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Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

One of the landmarks of Kyoto, the home of Japanese mathematician Masaki Kashiwara, is the Kamo River. At certain points, there are stepping stones that allow residents to cross the river away from ...

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 ...

Abstract: An adaptive algorithm of multi-point iterative method for simultaneous determination of all roots of polynomial equation is obtained. Its convergence rule was presented and proved. The ...

ChatGPT, Photomath, Symbolab, and other artificial intelligence-powered platforms can solve a complicated math equation in just seconds—and provide a step-by-step explanation of the answer. That power ...

Abstract: Although a variety of techniques have been developed to reduce the appearance of B-mode speckle, quantitative ultrasound (QUS) aims at extracting the hidden properties of the tissue. Herein, ...