On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System

In a previous work [1] matter models such that the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1, were considered in the context of Buchdahl’s inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R ₀, R ₁], R ₀ > 0, satisfies R ₁/R ₀ < 1/4. Moreover, given a sequence of solutions such that R ₁/R ₀ → 1, then the limit supremum of 2M/R ₁ was shown to be bounded by ((2Ω + 1)² − 1)/(2Ω + 1)². In this paper we show that the hypothesis that R ₁/R ₀ → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R ₁ is bounded, but that the limit is ((2Ω + 1)² − 1)/(2Ω + 1)² = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R ₁ arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R ₁ of any static solution of the spherically symmetric Einstein-Vlasov system.     

Two-atom van der Waals interaction between polarizable/magnetizable atoms near magnetoelectric bodies

The van der Waals potential of two atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetoelectric bodies is studied. Starting from a polarizable atom placed within a given geometry, its interaction with a second polarizable/magnetizable atom is deduced from its Casimir-Polder interaction with a weakly polarizable/magnetizable test body. The general expressions for the van der Waals potential obtained thusly are illustrated by considering first the case of two atoms in free space, with special emphasis on the interaction between (i) two polarizable atoms and (ii) a polarizable and a magnetizable atom. Furthermore, the influence of magnetoelectric bodies on the van der Waals interaction is studied in detail for the example of two atoms placed near a perfectly reflecting plate or a magnetoelectric half space, respectively. The text was submitted by the authors in English.     

Study of gain flatness for multi-channel amplification in single stage EDFA for WDM applications

In this paper, gain flatness is studied for simultaneous 16-ITU-T channel amplifications at C-band (1,532–1,558 nm) in a single stage EDFA for WDM application at different average inversion levels. The inversion levels are varied due to the change of the input signal levels from the targeted operating point and also for dropping few numbers of channels. Specially designed gain flattening filter (GFF) is used in order to get the flat gain with gain variation ±0.5 dB for −20 dBm/ch input signal power (total input signal power is −8.0 dBm) at a fixed average inversion level which is maintained by proper selection of optimum fibre length and pump power. A specific loss spectrum of GFF is obtained by writing a chirped fibre Bragg grating of length 20 mm. Gain variations are studied by changing the total input signal levels from −8.0 dBm to −20.0 dBm and maintained within 20.0 ± 0.5 dB by using automatic gain control (AGC) circuit. About 15 out of 16 channels are dropped and observed ± 0.5 dB gain-variation which is an important parameter in optical network system.     

Compatibility and Marginality

We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can be used to better explain some classical phenomena in stochastic processes.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.     

Temperature Dependence for Fluorescence of β-NADH in Glycerol/Water Solution and in Trehalose/Sucrose Glass

Fluorescence imaging of cells and tissue can be used to evaluate β-NADH redox and location. At low temperature, β-NADH fluorescence intensity increases and therefore sensitivity of imaging increases. In this paper, the temperature dependence of fluorescence was evaluated for β-NADH in glycerol/water solution and in trehalose/sucrose glass. The average fluorescence lifetime for NADH in glycerol/water is 0.66 ns, compared with 5.3 ns in trehalose/ sucrose at 20°C. Emission spectra were recorded from 290 to 12 K. The fluorescence of β-NADH in glycerol/water increases ∼16 fold and the emission shifts about 35 nm to the blue as temperature decreases. Much smaller change is seen for fluorescence of β-NADH in sugar glass. Below 77 K, the β-NADH spectral features did not change significantly with temperature change, and so no increase in sensitivity is obtained by going to very low temperatures. It is suggested that the sensitivity of β-NADH fluorescence is related to water relaxation around the excited state molecule. Differences in water in various tissues may contribute to β-NADH fluorescence changes when cells are altered.     

Subwavelength-resolution near-field Raman spectroscopy

The resolution capabilities of near-field Raman spectroscopy based on a giant enhancement of the electric field near a nanosized metal probe are studied. As a test sample, bundles of single-walled carbon nanotubes deposited on glass substrates are used. It is shown that this method ensures a subwavelength spatial resolution of about 50 nm and demonstrates a Raman scattering enhancement of the order of 10⁴.     

A convergent star product for linear Poisson structures

An explicit star product ⋆ _α ^Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K₁] is given and diverse properties of the star product ⋆ _α ^Γ are studied. It is also proved that the star product ⋆ _α ^Γ provides a convergent deformation quantization in the sense of Rieffel [R₁].