Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out…
Mathematical Modelling and Industrial Mathematics
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The Conjugate Gradient Method is the most prominent iterative method for solving sparse systems of linear equations. Unfortunately, many textbook treatments of the topic are written with neither illustrations nor intuition, and their victims can be…

We are developing a dual panel breastdedicated PET system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA3 ASICs. This paper shows that the coincidence…

Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices.

Introduction This is a concise summary of recommended features in LATEX and a couple of extension packages for writing math formulas. Readers needing greater depth of detail are referred to the sources listed in the bibliography, especially…

Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady…

A precise definition of the basic reproduction number, ??? 0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if ???…

Despite application of cryogen spray (CS) precooling, customary treatment of port wine stain (PWS) birthmarks with a single laser pulse does not result in complete lesion blanching for a majority of patients. One obvious reason is nonselective…

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and timedependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal…

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other selforganizing systems. Ordinarily, the…

The term immersed boundary methodwas first used in reference to a method de veloped by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this methodwas that the entire simulationwas carried out on…

Creating amesh is the first step in a wide range of applications, including scientific comput ing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and…

The recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signaltonoise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important…

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement…

Muchacclaimed, this book is now available in paperback. It provides an analytical framework for evaluating public health measures aimed at eradicating or controlling communicable diseases such as malaria, measles, river blindness, sleeping…

In this series of lectures, we describe the analytic and computational foundations of fast multipole methods, as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the…

We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an /2orthogonal…

This paper describes mathematical and software developments for a suite of programs for solving ordinary differential equations in Matlab.

Jacobianfree NewtonKrylov (JFNK) methods are synergistic combinations of Newtontype methods for superlinearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations. The link between the…

The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of…
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