A population biological model with a singular nonlinearity

We consider the existence of positive solutions of the singular nonlinear semipositone problem of the form $\left\{ \begin{gathered} - div(|x|^{ - \alpha p} |\nabla u|^{p - 2} \nabla u) = |x|^{ - (\alpha + 1)p + \beta } \left( {au^{p - 1} - f(u) - \frac{c} {{u^\gamma }}} \right),x \in \Omega , \hfill \\ u = 0,x \in \partial \Omega , \hfill \\ \end{gathered} \right. $ where Ω is a bounded smooth domain of ? ^N with 0 ∈ Ω, 1 < p < N, 0 ? α < (N ? p)/p, γ ∈ (0, 1), and a, β, c and λ are positive parameters. Here f: [0,∞) → ? is a continuous function. This model arises in the studies of population biology of one species with u representing the concentration of the species. We discuss the existence of a positive solution when f satisfies certain additional conditions. We use the method of sub-supersolutions to establish our results.     

Purity in the category of S-posets

In this paper, purity of S-posets over a pomonoid S is investigated. We first study some basic properties of absolutely po-pure S-posets. Among other results, it is proved that every regular injective S-poset is absolutely po-pure, and every absolutely po-pure inequationally compact S-poset is regular injective. Then, using the notion of semi-finitely presented S-poset based on the finitely induced S-poset congruence, we find an equivalent condition for an S-poset to be 1-po-pure in a regular extension. Finally, a characterization of an absolutely 1-po-pure S-poset is presented.     

Microlenses focal length measurement using Z-scan and parallel moiré deflectometry

In this paper, a simple and accurate method based on Z-scan and parallel moiré deflectometry for measuring the focal length of microlenses is reported. A laser beam is focused by one lens and is re-collimated by another lens, and then strikes a parallel moiré deflectometer. In the presence of a microlens near the focal point of the first lens, the radius of curvature of the beam is changed; the parallel moiré fringes are formed only due to the beam divergence or convergence. The focal length of the microlens is obtained from the moiré fringe period graph without the need to know the position of the principal planes. This method is simple, more reliable, and completely automated. The implementation of the method is straightforward. Since a focused laser beam and Z-scan in free space are used, it can be employed for determining small focal lengths of small size microlenses without serious limitation on their size.     

Accurate Sensitivity of Quantum Dots for Detection of HER2 Expression in Breast Cancer Cells and Tissues

Here we introduce novel optical properties and accurate sensitivity of Quantum dot (QD)-based detection system for tracking the breast cancer marker, HER2. QD525 was used to detect HER2 using home-made HER2-specific monoclonal antibodies in fixed and living HER2⁺ SKBR-3 cell line and breast cancer tissues. Additionally, we compared fluorescence intensity (FI), photostability and staining index (SI) of QD525 signals at different exposure times and two excitation wavelengths with those of the conventional organic dye, FITC. Labeling signals of QD525 in both fixed and living breast cancer cells and tissue preparations were found to be significantly higher than those of FITC at 460–495 nm excitation wavelengths. Interestingly, when excited at 330–385 nm, the superiority of QD525 was more highlighted with at least 4–5 fold higher FI and SI compared to FITC. Moreover, QDs exhibited exceptional photostability during continuous illumination of cancerous cells and tissues, while FITC signal faded very quickly. QDs can be used as sensitive reporters for in situ detection of tumor markers which in turn could be viewed as a novel approach for early detection of cancers. To take comprehensive advantage of QDs, it is necessary that their optimal excitation wavelength is employed.     

Naked singularity formation in $${f({\mathcal R})}$$ gravity

We study the gravitational collapse of a star with barotropic equation of state p = wρ in the context of f(R){f({\mathcal R})} theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as f(R)=aR^m{f({\mathcal R})=\alpha{\mathcal R}^{m}} , we show that for an appropriate initial value of the energy density, if α and m satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter α obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.     

Investigation of coupling length in a semi-cylindrical surface plasmonic coupler

We have investigated the performance of a nano-optical directional coupler based on gap plasmon waveguides. The coupler consists of two waveguides having a localized coupled plasmon propagating between two semi-cylindrical surfaces. After introducing a fundamental mode of studied waveguides, effects of the structure parameters on the coupling length are shown. Simulation results of the coupler obtained by the compact-2D finite-difference time-domain (FDTD) method comply with those derived by an analytic method with the aid of the finite-element frequency-domain (FEFD) software package of COMSOL.     

C–S Targeted Biodegradation of Dibenzothiophene by Stenotrophomonas sp. NISOC-04

Crude oil-contaminated soil samples were gathered across Khuzestan oilfields (National Iranian South Oil Company, NISOC) consequently experienced a screening procedure for isolating C-S targeted dibenzothiophene-biodegrading microorganisms with previously optimized techniques. Among the isolates, a bacterial strain was selected due to its capability of biodegrading dibenzothiophene in a C-S targeted manner in aqueous phases and medium mostly consisting of separately biphasic water-gasoline. The 16S rDNA of the isolate was amplified using eubacterial-specific primers and then sequenced. Based on sequence data analysis, the microorganism, designated NISOC-04, clustered most closely with the members of the genus Stenotrophomonas. Gas chromatography indicated that Stenotrophomonas sp. NISOC-04 utilizes 82% of starting 0.8 mM dibenzothiophene within a 48-h-long exponential growth phase. Growth curve analysis revealed the inability of Stenotrophomonas sp. NISOC-04 to utilize dibenzothiophene (DBT) as the exclusive carbon or carbon/sulfur source. Gibbs' assay showed no 2-hydroxy biphenyl accumulation, but HPLC confirmed the presence of 2-hydroxy biphenyl as the final product of DBT desulfurization. Under sulfur starvation, Stenotrophomonas sp. NISOC-04 produced a huge biomass with untraceable sulfur and utilized atmospheric insignificant sulfur levels.     

Dyadic Green’s function of a PEMC cylinder

The dyadic Green’s function of a PEMC cylinder is derived with the aid of the principle of scattering superposition and Ohm–Rayleigh method. The PEMC boundary conditions are presented in dyadic form and it shows that how the impedance parameter of PEMC and cross-polarized fields appear in the Green’s function. The asymptotic expansions of the dyadic function is calculated in order to attain a closed form for the electrical field.