A de Montessus de Ballore theorem for best rational approximation over the whole plane

AbstractWe prove a de Montessus de Ballore type theorem for rational functions Rnq of type (n, q) formed by best approximation over the whole plane to functions f(z) meromorphic in the plane with exactly q poles. This resolves a question raised by Lubinsky and Shisha (J. Approx. Theory 36 (1982), 277–293)

An equation admitting infinite true contact transformations

AbstractThe linear wave equation is shown to possess the unique property that if wn is a true contact transformation admitted by the wave equation, i.e., wn is not linear in the first derivatives of the dependent variable, then so is ∑nwn. We comment of the physical implications

An investigation into the accuracy of orbital X-rays, when using CR, in detecting ferromagnetic intraocular foreign bodies

Purpose The aim of this study is to determine the accuracy of orbital X-rays, when using computed radiography (CR), in detecting ferromagnetic intra-ocular foreign bodies (IOFBs) prior to magnetic resonance imaging (MRI). Methods A total of 64 orbital X-rays of an anthropomorphic head phantom were acquired using CR. For each image 1, 2, 3, or 4, large, medium, or small IOFBs were fixed to the anterior surface of the left or right orbit. Each of the acquired images with an IOFB was duplicated in order to increase the sample size. A further 16 normal images (no IOFB) were also included in the sample. Observers were invited to review the images and were permitted to manually magnify and window the images to detect any IOFBs present on each image. Results 10 observers (4 radiographers; 4 reporting radiographers; 2 consultant radiologists) independently reviewed the images. The mean (SD) sensitivity and specificity were 72.1% (7.3%) and 99.2% (0.8%) for all observers, respectively. According to size the sensitivity in detecting small, medium and large IOFB were 46%, 76% and 93%, respectively. According to location, the lower lateral quadrants had the lowest sensitivity (53%) whereas the upper medial had the greatest (88%). Conclusion Findings from this study using CR support previous conclusions that conventional X-rays fail to detect metallic IOFBs in all cases. Diagnostic performance is governed by IOFB size and location

Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs

Symmetries of the fundamental first integrals for scalar second-order ordinary differential equations (ODEs) which are linear or linearizable by point transformations have already been obtained. Firstly we show how one can determine the relationship between the symmetries and the first integrals of linear or linearizable scalar ODEs of order two. Secondly, a complete classification of point symmetries of first integrals of such linear ODEs is studied. As a consequence, we provide a counting theorem for the point symmetries of first integrals of scalar linearizable second-order ODEs. We show that there exists the 0-, 1-, 2-, or 3-point symmetry cases. It is shown that the maximal algebra case is unique

Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a) prescribed surface temperature (PST) and (b) prescribed heat flux (PHF). The effect of involved parameters on velocity and temperature is investigated

Constructing a Space from the System of Geodesic Equations

Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from the Christoffel symbols. The procedure is extended for determining if a second order quadratically semi-linear system can be expressed as a system of geodesic equations, provided it has terms only quadratic in the first derivative apart from the second derivative term. A computer code has been developed for dealing with larger systems of geodesic equations

Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM.

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics

Endoscope effects on MHD peristaltic flow of a power-law fluid

To understand the influence of an inserted endoscope and magnetohydrodynamic (MHD) power-law fluid on peristaltic motion, an attempt has been made for flow through tubes. The magnetic field of uniform strength is applied in the transverse direction to the flow. The analysis has been performed under long wavelength at low-Reynolds number assumption. The velocity fields and axial pressure gradient have been evaluated analytically. Numerical results are also presented and discussed

On generalized Carleson operators of periodic wavelet packet expansions

Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied