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- J B Mcleod, P J Olver
- 1983

A completely integrable partial differential equation is one which has a Lax representation, or, more precisely, can be solved via a linear integral equation of Gel'fand-Levitan type, the classic example being the Korteweg-de Vries equation. An ordinary differential equation is of Painlev type if the only singularities of its solutions in the complex plane… (More)

The equation studied is u 00 + n1 r u 0 + "u u 0 = 0; with boundary conditions u (1) = 0; u (1) = 1. This model equation has been studied by many authors since it was introduced in the 1950s by P. A. Lagerstrom. We use an elementary approach to show that there is an innnite series solution which is uniformly convergent on 1 r < 1: The rst few terms are… (More)

The paper studies the Bardeen{Cooper{Schrieeer energy gap equation at nite temperatures. When the kernel is positive representing a phonon-dominant phase in a superconductor, the existence and uniqueness of a gap solution is established in a class which contains solutions obtainable from bounded domain approximations. The critical temperatures that… (More)

Serum samples and sociodemographic data were obtained from 1,209 Ohio residents. West Nile virus immunoglobulin M (IgM) and IgG antibodies were detected by enzyme-linked immunosorbent assay and confirmed. Children were 4.5 times more likely to become infected yet 110 times less likely to have neuroinvasive disease develop.

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical motion. Nanoscale motors like kinesins tow organelles and other cargo on microtubules or filaments, have a role separating the mitotic spindle during the cell cycle, and perform many other functions. The simplest description gives rise… (More)

Human West Nile virus (WNV) infection was first detected in Cuyahoga county, Ohio, USA, in 2002. During that year's extensive epidemic/epizootic among non-immune human and bird populations, the county experienced 155 cases of severe human West Nile neurological disease (WNND, incidence = 11.1 cases/100,000), with 11 fatalities. Structured serosurveys… (More)

- J.-E Eckmann, R St~nt~0r, J B Mcleod
- 2004

In his book "Th6orie des Perturbations et M6thodes Asymptotiques" V.P.MAsLOV has given an ingenious approximation method which overcomes certain well known difficulties in the classical WKB approach. One of these difficulties is connected with the singularities of the amplitudes of the wave function which appear at turning points of a classical motion.… (More)

Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel K(ξ, η) = (ξη) λ with λ ∈ (0, 1/2). It is known that such self-similar solutions g(x) satisfy that x −1+2λ g(x) is bounded above and below as x → 0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled… (More)