Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Chemical elementA chemical element is a chemical substance that cannot be broken down into other substances. The basic particle that constitutes a chemical element is the atom, and each chemical element is distinguished by the number of protons in the nuclei of its atoms, known as its atomic number. For example, oxygen has an atomic number of 8, meaning that each oxygen atom has 8 protons in its nucleus. This is in contrast to chemical compounds and mixtures, which contain atoms with more than one atomic number.
Approximation propertyIn mathematics, specifically functional analysis, a Banach space is said to have the approximation property (AP), if every compact operator is a limit of finite-rank operators. The converse is always true. Every Hilbert space has this property. There are, however, Banach spaces which do not; Per Enflo published the first counterexample in a 1973 article. However, much work in this area was done by Grothendieck (1955). Later many other counterexamples were found. The space of bounded operators on does not have the approximation property.
Fire (classical element)Fire is one of the four classical elements along with earth, water and air in ancient Greek philosophy and science. Fire is considered to be both hot and dry and, according to Plato, is associated with the tetrahedron. Fire is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with the qualities of energy, assertiveness, and passion. In one Greek myth, Prometheus stole fire from the gods to protect the otherwise helpless humans, but was punished for this charity.
Field with one elementIn mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted F1, or, in a French–English pun, Fun. The name "field with one element" and the notation F1 are only suggestive, as there is no field with one element in classical abstract algebra. Instead, F1 refers to the idea that there should be a way to replace sets and operations, the traditional building blocks for abstract algebra, with other, more flexible objects.
