Static spherically symmetric solutions in <Emphasis Type=Italic>F</Emphasis>(<Emphasis Type=Italic>R</Emphasis>) gravity

A Lagrangian derivation of the Equations of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits one to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in F(R)-gravity. All known exact solutions are recovered. We also exhibit a new non-trivial solution with non-constant Ricci scalar.     

<Emphasis Type=Italic>Y</Emphasis> and <Emphasis Type=Italic>Z</Emphasis> luminescence of polycrystalline cadmium telluride

The properties of polycrystalline CdTe with a grain size of 5–30 μm have been investigated using the microphotoluminescence methods of spectral analysis and topography. This material has been prepared by direct synthesis in a vapor flow of components at a low temperature. The dominance of the Y and Z bands in the spectra reflects a nonequilibrium character of the crystallization processes. The superlinear dependences of the luminescence intensity on the level of the band-to-band excitation indicate the exciton nature of the corresponding transitions. The activation energies for temperature quenching of luminescence in the temperature range T = 100–150 K are found to be 120 meV for the Y luminescence and 180 meV for the Z luminescence, which correspond to the dissociation of excitons bound to defects with the transition of charge carriers to the conduction and valence bands. The monochromatic topography data indicate that Y and Z defects have different material bases.     

Cosmology based on <Emphasis Type=Italic>f</Emphasis>(<Emphasis Type=Italic>R</Emphasis>) gravity with <Emphasis Type=Italic>O</Emphasis>(1)eV sterile neutrino

We confront different up to date cosmological data with different gravity models of the Universe with one additional massive sterile neutrino [1].     

The Fermi-Pasta-Ulam recurrence and related phenomena for 1<Emphasis Type=Italic>D</Emphasis> shallow-water waves in a finite basin

Different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear “one-dimensional” potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in analytic form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on the number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderate-height waves.     

<Emphasis Type=Italic>T</Emphasis>-solutions of different types and their relations to <Emphasis Type=Italic>R</Emphasis>-solutions

Different types of T-solutions are investigated. The conditions at which one region of space-time can be described only by a statistic R-solution and another region can be described only by a T-solution are obtained. The common metric for R- and T-solutions is obtained where the spatial and temporal variables are interchanged. The T-solution which has the same mass function as for the internal static Schwarzschild solution is obtained.     

Casimir effect within (3 + 1)<Emphasis Type=Italic>D</Emphasis> Maxwell-Chern-Simons electrodynamics

Within the framework of the Lorentz-violating (3 + 1)-dimensional extended electrodynamics including the Lorentz-violating CPT-odd Chern-Simons term, we consider the electromagnetic field between two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one calculated in [1] and based on wrong equations of motion. Compared with the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.     

Unitarity of the tree approximation to the Glauber <Emphasis Type=Italic>AA</Emphasis> amplitude for large <Emphasis Type=Italic>A</Emphasis>

The nucleus-nucleus Glauber amplitude in the tree approximation is studied for heavy participant nuclei. It is shown that, contrary to previous published results, it is not unitary for realistic values of nucleon-nucleon cross sections.     

Idempotents as <Emphasis Type=Italic>J</Emphasis>-Projections

Let B(H) ^Id be the set of all bounded idempotents on a Hilbert space H. Fix p∈B(H) ^Id . The aim of the paper is to show a set of symmetries J on H for which p is a J-projection.