background cavitary pulmonary tuberculosis (tb) is rare in children. objectives the aim of this study was to evaluate the characteristics of cavitary pulmonary tb in children. patients and methods this retrospective study was conducted on 97 children less than 15 years old with pulmonary tb to assess the clinical characteristics and radiographic findings of patients with cavitary lesions. resul...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...

we inverse the surface gravity data to recover subsurface 3d density distribution with two strategy. in the first strategy, we assumed wide density model bound for inverting gravity data and in the second strategy, the inversion procedure have been carried out by limited bound density. wediscretize the earth model into rectangular cells of constant andunidentified density. the number of cells i...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...

We give elementary proofs of the fact that the Loewner matrices [ f(pi)−f(pj) pi−pj ] corresponding to the function f(t) = t on (0,∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0,∞) the Loewner matrices corresponding to an operator convex function on...

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...