band the majorants remain bounded as h → +0. The latter is a rather unexpected fact, because for the first eigenfunction u¹ of a similar boundary-value problem for a scalar second order differential operator with variable coefficients, the norm ‖∇ _x ² u⁰; L₂(Ω_h)‖ is of order h⁻¹ and grows as h tends to zero. Bibliography: 35 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 161–180.     

Analogue of a spin flop phase transition for an array of magnetic moments with dipole interaction

In a two-dimensional array of magnetic moments with planar magnetization and relatively weak anisotropy in the basal plane, a stepwise phase transition is induced by an external magnetic field parallel to the easy axis of the system. This transition is similar to the spin flop phase transition in weakly anisotropic Heisenberg antiferromagnets with the significant difference that it is accompanied by the rearrangement of the sublattice structure of the magnet; i.e., it can be interpreted as a topological transition. The transition should manifest itself for arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates, which have recently become the object of intensive research.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Luminescence investigations of the GaP-based dilute nitride Ga(NAsP) material system

Multi-quantum well heterostructures (MQWHs) of the novel Ga(NAsP)/GaP material system have been grown, pseudomorphically strained to GaP-substrate. The crystalline perfection is verified by transmission electron microscopy (TEM). For As-concentrations in excess of about 70%, a direct band structure and adequate luminescence efficiency for laser device application is observed. Temperature-dependent photoluminescence (PL) investigations show the influence of carrier localisation and non-radiative recombination processes typical for dilute nitride materials. With rising N content in the active material, the emission wavelength shifts towards longer wavelength, leading to Ga(NAs)/GaP MQW structures with photon energies below the indirect band gap of silicon (Si). At the same time the luminescence intensity drops due to an increase in non-radiative carrier traps and/or structural degradation.     

ON THE ROLES OF COMPLEMENTARY AND ADMISSIBLE BOUNDARY CONSTRAINTS IN FOURIER SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS OF COMPLETELY COUPLED r TH ORDER PDES

A heretofore unavailable double Fourier series based approach, for obtaining non-separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions, has been presented. The method has been successfully implemented to solve a class of hitherto unsolved boundary-value problems, pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform, with arbitrarily prescribed (both symmetric and asymmetric with respect to the panel centerlines) admissible boundary conditions and subjected to general transverse loading.Existing solutions such as those due to Navier or Levy are based on the well-known method of separation of variables. Such solutions represent particular solutions whenever the method of separation of variables work, and when these particular solution functions fortuitously satisfy the boundary conditions. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form sets of measure zero.Various cases of lamination, geometry and dynamic response (forced and free vibrations) of a class of thin anisotropic laminated shells (curved panels) have been shown to follow from the above. Six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions. Navier-type solutions whenever available form special cases of the present general solution.     

Raman spectroscopy of topotecan, an inhibitor of DNA topoisomerase I

Topotecan (TPT), a water-soluble derivative of camptothecin (inhibitor of human DNA topoiomerase I), has found wide application in cancer chemotherapy. The central problem in using topotecan is the presence of lactone rings in its molecules, which undergo hydrolysis at a physiological pH yielding an inactive and even toxic form of the drug. The analysis of Raman spectra of TPT in H₂O and D₂O solutions made it possible to assign the spectral bands to the vibrations of particular molecular groups. Spectral features indicative of the opening of the lactone rings of the TPT molecules, deprotonation of the hydroxyl groups in their quinoline fragments, and of possible participation of the hydroxyl and carbonyl groups in H bonding are found. The data obtained are necessary to study the molecular mechanisms of TPT-DNA interaction and the formation of ternary complexes between TPT, DNA, and DNA topoisomerase I.     

VIBRATION AND STABILITY OF ANNULAR PLATES IN NON-LINEAR CREEP CONDITIONS

This paper presents a study on the influence of the physical non-linearity of material in creep conditions on vibration and stability of non-uniform annular plates subjected to a follower force radially distributed at the outer edge. The stability analysis requires first the calculation of a membrane stress distribution and then the application of the kinetic stability criterion, making use of small superposed vibrations. The differential equations of the membrane and vibration states have been integrated by means of the transfer matrix method which allowed the determination of the relationships between the real and imaginary parts of the complex frequency and compressive force (characteristic curves). The results have been presented in numerous figures.