A method for trimming surfaces generated as solutions to Partial Differential Equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order e...

This paper presents a method to extend PDE surfaces to high dimensional spaces. We review a common existing analytic solution, and show how it can be used straightforwardly to increase the dimension of the space the surface is embedded within. We then further develop a numerical scheme suitable for increasing the number of variables that parametrise the surface, and investigate some of the prop...

<p style='text-indent:20px;'>In this paper, we study the numerical approximation of a system PDEs which arises from an optimal control problem for time-fractional Fokker-Planck equation with time-dependent drift. The is composed backward Hamilton-Jacobi-Bellman and forward equation. We approximate Caputo derivatives in by means L1 schemes Hamiltonian finite differences. scheme constructed...

The question about behavior of gaps between zeros polynomials under differentiation is classical and goes back to Marcel Riesz. Recently, Stefan Steinerberger [42] formally derived a nonlocal nonlinear partial differential equation which models dynamics roots differentiation. In this paper, we connect rigorously solutions Steinerberger’s PDE evolution for class trigonometric polynomials. Namely...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the network itself. PINNs nowadays used to solve PDEs, fractional integral-differential and stochastic PDEs. This novel methodology has arisen multi-task learning framework in which NN must fit observed data while reducing PDE resid...

Phophodiesterase (PDE) isoenzyme profiles of human cell preparations and tissues have been analysed by a semiquantitative method using selective PDE inhibitors and activators. Neutrophils, eosinophils and monocytes contain PDE IV exclusively. Lymphocytes, alveolar macrophages and endothelial cells contain PDE IV and PDE III, and in addition, PDE I is measured in macrophages and PDE II in endoth...

This work applies fractional differentiation (differentiation to non-integer order) to the gradients determined from image intensities for enhanced image registration. The technique is used to correct known simulated deformations of volumetric breast MR data using two algorithms: direct registration of gradient magnitude images and an extension of a previously published method that incorporates...

In rod outer segments the light activation of cGMP phosphodiesterase (PDE alpha beta gamma 2) is accomplished by removal of the gamma inhibitory subunit (PDE gamma) from the PDE alpha beta catalytic subunits. A light activation of the inositol signaling pathway also occurs, but there is little information linking these two signal transduction pathways. Here we report that protein kinase C (PKC)...

Four cyclic nucleotide phosphodiesterase (PDE) activities were separated from low-speed supernatants of homogenates of human cardiac ventricle by DEAE-Sepharose chromatography, and designated PDE I-PDE IV in order of elution with an increasing salt gradient. PDE I was a Ca2+/calmodulin-stimulated activity, and PDE II was an activity with a high Km for cyclic AMP which was stimulated by low conc...