Di€usion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection di€usion partial di€erential equation. The governing equation includes the di€usion coecient and the convection coecient, which are taken as the control variables to minimize a ...

Diff ering lifehistory strategies may act as a constraint on reproductive expression that ultimately limits the ability of individual species to respond to changes in the magnitude or frequency of environmental variation, and potentially underlies the variation oft en inherent in phenotypic and evolved responses to anthropogenic change. Alternatively, if there are environmental cues that predic...

We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applie...

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of order integration and use it to solve integro-di?erential equations. The is described illustrated with examples. Also, we give error analysis.

Our goal in this paper is to use combined Laplace transform (CLT) and Adomian decomposition method(ADM) (that will be explained section 3), study approximate solutions for non-linear time-fractionalBurger's equation, fractional Burger's Kdv equation the modi?ed theCaputo Conformable derivatives. Comparison between two exact solution made.Here we report that method (LTDM) proved e?cient beused o...

In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

Pain represents a frequent symptom in various psychiatric disorders ranging from so called psychogenic or somatoform disorders to depression, to schizophrenia and to organic brain syndromes including dementia. Th alamic lesions are long known to induce painful symptoms. Th e cortex is involved in pain awareness. Th e locus coeruleus modulates pain perception. Various facets of pain in a range o...

This paper proposes a method of discovering some kinds of di erential equations with interval coe cients, which characterize or explain numerical data obtained by scienti c observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Based on these intervals, we design some interval inclusions which...

Edema is defi ned as abnormal accumulation of fl uid in the interstitium. Diff erential diagnosis of generalized edema is very broad. Most often, renal and cardiac causes lead to generalized edema. The potential gastrointestinal causes of edema are liver failure and protein losing enteropathy including celiac disease and protein malnutrition. Generalized edema is rarely an initial manifestation...

Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...