A new estimate of the Montgomery constant in the theory of zeros distribution of the Riemann zeta-function in the critical stripe

The new value α = 91/116 is obtained for the constant α such that for all σ ≥ α the “density hypothesis” is valid for the Riemann zeta-function in the critical stripe. The previous value α = 11/14 was obtained by M. Jutila in 1977.     

Partial Regularity up to the Boundary for Weak Solutions of Elliptic Systems with Nonlinearity q Greater Than Two

Nonlinear elliptic systems with q-growth are considered. It is assumed that additional nonlinear terms of the systems have q-growth in the gradient, q < 2. For Dirichlet and Neumann boundary-value problems we study the regularity of weak bounded solutions in the vicinity of the boundary. In the case of small dimensions (n q + 2), the Hölder continuity or partial Hölder continuity up to the boundary is proved for the solutions considered. In the previous article, the author studied the same problem for q = 2. Bibliography: 12 titles.     

“Astrometry” experiment to measure the temporal variations in the shape and diameter of the sun on the service module of the Russian segment of the international space station

The “Astrometry” project will provide coordinate—photometric monitoring of the sun’s limb shape and disk diameter with a 0.005″ accuracy and its oblateness at a ～ 10^?6 R _? level for 6 yr. The project will investigate the internal structure and dynamics of the sun and the variations of its global parameters up to the core. The project will also investigate the fine structure and dynamics of the photosphere both on the disk and at the limb. The project is scheduled to be implemented at the ascending phase of new solar cycle 24.     

Regularity of solutions of the model Venttsel’ problem for quasilinear parabolic systems with nonsmooth in time principal matrices

The Venttsel’ problem in the model statement for quasilinear parabolic systems of equations with nondiagonal principal matrices is considered. It is only assumed that the principal matrices and the boundary condition are bounded with respect to the time variable. The partial smoothness of the weak solutions (Hölder continuity on a set of full measure up to the surface on which the Venttsel’ condition is defined) is proved. The proof uses the A(t)-caloric approximation method, which was also used in [1] to investigate the regularity of the solution to the corresponding linear problem.     

Structure and supramolecular organization of tri-n-butyl(octadecyl)phosphonium tetrafluoroborate and its influence on catalytic activity of stabilized palladium nanoparticles

Russian Chemical Bulletin - A crystal structure and aggregation properties of tri-n-butyl(octadecyl)phosphonium tetrafluoroborate were studied. Palladium nanoparticles stabilized by this...     

Formation of Low-Resistivity Au/Mo/Ti Ohmic Contacts to p-Diamond Epitaxial Layers

Technical Physics - The formation of Au/Mo/Ti ohmic contacts to p-diamond epitaxial films has been studied. Specifically, the influence of annealing on the electrical properties and structure of...     

Vibrational stabilization of the upright statically unstable position of a double pendulum

The phenomenon of stabilization by parametric excitation of an unstable, elastically restrained double inverted pendulum under its own weight is addressed. The solution is pursued by the Multiple Scale Method, as a perturbation of a critical Hamiltonian system, possessing a zero- and a real frequency. Several asymptotic expansions are carried out, which are able to capture the long-term behavior of the system, for generic (non-resonant) values of the excitation frequency, and some special (resonant) values of excitation-to-natural frequency ratio. It is shown that a proper ordering of the control parameters must be performed, and proper use of integer or fractional power expansions must be made, according to the resonance under study. In particular, a non-standard application of the Multiple Scale Method is illustrated for the 1:1 resonant case, requiring fractional powers and accounting for the ‘arbitrary constants’, generally omitted in regular cases. A comprehensive scenario of the stabilization regions is given in which lower-bound as well as upper-bound curves are evaluated, thus integrating results that recently appeared in the literature.     

Variational problem with an obstacle in ℝ<Superscript><Emphasis Type="Italic">N</Emphasis></Superscript> for a class of quadratic functionals

  A variational problem with an obstacle for a certain class of quadratic functionals is considered. Admissible vector-valued functions are assumed to satisfy the Dirichlet boundary condition, and the obstacle is a given smooth (N − 1)-dimensional surface S in ℝ ^N . The surface S is not necessarily bounded. It is proved that any minimizer u of such an obstacle problem is a partially smooth function up to the boundary of a prescribed domain. It is shown that the (n − 2)-Hausdorff measure of the set of singular points is zero. Moreover, u is a weak solution of a quasilinear system with two kinds of quadratic nonlinearities in the gradient. This is proved by a local penalty method. Bibliography: 25 titles. Dedicated to V. A. Solonnikov on the occasion of his jubilee Published in Zapiski Nauchnykh. Seminarov POMI, Vol. 362, 2008, pp. 15–47.     

Synthesis and spectral properties of fluorescent dyes based on 4-styryl-1,8-naphthalimide

The paper reports on synthesis and spectroscopic study of novel N-butyl-4-styryl-1,8-naphthalimide dyes bearing methoxy (1), dimethoxy (2), and dimethylamino (3) groups in the styryl fragment. It is shown that all synthesized compounds demonstrate positive solvatochromism, high values of Stokes shift in polar solvents, and fluorescence in the long wavelength part of visible range. These facts indicate a potential application of these compounds as fluorescent dyes in the biochemistry. The changes in the dipole moments of the molecules caused by excitation were estimated using Lippert—Mataga equation. The obtained results could be assigned to the formation of the excited states with intramolecular charge transfer. The formation of the twisted states with charge transfer was suggested in the case of compound 3, while the fluorescence quantum yield was significantly reduced in polar protic solvents.