The convex envelope of a given function was recently characterized as the solution of a fully nonlinear partial differential equation (PDE). In this article we study a modified problem: the Dirichlet problem for the underlying PDE. The main result is an optimal regularity result. Differentiability (C1,α regularity) of the boundary data implies the corresponding result for the solution in the in...

Weighted averaging filters and nonlinear partial differential equations (PDEs) are two popular concepts for discontinuity-preserving denoising. In this paper we investigate novel relations between these filter classes: We deduce new PDEs as the scaling limit of the spatial step size of discrete weighted averaging methods. In the one-dimensional setting, a simple weighted averaging of both neigh...

The goal in multiobjective optimization is to determine the so-called Pareto set. Our problem governed by a parameter-dependent semi-linear elliptic partial differential equation (PDE). To solve it, we use gradient-based set-oriented numerical method. solution of PDE standard discretization methods usually leads high computational effort. overcome this difficulty, reduced-order modeling (ROM) d...

background: the increasing use of nuclear radiation for human welfare necessitates the search for new, safe, cost effective radio protectors not only for the personnel’s charged with the responsibility of working or testing with radiations in laboratories, but also for general public. with this view the present study has been undertaken to determine the deleterious effects of sub lethal gamma r...

Rat liver nucleotide pyrophosphatase/phosphodiesterase I (NPP/PDE) catalysed efficiently the transfer of adenylate from ATP to alcohols (methanol, ethanol, propanol, ethylene glycol, glycerol, 2, 2-dichloroethanol and glycerol 2-phosphate), which acted as adenylate acceptors competing with water with different efficiencies. NPP/PDE kinetics in alcohol/water mixtures were accounted for by rate e...

This note is devoted to stabilizing a coupled PDE–ODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE–ODE cascadewith an invertible integral transformation,where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, a...

Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge throug...

A detailed characterization of the cyclic nucleotide phosphodiesterase (PDEs) from normal Drosophila melanogaster was made, including purification of the two major enzymes to near homogeneity. A third more labile phosphodiesterase also was identified in crude homogenates. The total activity per fly of one of these three enzymes, PDE-II, is strongly influenced by the dunce locus. Two independent...