Tail callIn computer science, a tail call is a subroutine call performed as the final action of a procedure. If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations. Tail calls can be implemented without adding a new stack frame to the call stack.
RotationRotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.
Iterated function systemIn mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981. IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system").
Euler's rotation theoremIn geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group. The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry.
Complete latticeIn mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra.
Mutual recursionIn mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, where the datatypes are naturally mutually recursive. The most important basic example of a datatype that can be defined by mutual recursion is a tree, which can be defined mutually recursively in terms of a forest (a list of trees).
Fixed-point iterationIn numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.
Density functional theoryDensity-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.
Semisimple representationIn mathematics, specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation of a group or an algebra that is a direct sum of simple representations (also called irreducible representations). It is an example of the general mathematical notion of semisimplicity. Many representations that appear in applications of representation theory are semisimple or can be approximated by semisimple representations.
Rigid bodyIn physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light.
