The film "The Colloidal State" explores the concept of colloids, which are materials in a dispersion where small particles of one substance are distributed throughout another. It distinguishes ...

ABSTRACT: This work focuses on the development and analysis of a financial system using advanced mathematical modeling techniques. Starting from an ordinary financial system, we extend it to a ...

To view the SciML Tutorials, go to tutorials.sciml.ai. By default, this will lead to the latest tagged version of the tutorials. To see the in-development version of the tutorials, go to ...

In this paper, we consider a mean-field stochastic differential equation, also called the McKean-Vlasov equation, with initial data (t, x) ∈ [0, T] × ℝd, whose ...

We study the existence of positive solutions of the equation u״ (t) + a (t) f (u(g(t))) = 0, 0 < t < 1 with linear boundary conditions. We show the existence of at least one positive solution if f is ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

Abstract: The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e., Lyapunov functionals, for a linear time-delay system with a constant and a ...

There are lockers and knockers, limited slips and Sure Grips. Sometimes they're called Positractions and sometimes much worse. But this name game is really about the concept of pushing equal measures ...

Abstract: Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential ...

The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other ...