Cheng Equation: A Revisit Through Symmetry Analysis

The symmetry analysis of the Cheng Equation is performed. The Cheng Equation is reduced to a first-order equation of either Abel's Equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati Equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng Equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae journa

Effect of cation ratio on microstructure and optical absorbance of magnesium aluminate spinel

This work is pertaining to the synthesis of fine magnesium aluminate spinel (MgAl2O4) powders of varied trivalent:bivalent cation ratio along line of homogeneity of the solid solution (MgO. xAl(2)O(3), x = 1, 1.25, 1.50, 1.75, and 2) via gel combustion method. Magnesium- and aluminum- nitrate were used as the oxidants in combustion reaction fuelled by urea in combination with stoichiometric formaldehyde solution acting as reductant. Synthesized powders were characterized in terms of microscopic analysis and optical absorbance measurements. The cation ratio, through a change in gel structure influences the nature of crystallization of the product, while on the other hand does not affect grain shapes and sizes. Distinct enhancement in both absorption intensity and the corresponding estimated energy band gap has been observed against increasing excess than stiochiometric alumina concentrations. Evaluated optical band gaps were widened in proportion to the Al: Mg ratio which may be attributed to Burstein-Moss effect in consequence of substitutional insertion of introduced Al3+ ions in spinel lattices

Gastric Follicular Dendritic Cell Sarcoma: A Case Report of a Rare Entity

Follicular Dendritic cell sarcoma arises from the follicular dendritic cells present in the lymphnode.Though are commonly seen in head and neck area but are extremely rare in the abdomen. Less than eighty cases are reported in the indexed literature. We herein describe a case of follicular dendritic cell sarcoma arising from the stomach wall with infiltration into pancreas in an 85 year old patient

Detector imperfections in photon-pair source characterization

We analyze how imperfections in single-photon detectors impact the characterization of photon-pair sources. We perform exact calculations to reveal the effects of multi-pair emissions and of noisy, non-unit efficiency, non photon-number resolving detections on the Cauchy-Schwarz parameter, on the second order auto-correlation and cross-correlation functions, and on the visibilities of both Hong-Ou-Mandel and Bell-like interferences. We consider sources producing either two-mode squeezed states or states with a Poissonian photon distribution. The proposed formulas are useful in practice to determine the impacts of multi-pair emissions and dark counts in standard tests used in quantum optics.Comment: 9 pages, 11 figure

SNARE-mediated membrane fusion trajectories derived from force-clamp experiments.

Fusion of lipid bilayers is usually prevented by large energy barriers arising from removal of the hydration shell, formation of highly curved structures, and, eventually, fusion pore widening. Here, we measured the force-dependent lifetime of fusion intermediates using membrane-coated silica spheres attached to cantilevers of an atomic-force microscope. Analysis of time traces obtained from force-clamp experiments allowed us to unequivocally assign steps in deflection of the cantilever to membrane states during the SNARE-mediated fusion with solid-supported lipid bilayers. Force-dependent lifetime distributions of the various intermediate fusion states allowed us to propose the likelihood of different fusion pathways and to assess the main free energy barrier, which was found to be related to passing of the hydration barrier and splaying of lipids to eventually enter either the fully fused state or a long-lived hemifusion intermediate. The results were compared with SNARE mutants that arrest adjacent bilayers in the docked state and membranes in the absence of SNAREs but presence of PEG or calcium. Only with the WT SNARE construct was appreciable merging of both bilayers observed