This paper studies the scattering matrix S(E;~) of the problem −~ψ(x) + V (x)ψ(x) = Eψ(x) for positive potentials V ∈ C(R) with inverse square behavior as x→ ±∞. It is shown that each entry takes the form Sij(E;~) = S (0) ij (E;~)(1 + ~σij(E;~)) where S (0) ij (E;~) is the WKB approximation relative to the modified potential V (x) + ~ 2 4 〈x〉−2 and the correction terms σij satisfy |∂ k Eσij (E;...

We correct the proof of Theorem 6 in the letter ‘‘Fixed point theory for cyclic weak φ-contraction’’ [E. Karapınar, Fixed point theory for cyclic weak φ-contraction, Appl. Math. Lett. 24 (6) (2011) 822–825]. © 2010 Elsevier Ltd. All rights reserved.

There exist (C0) semigroups Tx(i), T2(t) on Hubert space with the following properties: 7f has a bounded generator and is uniformly bounded, but is not similar to a contraction semigroup. T2 is uniformly bounded, and there exists no scalar a such that e~"'T2(t) is similar to a contraction semigroup.

BACKGROUND The relationship between regional and global left ventricular function has not been evaluated. The present study aimed to assess whether regional myocardial contraction and relaxation reflect global left ventricular systolic and early diastolic function, respectively. METHODS AND RESULTS The study involved 45 patients with coronary artery disease (CAD). Conventional echocardiograph...

It is well known that Zk,m(t) is related to the virial coefficients of a quantum system of obstacles K at inverse temperature t. For example, G. E. Uhlenbeck [15] calculated the asymptotic behaviour of Zk,m(t) as t → ∞ in the special case where k = 1, m = 3, and K is a ball. I. McGillivray [14] obtained the full asymptotic series as t → ∞ for k = 1, m ≥ 3, and K an arbitrary, non-polar compact ...

We prove the time-asymptotic stability of composite waves consisting superposition a viscous shock and rarefaction for one-dimensional compressible barotropic Navier-Stokes equations. Our result solves long-standing problem first mentioned in 1986 by Matsumura Nishihara [28]. The same authors introduced it officially as an open 1992 [29] was again described very challenging 2018 survey paper [2...

We address the question of how a neuron integrates excitatory (E) and inhibitory (I ) synaptic inputs from different dendritic sites. For an idealized neuron model with an unbranched dendritic cable, we construct its Green’s function and carry out an asymptotic analysis to obtain its solutions. Using these asymptotic solutions, in the presence of E and I inputs, we can successfully reveal the u...

A quantum system S interacts in a successive way with elements E of a chain of identical independent quantum subsystems. Each interaction lasts for a duration τ and is governed by a fixed coupling between S and E . We show that the system, initially in any state close to a reference state, approaches a repeated interaction asymptotic state in the limit of large times. This state is τ–periodic i...

We evaluate the next-to-leading order radiative corrections to a process in the massless Schwinger model that is the analogue of the ee inclusive annihilation into hadrons process in QCD. We then carry out an asymptotic expansion of the calculable exact result and find that it agrees with the perturbative answer. However, we also find that higher orders in the asymptotic expansion involve terms...