Stokes phenomenon and matched asymptotic expansions

This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions

An integrable shallow water equation with peaked solitons

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques

Analytic linearization of nonlinear perturbations of Fuchsian systems

Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the case when the linear part has commuting monodromy, and the eigenvalues have positive real parts, there exists a unique correction function of the nonlinear part so that the corrected system becomes analytically linearizable

Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we \emph{reduce} the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is \emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the system behavior by studying the system's Lie symmetrie

Continuation treatment of major depressive disorder: is there a case for duloxetine?

Duloxetine is a serotonin–noradrenaline reuptake inhibitor with established efficacy for the short-term treatment of major depressive disorder. Efficacy in continuation treatment (greater than six months of continuous treatment) has been established from both open and placebo-controlled relapse prevention and comparative studies. Seven published studies were available for review and showed that in both younger and older populations (aged more than 65 years) the acute efficacy of duloxetine was maintained for up to one year. Response to treatment was based on accepted criteria for remission of depression and in continuation studies remission rates were greater than 70%. Comparative studies showed that duloxetine was superior to placebo and comparable to paroxetine and escitalopram in relapse prevention. Importantly a study of duloxetine in patients prone to relapse of major depressive disorder showed that the medication was more effective than placebo in this difficult to treat population. Side effects of duloxetine during continuation treatment were predictable on the basis of the known pharmacology of the drug. In particular there were no significant life-threatening events which emerged with continued use of the medication. On the other hand vigilance is required since the data base on which to judge very rare events is limited by the relatively low exposure to the drug. Duloxetine has established both efficacy and safety for continuation treatment but its place as a first-line treatment of relapse prevention requires further experience. In particular further comparative studies against established agents would be useful in deciding the place of duloxetine in therapy

Duloxetine in the treatment of generalized anxiety disorder

Duloxetine, a medication with effects on both serotonin and noradrenaline transporter molecules, has recently been approved for the treatment of generalized anxiety disorder. The evidence for its efficacy lies in a limited number of double blind, placebo controlled comparisons. Statistically significant improvements in the Hamilton Anxiety Rating Scale from baseline were demonstrated in all studies at doses of 60 to 120 mg per day. The significance of such changes in terms of clinical improvements compared to placebo is less certain, particularly when the effect size of the change is calculated. In comparative trials with venlafaxine, duloxetine was as effective in providing relief of anxiety symptoms. In addition to improvements in clinical symptoms duloxetine has also been associated with restitution of role function as measured by disability scales. Duloxetine use is associated with nausea, dizziness, dry mouth, constipation, insomnia, somnolence, hyperhidrosis, decreased libido and vomiting. These treatment emergent side effects were generally of mild to moderate severity and were tolerated over time. Using a tapered withdrawal schedule over two weeks in the clinical trials, duloxetine was associated with only a mild withdrawal syndrome in up to about 30% of patients compared to about 17% in placebo treated patients. Duloxetine in doses of up to 200 mg twice daily did not prolong the QTc interval in healthy volunteers. Like other agents with dual neurotransmitter actions duloxetine reduces the symptoms of generalized anxiety disorder in short term treatments. Further evidence for its efficacy and safety in long term treatment is required

On a Order Reduction Theorem in the Lagrangian Formalism

We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.Comment: 9 pages, LATEX, no figures; appear in Il Nuovo Cimento

Hawking radiation of massive modes and undulations

We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in the supersonic region, which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what was recently found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime.Comment: 37 pages, 8 figures, published versio

The general dielectric tensor for bi-kappa magnetized plasmas

In this paper we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.Comment: Accepted for publication in Physics of Plasma

Nearsightedness of Electronic Matter in One Dimension

The concept of nearsightedeness of electronic matter (NEM) was introduced by W. Kohn in 1996 as the physical principal underlining Yang's electronic structure alghoritm of divide and conquer. It describes the fact that, for fixed chemical potential, local electronic properties at a point $r$, like the density $n(r)$, depend significantly on the external potential $v$ only at nearby points. Changes $\Delta v$ of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$, have {\it limited} effects on local electronic properties, which tend to zero as function of $\textsf{R}$. This remains true even if the changes in the external potential completely surrounds the point $r$. NEM can be quantitatively characterized by the nearsightedness range, $\textsf{\textsf{R}}(r,\Delta n)$, defined as the smallest distance from $r$, beyond which {\it any} change of the external potential produces a density change, at $r$, smaller than a given $\Delta n$. The present paper gives a detailed analysis of NEM for periodic metals and insulators in 1D and includes sharp, explicit estimates of the nearsightedness range. Since NEM involves arbitrary changes of the external potential, strong, even qualitative changes can occur in the system, such as the discretization of energy bands or the complete filling of the insulating gap of an insulator with continuum spectrum. In spite of such drastic changes, we show that $\Delta v$ has only a limited effect on the density, which can be quantified in terms of simple parameters of the unperturbed system.Comment: 10 pages, 9 figure