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An algorithm is proposed for obtaining global solutions of the biconfluent Heun equation, which appears when dealing with a variety of physical problems. The procedure, which provides algebraic expressions of the solutions in the form of convergent series or asymptotic expansions, lies on the determination of the connection factors relating the solutions about the regular singular point at the origin and the irregular one at infinity. The algorithm is illustrated by examples. [ABSTRACT FROM AUTHOR]

Solar activity (SA) oscillations over the past millennia are analyzed and extrapolated based on reconstructed solar-related records. Here, simple recurrent models of SA signal are applied and tested. The consequent results strongly suggest: (a) the existence of multi-millennial (~ 9500 years) scale solar oscillations, and (b) their persistence, over at least the last glacial-interglacial cycle. This empirical modelling of solar recurrent oscillations has also provided a consequent multi-millennial-scale experimental forecast, suggesting a solar decreasing trend toward Grand (Super) Minimum conditions for the upcoming period, AD2050-2250 (AD 3750-4450). Also, a recurrent linear influence of solar variation on continental tropical climate (CTC) has been assessed for the last 20 kyr, and extrapolated for the next centuries. Taking into account the importance of these estimated SA scenarios a comparison is made with other SA forecasts, and their possible associated astronomical forcing and influences on past and future CTC discussed. [ABSTRACT FROM AUTHOR]

The Schrödinger equation with a Lennard-Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the connection factors between Floquet and Thomé solutions. The energies of the bound states result as zeros of a function defined by a convergent series whose successive terms are calculated by means of recurrence relations. The procedure gives also the wave functions expressed either as a linear combination of two Laurent expansions, at moderate distances, or as an asymptotic expansion, near the singular points. A table of the critical intensities of the potential, for which a new bound state (of zero energy) appears, is also given. [ABSTRACT FROM AUTHOR]

Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schrödinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A complete discussion of the scattering function reveals the existence of Gamow (decaying) states and of resonances. [ABSTRACT FROM AUTHOR]

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The P2Y14 receptor is a relatively broadly expressed G protein-coupled receptor that is prominently associated with immune and inflammatory cells as well as with many epithelia. This receptor historically was thought to be activated selectively by UDP-glucose and other UDP-sugars. However, UDP is also a very potent agonist of this receptor, and may prove to be one of its most important cognate activators. [ABSTRACT FROM AUTHOR]

The asymptotic expansion of the hypergeometric function [sub 2]F[sub 1] (a, b;c;z/b) in the case of quasiconfluence, i.e., for b → ∞ is revised. A very simple expansion, in terms of a semiasymptotic sequence of polynomials, is presented. Some properties of those polynomials are discussed. [ABSTRACT FROM AUTHOR]

The dependence of the Whittaker function M[SUBκ, μ] (z) on the parameter κ is considered. A convergent expansion in ascending powers and an asymptotic expansion in descending powers of κ are discussed. Some properties of the coefficients of the convergent expansion are shown. [ABSTRACT FROM AUTHOR]

The possibility of expanding the S matrix in a multiple-reflection series (Debye expansion) is shown for an arbitrary-shape short-range potential. Ambiguity in the definition of outgoing and incoming waves inside the potential leads to an infinity of expansions. These are analyzed in a simple example (square well or barrier) in order to characterize the correct choice of outgoing and incoming waves. [ABSTRACT FROM AUTHOR]

The possibility of confining a quantum particle in an optical potential, the imaginary part of which would be related to the existence of inelastic reaction channels coupled to the elastic one, is considered. Pure imaginary potentials of various (constant, linear, and parabolic) radial shapes are studied. The numerical dependence of the energies and mean-lives of the confined states is explicitly shown. Analytical expressions for such dependence are also given in some cases. [ABSTRACT FROM AUTHOR]

Purpose To analyze the morphological changes of corneal nerves and its influence on corneal epithelial wound healing in a lacrimodeficient dry eye model in the guinea‐pig. Methods Corneal nerve architecture and the rate of corneal epithelial wound healing were studied in guinea‐pigs to whom the main lacrimal gland was removed 4 weeks before (dry eye) and in control animals. Eyes were fixed, cryoprotected and incubated with neuronal class III Beta‐tubulin antibody. Epithelial migration rate (EMR) and estimated time of healing (ETH) were calculated for 2mm‐diameter epithelial corneal debridations stained with fluorescein, photographed regularly until complete closure and analyzed with image processing software. Results Density (16±6 vs 27±11 nerves/mm2) and length (115±45 vs 186±74 µm) of subbasal nerves decreased significantly in dry eye. Subbasal nerves were less branched and tortuous. Epithelial nerve terminals were also reduced. EMR decreased significantly (63±4 vs 110±1 µm/h) and ETH increased significantly (38.6±1.8 vs 20.1±0.1 h) in dry eye. Conclusion The morphological appearance and the decreased density, length and branches of corneal subbasal nerves are suggestive of corneal nerve degeneration at 4 weeks after lacrimal gland removal. Lacrimodeficient eyes presented also a slowing‐down in corneal epithelial wound healing suggesting an early trophic defect consecutive to nerve damage. (Supported by: SAF2008‐00529, CSD2007‐00023, BFU2008‐04425, BFU2009‐07793 and RETICS RD07/0062/0012 from Ministerio de Ciencia e Innovación, Spain, and the Leonardo da Vinci Lifelong Learning Program.) [ABSTRACT FROM AUTHOR]