Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Differential phosphorylation, desensitization, and internalization of α1A-adrenoceptors activated by norepinephrine and oxymetazoline

Loss of response on repetitive drug exposure (i.e., tachyphylaxis) is a particular problem for the vasoconstrictor effects of medications containing oxymetazoline (OXY), an α1-adrenoceptor (AR) agonist of the imidazoline class. One cause of tachyphylaxis is receptor desensitization, usually accompanied by phosphorylation and internalization. It is well established that a1A-ARs are less phosphorylated, desensitized, and internalized on exposure to the phenethylamines norepinephrine (NE), epinephrine, or phenylephrine (PE) than are the a1B and a1D subtypes. However, here we show in human embryonic kidney-293 cells that the low-efficacy agonist OXY induces G protein-coupled receptor kinase 2-dependent a1A-AR phosphorylation, followed by rapid desensitization and internalization (∼40% internalization after 5 minutes of stimulation), whereas phosphorylation of α1A-ARs exposed to NE depends to a large extent on protein kinase C activity and is not followed by desensitization, and the receptors undergo delayed internalization (∼35% after 60 minutes of stimulation). Native α1A-ARs from rat tail artery and vas deferens are also desensitized by OXY, but not by NE or PE, indicating that thisproperty of OXY is not limited to recombinant receptors expressed in cell systems. The results of the present study are clearly indicative of agonist-directed a1A-AR regulation. OXY shows functional selectivity relative to NE and PE at a1A-ARs, leading to significant receptor desensitization and internalization, which is important in view of the therapeutic vasoconstrictor effects of this drug and the varied biologic process regulated by α1A-ARs. Copyright © 2013 by The American Society for Pharmacology and Experimental Therapeutics.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

General method for reducing the two-body Dirac equation

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed. © 1992 American Institute of Physics.