Non-linear physics is the study of systems where the output is not directly proportional to the input. Unlike linear systems, which follow simple, predictable relationships, non-linear systems exhibit ...

Finite-energy Airy beams were first introduced in the field of optics in 2007 (refs 1, 2) as new non-diffracting wavepackets in one and two spatial dimensions. The Airy function, describing the ...

A number of finite element discretization techniques based on two (or more) subspaces for nonlinear elliptic partial differential equations (PDEs) is presented. Convergence estimates are derived to ...

Pair of Linear Equations in Two Variables Class 10 Notes: Revision notes for CBSE Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables have been presented in the article along with ...

Some important points to revise from the chapter are: • An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in ...

An equation is a statement with an equals sign, stating that two expressions are equal in value, for example: \(3x + 5 = 11\). Solving an equation means finding the value or values for which the two ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...