Abstract artAbstract art uses visual language of shape, form, color and line to create a composition which may exist with a degree of independence from visual references in the world. Western art had been, from the Renaissance up to the middle of the 19th century, underpinned by the logic of perspective and an attempt to reproduce an illusion of visible reality. By the end of the 19th century many artists felt a need to create a new kind of art which would encompass the fundamental changes taking place in technology, science and philosophy.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
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.
Absorbing elementIn mathematics, an absorbing element (or annihilating element) is a special type of element of a set with respect to a binary operation on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is no risk of confusion with other notions of zero, with the notable exception: under additive notation zero may, quite naturally, denote the neutral element of a monoid.
Constructivism (philosophy of mathematics)In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption. Such a proof by contradiction might be called non-constructive, and a constructivist might reject it.
Algebraic K-theoryAlgebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups of the integers.
Abstract simplicial complexIn combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking subsets, i.e., every subset of a set in the family is also in the family. It is a purely combinatorial description of the geometric notion of a simplicial complex. For example, in a 2-dimensional simplicial complex, the sets in the family are the triangles (sets of size 3), their edges (sets of size 2), and their vertices (sets of size 1).
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Chemical symbolChemical symbols are the abbreviations used in chemistry for chemical elements, functional groups and chemical compounds. Element symbols for chemical elements normally consist of one or two letters from the Latin alphabet and are written with the first letter capitalised. Earlier symbols for chemical elements stem from classical Latin and Greek vocabulary. For some elements, this is because the material was known in ancient times, while for others, the name is a more recent invention.
DubniumDubnium is a synthetic chemical element with the symbol Db and atomic number 105. It is highly radioactive: the most stable known isotope, dubnium-268, has a half-life of about 16 hours. This greatly limits extended research on the element. Dubnium does not occur naturally on Earth and is produced artificially. The Soviet Joint Institute for Nuclear Research (JINR) claimed the first discovery of the element in 1968, followed by the American Lawrence Berkeley Laboratory in 1970.
Binary relationIn mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation.
Binary operationIn mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation on a set is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups.
