Ill PREFACE This Memorandum is part of RAND's continuing search for new ways of utilizing the modern digital computer. The authors present a method for numerically Integrating nonlinear partial differential integral equations, which occur In such fields as radiative transfer and mathematical biology. The method Is then specifically applied to solving a basic equation of transport In a spherical...

is considered. Stationary traveling waves of above equation are proved to exist when f(u) is symmetric and g(u) is antisymmetric about u = 0. Solutions of initial value problems tends to almost piecewise constant functions within O(1) time. The almost constant pieces are separated by sharp interior layers, called fronts. The motion of these fronts are studied by asymptotic expansion. The equati...

In 1930 Moore and Van Slyke (1) reviewed the various physical measurements, refractometric and others, that might serve as measures of the protein concentration of plasma, and concluded that specific gravity was the most reliable if application was required to pathological as well as normal plasmas. For plasma of nephritic patients they found that the relation between protein concentration and ...

It is shown that the celebrated Menelaus relation, Hirota–Miwa bilinear equation for KP hierarchy and Fay's trisecant formula similar to WDVV are associativity conditions structure constants of certain three-dimensional quasi-algebra.

The classic Beverton-Holt (discrete logistic) difference equation, which arises in population dynamics, has a globally asymptotically stable equilibrium (for positive initial conditions) if its coefficients are constants. If the coefficients change in time, then the equation becomes nonautonomous and the asymptotic dynamicsmight not be as simple. One reason the coefficients can change in time i...

Recent time-intensity data by Rushton (1932) on the sciatic nerve of the frog are shown to provide additional support to the writer's suggestion (1932, a) that integrals of the equation See PDF for Equation where V is the applied voltage, p is the local excitatory process and K and k are constants adequately represent the just effective direct current stimuli when the threshold value of p is ma...

The Stern equation, a combination of the Langmuir adsorption isotherm, the Boltzmann relation, and the Grahame equation from the theory of the diffuse double layer, provides a simple theoretical framework for describing the adsorption of charged molecules to surfaces. The ability of this equation to describe the adsorption of divalent cations to membranes containing brain phosphatidylserine (PS...

In this paper we derive a number of exact solutions of the discrete equation xn+1xn−1 + xn(xn+1 + xn−1) = −2znxn + (η − 3δ − z n)xn + μ (xn + zn + γ)(xn + zn − γ) , (1) where zn = nδ and η, δ, μ and γ are constants. In an appropriate limit (1) reduces to the fourth Painlevé (PIV) equation dw dz2 = 1 2w ( dw dz )2 + 32w 3 + 4zw + 2(z − α)w + β w , (2) where α and β are constants and (1) is commo...

In this paper, we present the numerical investigations of self-similar solutions for the nonlinear diffusion equation ht = −(hhxxx)x, which arises in the context of surface-tension-driven flow of a thin viscous liquid film. Here, h = h(x, t) is the liquid film height. A self-similar solution is h(x, t) = h(α(t)(x − x0) + x0, t0) = f (α(t)(x − x0)) and α(t) = [1 − 4A(t − t0)], where A and x0 are...