Abstract: We derive the exact probability density functions (pdf) and distribution functions (cdf) of a product of n independent Rayleigh distributed random variables. The case n=1 is the classical ...

Abstract: Although the direct sampling method (DSM) has demonstrated its feasibility and robustness for imaging of small inhomogeneities, mathematical analyses of DSM have been conducted only on the ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P. R.

This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using finite basis physics-informed neural networks (FBPINNs). To improve the ...

You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. In the first script, students learn to derive transfer functions from ODEs and ...

Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the first two series of mini-courses from “Shanghai Summer School on Analysis and Numerics in Modern Sciences” ...

Functions are one of the most fundamental concepts in mathematics, forming the foundation for topics in algebra, calculus and many other areas. A solid understanding of the basics of functions, ...

This section focuses on the key features and methods for working with linear graphs. It demonstrates how to sketch graphs from rules, derive rules from graphs, and calculate key features such as the ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

National Council of Educational Research and Training (NCERT) has introduced a new initiative where students will be offered ...

The National Council of Educational Research and Training (NCERT) has launched a free online Class 12 mathematics course via ...