Deformation of the J-Matrix Method of Scattering

Using the tools of the J-matrix method we show that truncating the background interaction in the reference Hamiltonian leads to a significant loss of scattering information. Moreover, this loss is not recoverable by numerical means even if the truncated region in configuration or function space were to be extended substantially. We demonstrate this by calculating the nonrelativistic scattering for a system whose reference Hamiltonian is enhanced by one-parameter linear deformation as a clear and simple example for the background interaction to be truncated. This will result in an additional phase shift component that could be used to account for persistent deviations in the scattering data from those obtained by proposed potential models. The compensating phase shift component, which is obtained by taking the full effect of the deformation in the H ₀-problem, is confined to low energy regions whose extent depends on the value of the deformation parameter. Higher order deformations are briefly discussed and illustrated in a simple example. We also show that the deformation is equivalent to the addition of a separable potential, with Laguerre-type form factors, to the reference Hamiltonian and that the coupling parameters of the potential correspond to the deformation parameters.     

Femtosecond vibrational dynamics of self-trapping in a quasi-one-dimensional system

We have directly time resolved the lattice motions associated with the formation of the self-trapped exciton in the quasi-one-dimensional system [Pt(en)(2)] [Pt(en)2Br2];(PF6)(4) ( en = ethylene-diamine, C2H8N2), using femtosecond impulsive excitation techniques. A strongly damped, low-frequency wave packet modulation at approximately 110 cm(-1) accompanies the formation of the self-trapped exciton on a approximately 200 fs time scale following excitation of the intervalence charge-transfer transition. Coherent oscillations at the ground state vibrational frequency and its harmonics are also detected.     

Spectral Asymptotics for Higher-Order Ordinary Differential Equations

This paper gives one-term componentwise asymptotics for theM and spectral matrices of a self-adjoint realisation of aneven-order ordinary differential expression. The underlyinginterval is assumed to have at least one regular endpoint, andthe boundary conditions are supposed to be separated. Furthermore,the weight function and the reciprocal of the highest-ordercoefficient are supposed to be of regular variation at the regularendpoint, in the sense of Bingham, Goldie and Teugels. 1991Mathematics Subject Classification: 34B24, 34E05.     

TRPM5-expressing microvillous cells in the main olfactory epithelium

Background  

The main olfactory epithelium (MOE) in the nasal cavity detects a variety of air borne molecules that provide information regarding the presence of food, predators and other relevant social and environmental factors. Within the epithelium are ciliated sensory neurons, supporting cells, basal cells and microvillous cells, each of which is distinct in morphology and function. Arguably, the least understood, are the microvillous cells, a population of cells that are small in number and whose function is not known. We previously found that in a mouse strain in which the TRPM5 promoter drives expression of the green fluorescent protein (GFP), a population of ciliated olfactory sensory neurons (OSNs), as well as a population of cells displaying microvilli-like structures is labeled. Here we examined the morphology and immunocytochemical properties of these microvillous-like cells using immunocytochemical methods.     

Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters

We present a formulation of quantum mechanics based on the theory of orthogonal polynomials.The wavefunction is expanded over a complete set of square integrable basis where the expansion coefficients are orthogonal polynomials in the energy and physical parameters. Information about the corresponding physical systems(both structural and dynamical) are derived from the properties of these polynomials. We demonstrate that an advantage of this formulation is that the class of exactly solvable quantum mechanical problems becomes larger than in the conventional formulation(see, for example, table 3 in the text). We limit our investigation in this work to the Askey classification scheme of hypergeometric orthogonal polynomials and focus on the Wilson polynomial and two of its limiting cases(the Meixner–Pollaczek and continuous dual Hahn polynomials). Nonetheless, the formulation is amenable to other classes of orthogonal polynomials.     

An adeno-associated viral vector transduces the rat hypothalamus and amygdala more efficient than a lentiviral vector

Background  

This study compared the transduction efficiencies of an adeno-associated viral (AAV) vector, which was pseudotyped with an AAV1 capsid and encoded the green fluorescent protein (GFP), with a lentiviral (LV) vector, which was pseudotyped with a VSV-G envelop and encoded the discosoma red fluorescent protein (dsRed), to investigate which viral vector transduced the lateral hypothalamus or the amygdala more efficiently. The LV-dsRed and AAV1-GFP vector were mixed and injected into the lateral hypothalamus or into the amygdala of adult rats. The titers that were injected were 1 × 10⁸ or 1 × 10⁹ genomic copies of AAV1-GFP and 1 × 10⁵ transducing units of LV-dsRed.     

Series Solution of a Ten-Parameter Second-Order Differential Equation with Three Regular Singularities and One Irregular Singularity

Theoretical and Mathematical Physics - We consider a ten-parameter second-order ordinary linear differential equation with four singular points. Three of them are finite and regular, while the...     

Four-Parameter 1/<Emphasis Type="Italic">r</Emphasis><Superscript>2</Superscript> Singular Short-Range Potential with Rich Bound States and A Resonance Spectrum

We use the tridiagonal representation approach to enlarge the class of exactly solvable quantum systems. For this, we use a square-integrable basis in which the matrix representation of the wave operator is tridiagonal. In this case, the wave equation becomes a three-term recurrence relation for the expansion coefficients of the wave function with a solution in terms of orthogonal polynomials that is equivalent to a solution of the original problem. We obtain S-wave bound states for a new four-parameter potential with a 1/r² singularity but short-range, which has an elaborate configuration structure and rich spectral properties. A particle scattered by this potential must overcome a barrier and can then be trapped in the potential valley in a resonance or bound state. Using complex rotation, we demonstrate the rich spectral properties of the potential in the case of a nonzero angular momentum and show how this structure varies with the parameters of the potential.     

Dirac Equation with Coupling to 1/<Emphasis Type="Italic">r</Emphasis> Singular Vector Potentials for all Angular Momenta

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r ² term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials.