Homogenization and Hydrodynamic Limit for Fermi‐Dirac Statistics Coupled to a Poisson Equation

This paper deals with the diffusion approximation of a Boltzmann‐Poisson system modeling Fermi‐Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in [19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in [19], here we use two‐scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of [3]. © 2015 Wiley Periodicals, Inc.     

On the diameter of a domination dot-critical graph

A graph G is domination dot-critical, or just dot-critical, if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. In this paper, we study an open question concerning of the diameter of a domination dot-critical graph G.     

On total domination vertex critical graphs of high connectivity

A graph is called γ-critical if the removal of any vertex from the graph decreases the domination number, while a graph with no isolated vertex is γ_t-critical if the removal of any vertex that is not adjacent to a vertex of degree 1 decreases the total domination number. A γ_t-critical graph that has total domination number k, is called k-γ_t-critical. In this paper, we introduce a class of k-γ_t-critical graphs of high connectivity for each integer k≥3. In particular, we provide a partial answer to the question “Which graphs are γ-critical and γ_t-critical or one but not the other?” posed in a recent work [W. Goddard, T.W. Haynes, M.A. Henning, L.C. van der Merwe, The diameter of total domination vertex critical graphs, Discrete Math. 286 (2004) 255-261].     

Photodynamic activity of substituted zinc trisulfophthalocyanines: role of plasma membrane damage

We recently reported that variations in cellular phototoxicity among a series of alkynyl-substituted zinc trisulfophthalocyanines (ZnPcS3Cn) correlates with their hydrophobicity, with the most amphiphilic derivatives showing the highest cell uptake and phototoxicity. In this study we address the role of the plasma membrane in the photodynamic response as it relates to the overall hydrophobicity of the photosensitizer. The membrane tracker dye 1-[4(trimethylamino)phenyl]-6-phenylhexa-1,3,5-triene (TMA-DPH), which is incorporated into plasma membranes by endocytosis, was used to establish plasma membrane uptake by EMT-6 cells of the ZnPcS3C, by colocalization, and TMA-DPH membrane uptake rates after photodynamic therapy were used to quantify membrane damage. TMA-DPH colocalization patterns show plasma membrane uptake of the photosensitizers after short 1 h incubation periods. TMA-DPH plasma membrane uptake rates after illumination of the photosensitizer-treated cells show a parabolic relationship with photosensitizer hydrophobicity that correlates well with the phototoxicity of the ZnPcS3C,. After a 1 h incubation period, overall phototoxicity correlates closely with the postillumination rate of TMA-DPH incorporation into the cell membrane, suggesting a major role of plasma membrane damage in the overall PDT effect. In contrast, after a 24 h incubation, phototoxicity shows a stronger but imperfect correlation with total cellular photosensitizer uptake rather than TMA-DPH membrane uptake, suggesting a partial shift in the cellular damage responsible for photosensitization from the plasma membrane to intracellular targets. We conclude that plasma membrane localization of the amphiphilic ZnPcS3C6-C9 is a major factor in their overall photodynamic activity.     

NMR investigation of methyl-2,4-dimethoxysalicylate: effect of solvent and temperature

(1)H NMR and (13)C NMR of methyl-2,4-dimethoxysalicylate 2 was measured in chloroform-d at the temperature range of 220-330 K, in dimethyl sulfoxide-d(6) at the temperature range of 300-400 K and in a polar protic solvent (CD(3)OD) at 300 K. The structure of 2 in liquid phase (solvent) is compared with those in solid phase (X-ray) and in the gas phase (quantum mechanical calculations). The relationship between molecular geometry, (1)H NMR chemical shift and W coupling of involved protons has a complex nature, but hydrogen bonds [C=O...H-O and C=O...H-CH(2)O] strength is the principle factor.     

Laser induced thermal lens spectrometry for cobalt determination after cloud point extraction

A new approach, employing cloud point extraction (CPE) in combination with thermal lens spectrometry (TLS), has been developed for the determination of cobalt. The CPE and TLS methods have good matching conditions for combination because TLS is suitable for low volume samples obtained after CPE and for organic solvents, which are used for dissolving the remaining analyte phase.1-(2-Pyridylazo)-2-naphthol (PAN) was used as a complexing agent and octylphenoxypolyethoxyethanol (Triton X-114) was added as a surfactant; then the pH of solution was adjusted. After phase separation at 50 °C based on the cloud point extraction of the mixture, the surfactant-rich phase was dried and the remaining phase was dissolved using 20 μL of carbon tetrachloride. The obtained solution was introduced into the quartz micro cell and the analyte was determined by thermal lens spectrometry. The He-Ne laser (632.8 nm) was used as both the probe and the excite source.Under optimum conditions, the analytical curve was linear for the concentration range of 0.2-40 ng mL⁻¹ and the detection limit was 0.03 ng mL⁻¹. The enhancement factor of 470 was achieved for a 10 mL sample. Relative standard deviations were lower than 5%.The method was successfully applied to the extraction and determination of cobalt in tap, river and sea water.     

Efficient in-depth trapping with an oil-immersion objective lens

Maximum trapping efficiency in optical tweezers occurs close to the coverslip because spherical aberration owing to a mismatch in the refractive indices of the specimen (water) and the immersion oil dramatically decreases the trap efficiency as the trap depth increases. Measuring the axial trap efficiency at various tube lengths by use of an oil-immersion objective has shown that such an aberration can be balanced by another source of spherical aberration, leading to a shift in the position of the maximum efficiency in the Z direction. For a 1.1 microm polystyrene bead we could achieve the maximal efficiency at a depth of 70 microm, whereas the trap was stable up to a depth of 100 microm.     

Can gravity distinguish between Dirac and Majorana neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and the gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavor system, as shown explicitly for SN 1987A.     

A class of models for uncorrelated random variables

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution of uncorrelated random variables, irrespective of the strength of dependence between them. We provide a method for the construction of bivariate SUM distributions through linking any pair of identical symmetric probability density functions. We also give a formula for measuring the strength of dependence of the SUM models. A final result shows that under the condition of positive or negative orthant dependence, the SUM property implies independence.