The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current number existing transforms such those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties prove some important results, including linearity property, existence theorem, convolution derivatives properties. Moreover, pro...

In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations PDEs in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semiinvariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting ...

This study-research project is about numerical methods of differential equations (ordinary differential equations (ODE), partial differential equation (PDE), and integro-differential equations (IDE).) Required courses for this project are Math 212/213 (Multivariable Calculus), Math 302 (Differential Equations); and additional training in Math 345 (Introduction in Mathematical Biology), Math 413...

Scientific Research context: In 1980, M.H.A. Davis [1] introduced in probability theory Piecewise Deterministic Markov Processes (PDMP) as a general class of models suitable for formulating optimization problems in queuing and inventory systems, maintenance-replacement models, investment scheduling and many other areas of operation research. In the continuous-time context, stochastic control th...

are based on the ansätze for the Yang–Mills field Aμ(x) suggested by Wu and Yang, Rosen, ’t Hooft, Corrigan and Fairlie, Wilczek, Witten (see [1] and references therein). There were further developments for the self-dual YMEs (which form the first-order system of nonlinear partial differential equations such that system (1) is its differential consequence). Let us mention the Atiyah–Hitchin–Dri...

In this paper, we consider the dynamics of solutions to complex-valued evolutionary partial differential equations (PDEs) and show existence heteroclinic orbits from nontrivial equilibria zero via computer-assisted proofs. We also that unbounded along unstable manifolds at equilibrium follows orbits. Our proof consists three separate techniques rigorous numerics: an enclosure a local manifold e...

We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamiltonian is convex only depends on the spatial gradient solution. To be specific, we prove that under certain assumptions, two proposed represent to sets HJ PDEs with zero error. also implement our using Tensorflow provide...

Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features the physics they describe. We present estimates, their limitations, three classic second PDEs mathematical (wave, heat, Laplace equations), first transport equations, two nonlinear wave equations. It is beneficial to expose beginning student these considerations before jumping in...

Partial Differential Equations (PDEs) have dominated image processing research recently. The three main reasons for their success are: first, their ability to transform a segmentation modeling problem into a partial differential equation framework and their ability to embed and integrate different regularizers into these models; second, their ability to solve PDEs in the level set framework usi...

15 Acknowledgements 17 Introduction 19 1 Dispersive Partial Differential Equations and Integrable Systems 29 1.1 Linear Dispersive Partial Differential Equations . . . . . . . . . . . . 29 1.2 Semilinear Dispersive PDEs . . . . . . . . . . . . . . . . . . . . . . . 32 1.2.1 Equations of NLS Type. . . . . . . . . . . . . . . . . . . . . . 33 1.2.2 Equations of KdV Type. . . . . . . . . . . . . ....