A rational basis for second-kind Abel integral equations

AbstractA rational basis set is constructed using [1, 1] rational interpolation. The basis is used in a product integration method for solving second-kind Abel integral equations. Criteria are established for determining the amount of bias to be used in the basis set when the integral equation has a nonsmooth solution. Several test problems are solved to illustrate the performance of the approximation method

Property investment considerations in South Africa

This treatise is concerned with property development in its role as an investment rather than as a speculative venture. The property is, therefore, one which is to be held as a rent producing development with the hope of capital appreciation as a hedge against inflation rather than for the realisation of a profit by means of a sale. Careful and thorough investigation must be undertaken by the developer with regard to a possible project. The aspects of such considerations are dealt with in this article as follows : 1. Investigations prior to the acquisition of a property investment. 2. The illustration of certain of the considerations necessary by means of a viability study of a hypothetical case of a block of flats. 3. The post-construction administration of the property

Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation.

The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates.The exact steady-state solution for the nonlinear problem is obtained.Thereduction of the nonlinear initial value problem is carried out by using a similarity transformation.The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented

Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis.

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number

Dynamics of the oxygen, carbon dioxide, and water interaction across the insect spiracle

This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect's spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analysis is carried out in continuous time. The purpose of the research is to determine bounds for the gas volumes and to discuss the complexity and stability of the equilibria. Numerical simulations also demonstrate the dynamics of our model utilizing the new conditions for stability and instability

SUBORDINATION CONDITIONS FOR A CLASS OF NON-BAZILEVIČ TYPE DEFINED BY USING FRACTIONAL Q-CALCULUS OPERATORS

In this article, we introduce and investigate a new class of non-Bazilevič functions with respect to k-symmetric points defined by using fractional q-calculus operators and q-differentiation. Several interesting subordination results are derived for the functions belonging to this class in the open unit disc. Furthermore, we point out some new and known consequences of our main result

Do We Practice What We Preach? A Review of Actual Clinical Practice with Regards to Preconception Care Guidelines

Objectives: To review what past studies have found with regard to existing clinical practices and approaches to providing preconception care. Methods: A literature review between 1966 and September 2005 was performed using Medline. Key words included preconception care, preconception counseling, preconception surveys, practice patterns, pregnancy outcomes, prepregnancy planning, and prepregnancy surveys. Results: There are no current national recommendations that fully address preconception care; as a result, there is wide variability in what is provided clinically under the rubric of preconception care. Conclusions: In 2005, the Centers for Disease Control and Prevention sponsored a national summit regarding preconception care and efforts are underway to develop a uniform set of national recommendations and guidelines for preconception care. Understanding how preconception care is presently incorporated and manifested in current medical practices should help in the development of these national guidelines. Knowing where, how, and why some specific preconception recommendations have been successfully adopted and translated into clinical practice, as well as barriers to implementation of other recommendations or guidelines, is vitally important in developing an overarching set of national guidelines. Ultimately, the success of these recommendations rests on their ability to influence and shape women's health policy

Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional burgers viscoelastic model

A theoretical analysis of magnetohydrodynamic (MHD) incompressible flows of Burger's fluid through a porous medium in a rotating frame of reference is presented. The constitutive model of a Burger's fluid is used based on a fractional calculus formulation. Hydrodynamic slip at the wall (plate) is incorporated and a fractional generalized Darcy model deployed to simulate porous medium drag force effects. Three different cases are considered- namely, flow induced by a general periodic oscillation at a rigid plate, periodic flow in a parallel plate channel and finally Poiseuille flow. In all cases the plate (s) boundary (ies) are electrically-non-conducting and small magnetic Reynolds is assumed, negating magnetic induction effects. The well-posed boundary value problems associated with each case are solved via Fourier transforms. Comparisons are made between the results derived with and without slip conditions. 4 special cases are retrieved from the general fractional Burgers model, viz Newtonian fluid, general Maxwell viscoelastic fluid, generalized Oldroyd-B fluid and the conventional Burger’s viscoelastic model. Extensive interpretation of graphical plots is included. We study explicitly the influence on wall slip on primary and secondary velocity evolution. The model is relevant to MHD rotating energy generators employing rheological working fluids

Components of Lens Power That Regulate Surface Principal Powers and Relative Meridians Independently

Paraxial light rays incident in air on alternate refracting surfaces of a thick lens can yield complementary powers. This paper aims to test when these powers are invariant as surface refractive powers interchange in the expression. We solve for relevant surface powers. Potential anticommutators yield the nature of surface principal refractions along obliquely crossing perpendicular meridians; commutators yield meridians that align with those on the next surface. An invariant power component orients relative meridians or the nature of the matrix power on each noncylindrical surface demands that the other component varies. Another component of lens power aligns relative meridian positions for distinct principal powers. Interchanging surface power matrices affects this component. A symmetric lens power results if perpendicular principal meridians are associated with meridians on an opposite rotationally symmetric surface. For thin lenses, meridian alignment may be waived. An astigmatic contact lens can be specified by symmetric power despite having separated surfaces