Brane Cosmology, Varying Speed of Light and Inflation in Models with One or More Extra Dimensions

We summarize the approach to brane cosmology known as mirage cosmology and use it to determine the Friedmann equation on a 3-brane embedded in different bulk spacetimes all with one or more extra dimensions. Usually, when there is more than one extra dimension the junction conditions, central to the usual brane world scenarios, are difficult to apply. This problem does not arise in mirage cosmology because the brane is treated as a test particle in the background spacetime. We discuss in detail the dynamics of a brane embedded in two specific 10D bulk spacetimes, namely Sch-AdS₅ × S₅ and a rotating black hole, and from the dynamics—which are now rather more complicated since the brane can move in all the extra dimensions—determine the new dark fluid terms in the brane Friedmann equation. Some of these, such as the cosmological constant term, are seen to be bulk dependent. We then show explicitly how this mirage cosmology approach matches with the familiar junction condition approach when there is just one extra dimension. The issue of a varying speed of light in mirage cosmology is addressed and we find a scenario in which c _eff always increases, tending asymptotically to c ₀ as the universe expands. Finally some comments are made regarding brane inflation and limitations of the mirage cosmology approach are also discussed.     

On Fuzzy Probability Theory

Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition.     

Electron Energies, Dipole Electric Moments, and Distribution of the Laurdan Molecule over the Conformation States of Methyl Groups

Using the methods of molecular simulation and HyperChem v.5.0 programs (PM3 method), we carried out calculations of the principal spectroscopic characteristics and of the structure of the laurdan molecule in the ground and the first excited electronic states. The thermal static distribution of molecules over various possible orientations of the plane of methyl groups relative to the plane of the naphthalene bicycle was taken into account. The energies and dipole moments of these electronic states have been calculated as functions of the torsion angle of methyl groups. The existence of an additional mechanism of electronic spectrum broadening is shown; it is associated with thermal mismatch of the equilibrium orientations of the rotational fragment of the molecule and with the dependence of the electron transition frequency on the degree of deviation of the angle from the equilibrium value. The dependence of dipole moments on this angle has been found and calculated. This dependence is the strongest for the ground state. The maximum values of dipole moments in the ground and excited states are 4.0 and 7.6 D.     

Optical Properties of Films of Cu x Ag1−x InSe2 Solid Solutions Obtained by Laser Evaporation

The structure and optical properties of the films of ternary compounds AgInSe₂, CuInSe₂ and Cu _x Ag_1–x InSe₂ solid solutions obtained by pulsed laser evaporation are investigated. It has been established that the films like bulk crystals have the structure of chalcopyrite. By the transmission and reflection spectra near the edge of natural absorption the refractive index and coefficient of optical absorption are calculated and the energies of interband transitions and the crystalline and spinorbit splitting are determined.     

Structural Characterization of Some Acylisoxazolone Extractants

From IR, UV, ³¹P, ¹H, and ¹³C NMR spectroscopic data, it is shown that the three 3-phenyl-4-acyl-isoxazol-5-ones, HPXI (HPBI, HPTI, and HPtbBI with acyl-, benzoyl-, toluoyl-, and para-(tert-butyl)benzoyl-, respectively), promising extractants of actinides, appear under the same major tautomeric forms, both in the solid and in solutions in various solvents: the diketo-enamine form in methanol, a -ketoenolic form in the solid, and in chloroform, benzene, and toluene. The radiocrystallographic structures of HPTI and HPtbBI have been determined. They appear as 3-phenyl-4-(-hydroxybenzylidene)isoxazol-5-ones, forming intramolecular chelates through H-bonds. -Aryl interactions might influence the relative positions of the -ketoenolic oxygen atoms and, hence, the bite angle and the cone angle of these ligands. Spectroscopic data give evidence of strong TOPO–HPXI interactions (TOPO: tri-n-octylphosphine oxide) in toluene, of the same order of magnitude for the three acylisoxazolones, in the order: HPBI > HPTI > HPtbBI.     

Design, synthesis, and characterization of a calcium-sensitive near infrared dye

Intracellular calcium concentration in biological cells varies from 0.1 to 10 μM depending upon cell signaling and disease states. A direct estimate of calcium concentration in cell tissues within this range is possible with a novel calcium-selective reagent 15C5-774. The molecule of 15C5-774 consists of a near-infrared (NIR) chromophore (λ_max=774 nm) and a metal complexing moiety of benzo-15-crown-5. The reagent shows a strong calcium binding affinity in a 1:1 ratio and metal selectivity in the order Ca²⁺>Mg²⁺>Sr²⁺≈K⁺≈Na⁺>Zn²⁺>Li⁺. The high sensitivity is achieved by conducting absorption measurements in the NIR region where background interference from the biological matrix is low.     

On a current mechanism in Ta2O5 thin films

Electrical conduction in the temperature range of 120–370 K has been studied in sandwiched structures of Al/Ta₂O₅/Si. The tantalum oxide films were prepared by evaporation of tantalum on a p-Si crystal substrate, followed by oxidation at a temperature of 600°C. The temperature-dependent current-voltage (I–V) characteristics are explained on the basis of a phonon-assisted tunnelling model. The same explanation is given for I–V data measured on Ta₂O₅ films by other investigators. From the comparison of experimental data with theory the density of states in the interface layer is derived and the electron-phonon interaction constant is assessed.      

Einstein<Emphasis Type="Italic">A</Emphasis>-coefficients for rotational transitions in the ring-chain isomer of C<Subscript>5</Subscript>H<Subscript>2</Subscript>

Laboratory formation of four isomers of C⁵H² molecule is reported and detection of the ring-chain isomer (isomer 1) of C₅H₂ in cosmic objects has been suggested. For identification of a molecule in cosmic objects, one of the required input data is EinsteinA-coefficients (radiative transition probabilities) for the molecule. Here, we report EinsteinA-coefficients for electric dipole transitions in the ring-chain isomer of C₅H₂ among the rotational levels of the ground electronic and ground vibrational states up to 21 cm⁻¹.