Behold the Manifold, the Concept that Changed How Mathematicians View Space

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...
YourTango

Born Unwanted: A Reflection On Survival, Womanhood, And The Price Of Becoming

Born in India in the early 1190s, author N. Azaar grew up in a culture where the desire for sons went unspoken but deeply ...
Scientific Research Publishing

Brauer, F. and Nohel, J.A. (1969) The Qualitative Theory of Ordinary Differential Equations. An Introduction. Dover Publications, Inc.

ABSTRACT: This work predicts theoretically the phase portrait including the existence and uniqueness of ω-limit cycle for an initial value problem y( 0 )= y 0 with an ordinary differential equation y ...
GitHub

Solving Ordinary Differential Equations Numerical Method Implementation in Python

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...
PNAS

Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels

This study centers on incorporating memory effects (the impact of past events on current states) into mathematical models for population dynamics. It introduces a framework based on the gamma ...
Frontiers

HiDeS: a higher-order-derivative-supervised neural ordinary differential equation for multi-robot systems and opinion dynamics

This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called ...
The New York Times

A Dead Child, Too Much Booze and a Family in Crisis

“Ordinary Human Failings,” a new novel by the Irish writer Megan Nolan, is a fierce and relentless account of characters trapped by circumstance and tragedy. By Harriet Lane Harriet Lane is the author ...
IEEE

Programmable Photonic Architecture Solving Systems of Ordinary Differential Equations

Abstract: Photonic integrated hardware accelerators promise to be a viable technology to complement digital electronic devices in applications requiring massive computing, such as high-performance ...