Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

In vivo and in vitro assessment of mirtazapine pharmacokinetics in cats with liver disease.

BackgroundLiver disease (LD) prolongs mirtazapine half-life in humans, but it is unknown if this occurs in cats with LD and healthy cats.Hypothesis/objectivesTo determine pharmacokinetics of administered orally mirtazapine in vivo and in vitro (liver microsomes) in cats with LD and healthy cats.AnimalsEleven LD and 11 age-matched control cats.MethodsCase-control study. Serum was obtained 1 and 4 hours (22 cats) and 24 hours (14 cats) after oral administration of 1.88 mg mirtazapine. Mirtazapine concentrations were measured by liquid chromatography with tandem mass spectrometry. Drug exposure and half-life were predicted using limited sampling modeling and estimated using noncompartmental methods. in vitro mirtazapine pharmacokinetics were assessed using liver microsomes from 3 LD cats and 4 cats without LD.ResultsThere was a significant difference in time to maximum serum concentration between LD cats and control cats (median [range]: 4 [1-4] hours versus 1 [1-4] hours; P = .03). The calculated half-life of LD cats was significantly prolonged compared to controls (median [range]: 13.8 [7.9-61.4] hours versus 7.4 [6.7-9.1] hours; P < .002). Mirtazapine half-life was correlated with ALT (P = .002; r = .76), ALP (P < .0001; r = .89), and total bilirubin (P = .0008; r = .81). The rate of loss of mirtazapine was significantly different between microsomes of LD cats (-0.0022 min-1 , CI: -0.0050 to 0.00054 min-1 ) and cats without LD (0.01849 min-1 , CI: -0.025 to -0.012 min-1 ; P = .002).Conclusions and clinical importanceCats with LD might require less frequent administration of mirtazapine than normal cats

The mean magnetic field of the sun: Observations at Stanford

A solar telescope was built at Stanford University to study the organization and evolution of large-scale solar magnetic fields and velocities. The observations are made using a Babcock-type magnetograph which is connected to a 22.9 m vertical Littrow spectrograph. Sun-as-a-star integrated light measurements of the mean solar magnetic field were made daily since May 1975. The typical mean field magnitude is about 0.15 gauss with typical measurement error less than 0.05 gauss. The mean field polarity pattern is essentially identical to the interplanetary magnetic field sector structure (seen near the earth with a 4 day lag). The differences in the observed structures can be understood in terms of a warped current sheet model

Spectra generated by a confined softcore Coulomb potential

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator potential terms, and also through `hard confinement' by means of an impenetrable spherical box. A byproduct of this work is the construction of polynomial solutions for a number of linear differential equations with polynomial coefficients, along with the necessary and sufficient conditions for the existence of such solutions. Very accurate approximate solutions for the general problem with arbitrary potential parameters are found by use of the asymptotic iteration method.Comment: 17 pages, 2 figure

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Immunocytochemical localization of the neuron-specific form of the c-src gene product, pp60c-src(+), in rat brain

Neurons express high levels of a variant form of the c-src gene product, denoted pp60c-src(+), which contains a 6 amino acid insert in the amino-terminal half of the c-src protein. We have determined the localization of pp60c-src(+) in neurons using an affinity-purified anti-peptide antibody, referred to as affi-SB12, that exclusively recognizes this neuron-specific form of the c-src gene product. Using affi-SB12, we examined the distribution of pp60c-src(+) by immunoperoxidase staining of sections through adult rat brains, pp60c-src(+) was widely distributed in rat brain and appeared to be differentially expressed in subpopulations of neurons. The majority of immunoreactive neurons was found in the mesencephalon, cerebellum, pons, and medulla. Telencephalic structures that contained substantial populations of pp60c-src(+)-immunoreactive neurons included layer V of the cerebral cortex and the ventral pallidum. Within individual neurons, pp60c-src(+) immunoreactivity was localized to the cell soma and dendritic processes, while labeling of axons and nerve terminals (puncta) was not as readily detected. Dense accumulations of immunoreactive axons were rare, being most prominent in portions of the inferior and superior olive, and in the spinal trigeminal nucleus. While the regional distribution of pp60c-src(+) immunoreactivity does not correlate with any specific neuronal cell type or first messenger system, this unique pattern of expression of pp60c-src(+) suggests the existence of a previously uncharacterized functional organization within the brain. Furthermore, the localization of this neuron-specific tyrosine kinase in functionally important areas of the nerve cell, namely, dendritic processes, axons, and nerve terminals, suggests that pp60c-src(+) may regulate pleiotropic functions in specific classes of neurons in the adult central nervous system

A Nonpolar Blueberry Fraction Blunts NADPH Oxidase Activation in Neuronal Cells Exposed to Tumor Necrosis Factor-α

Inflammation and oxidative stress are key to the progressive neuronal degeneration common to chronic pathologies, traumatic injuries, and aging processes in the CNS. The proinflammatory cytokine tumor necrosis factor-alpha (TNF-α) orchestrates cellular stress by stimulating the production and release of neurotoxic mediators including reactive oxygen species (ROS). NADPH oxidases (NOX), ubiquitously expressed in all cells, have recently emerged as pivotal ROS sources in aging and disease. We demonstrated the presence of potent NOX inhibitors in wild Alaska bog blueberries partitioning discretely into a nonpolar fraction with minimal antioxidant capacity and largely devoid of polyphenols. Incubation of SH-SY5Y human neuroblastoma cells with nonpolar blueberry fractions obstructed the coalescing of lipid rafts into large domains disrupting NOX assembly therein and abolishing ROS production characteristic for TNF-α exposure. These findings illuminate nutrition-derived lipid raft modulation as a novel therapeutic approach to blunt inflammatory and oxidative stress in the aging or diseased CNS

Clan Properties in Parton Showers

By considering clans as genuine elementary subprocesses, i.e., intermediate parton sources in the Simplified Parton Shower model, a generalized version of this model is defined. It predicts analytically clan properties at parton level in agreement with the general trends observed experimentally at hadronic level and in Monte Carlo simulations both at partonic and hadronic level. In particular the model shows a linear rising in rapidity of the average number of clans at fixed energy of the initial parton and its subsequent bending for rapidity intervals at the border of phase space, and approximate energy independence of the average number of clans in fixed rapidity intervals. The energy independence becomes stricter by properly normalizing the average number of clans.Comment: (27 pages in Plain TeX plus 10 Postscript Figures, all compressed via uufiles) DFTT 7/9

Mechanism of Disease:Recessive ADAMTSL4 Mutations and Craniosynostosis with Ectopia Lentis

Craniosynostosis, the premature fusion of the calvarial bones, has numerous etiologies. Among them, several involve mutations in genes related to the TGFb signaling pathway, a critical molecular mediator of human development. These TGFb pathway-associated craniosynostosis syndromes include Loeys-Dietz syndrome (LDS) and Shprintzen-Goldberg syndrome (SGS). LDS and SGS have many similarities common to fibrillinopathies, specifically Marfan syndrome (MFS), which is caused by mutations in FBN1. Historically discriminating features of MFS from LDS and SGS are (1) the presence of ectopia lentis (the subluxation/dislocation of the ocular lens) and (2) the absence of craniosynostosis. Curiously, several instances of a seemingly novel syndrome involving only craniosynostosis and ectopia lentis have recently been reported to be caused by recessive mutations in ADAMTSL4, a poorly characterized gene as of yet. Here, we report on two new cases of craniosynostosis with ectopia lentis, each harboring recessive mutations in ADAMTSL4. We also discuss a proposed mechanism for the relationship between ADAMTSL4, FBN1, and TGFb pathway-related syndromes.</p