Physics-informed Neural Network (PINN) is a promising tool that has been applied in variety of physical phenomena described by partial differential equations (PDE). However, it observed PINNs are difficult to train certain “stiff” problems, which include various nonlinear hyperbolic PDEs display shocks their solutions. Recent studies added diffusion term the PDE, and an artificial viscosity (AV...

Problem 198. Pi Mu Epsilon Journal 4(Fall 1967)296 A semi-regular solid is obtained by slicing off sections from the corners of a cube. It is a solid with 36 congruent edges, 24 vertices and 14 faces, 6 of which are regular octagons and 8 are equilateral triangles. If the length of an edge of this polytope is e, what is its volume? Problem E2017. American Mathematical Monthly 74(Oct 1967)1005 L...

Given the wavelet expansion of a function v, a non-linear adaptive approximation of v is obtained by neglecting those coeecients whose size drops below a certain threshold. We propose several ways to deene the threshold: all are based on the characterization of the local regularity of v (in a Sobolev or Besov scale) in terms of summability of properly deened subsets of its coeecients. A-priori ...

The International Society of Developmental Biologists (ISDB) is a non-profit scientific association which aims to promote the study of developmental biology:-by providing a forum for scientific discussion and for the publication of results of research, • by promoting the organization of international congresses and symposia, • by encouraging the establishment and improvement of research laborat...

Many birds do not breed until they are 2 or more years old. Such delayed breeding is generally found among large, long-lived, non-passerine species. Lack (1954) suggested that delayed breeding has probably evolved in species in which reproduction at an earlier age would not be likely to succeed or might be harmful to the parents. Ashmole (1963) and Amadon (1964) suggested that young birds might...