This paper establishes a connection between non-convex optimization and nonlinear partial differential equations (PDEs). We interpret empirically successful relaxation techniques motivated from ...

University of Utah engineers encode partial differential equations in light and feed them into newly designed optical neural engine, or ONE, to accelerate machine learning.

Partial differential equations (PDEs) are ubiquitous to the mathematical description of physical phenomena. Typical examples describe the evolution of a field in time as a function of its value in ...

In this connection the subject of singular solutions of ordinary differential equations, and the conception of the characteristic in partial differential equations may be particularly mentioned.” ...

ABSTRACT: In previous papers, we proposed the important Z transformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time.

NCERT Solutions Class 12 Maths Chapter 9 Differential Equations are available free for the students. Download exercise solutions PDF in an easy way.

Waveguide-based structures can solve partial differential equations by mimicking elements in standard electronic circuits. This novel approach, developed by researchers at Newcastle University in the ...

ABSTRACT: The concept of mass manifests in diverse forms, dimensions and configurations, and yet among all these manifestations, a unified origin is usually yearned for. This study aims to propose ...

All the latest science news on partial differential equations from Phys.org. Find the latest news, advancements, and breakthroughs.

Framework for solving parabolic partial differential equations could guide computer graphics and geometry processing by Alex Shipps, Massachusetts Institute of Technology Editors' notes ...

I love inequalities. The Sobolev and related inequalities estimate functions in terms of derivatives and form the basis for our understanding of partial differential equations.

This textbook is a self-contained introduction to partial differential equations. It is designed for undergraduate and first year graduate students who are mathematics, physics, engineering or, in ...