AlgebraAlgebra () is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields.
C*-algebraIn mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators.
*-algebraIn mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.
Lie algebraIn mathematics, a Lie algebra (pronounced liː ) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. Otherwise said, a Lie algebra is an algebra over a field where the multiplication operation is now called Lie bracket and has two additional properties: it is alternating and satisfies the Jacobi identity. The Lie bracket of two vectors and is denoted . The Lie bracket does not need to be associative, meaning that the Lie algebra can be non associative.
Associative algebraIn mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K. In this article we will also use the term [[algebra over a field|K-algebra]] to mean an associative algebra over the field K.
Algebra over a fieldIn mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear". The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras and non-associative algebras.
Jordan algebraIn abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: (commutative law) (). The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative, meaning that is independent of how we parenthesize this expression. They also imply that for all positive integers m and n.
Differential graded algebraIn mathematics, in particular in homological algebra, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. TOC A differential graded algebra (or DG-algebra for short) A is a graded algebra equipped with a map which has either degree 1 (cochain complex convention) or degree −1 (chain complex convention) that satisfies two conditions: A more succinct way to state the same definition is to say that a DG-algebra is a monoid object in the .
EmploymentEmployment is a relationship between two parties regulating the provision of paid labour services. Usually based on a contract, one party, the employer, which might be a corporation, a not-for-profit organization, a co-operative, or any other entity, pays the other, the employee, in return for carrying out assigned work. Employees work in return for wages, which can be paid on the basis of an hourly rate, by piecework or an annual salary, depending on the type of work an employee does, the prevailing conditions of the sector and the bargaining power between the parties.
Employment contractAn employment contract or contract of employment is a kind of contract used in labour law to attribute rights and responsibilities between parties to a bargain. The contract is between an "employee" and an "employer". It has arisen out of the old master-servant law, used before the 20th century. Employment contracts relies on the concept of authority, in which the employee agrees to accept the authority of the employer and in exchange, the employer agrees to pay the employee a stated wage (Simon, 1951).
Self-employmentSelf-employment is the state of working for oneself rather than an employer. Tax authorities will generally view a person as self-employed if the person chooses to be recognised as such or if the person is generating income for which a tax return needs to be filed. In the real world, the critical issue for the tax authorities is not whether a person is engaged in a business activity (called "trading" even when referring to the provision of a service) but whether the activity is profitable and therefore potentially taxable.
Periodic tableThe periodic table, also known as the periodic table of the elements, arranges the chemical elements into rows ("periods") and columns ("groups"). It is an organizing icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which says that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks.
Full employmentFull employment is a situation in which there is no cyclical or deficient-demand unemployment. Full employment does not entail the disappearance of all unemployment, as other kinds of unemployment, namely structural and frictional, may remain. For instance, workers who are "between jobs" for short periods of time as they search for better employment are not counted against full employment, as such unemployment is frictional rather than cyclical.
Likert scaleA Likert scale (ˈlɪkərt ,) is a psychometric scale named after its inventor, American social psychologist Rensis Likert, which is commonly used in research questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term (or more fully the Likert-type scale) is often used interchangeably with rating scale, although there are other types of rating scales. Likert distinguished between a scale proper, which emerges from collective responses to a set of items (usually eight or more), and the format in which responses are scored along a range.
HydrogenHydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, and highly combustible. Hydrogen is the most abundant chemical substance in the universe, constituting roughly 75% of all normal matter. Stars such as the Sun are mainly composed of hydrogen in the plasma state. Most of the hydrogen on Earth exists in molecular forms such as water and organic compounds.
RubidiumRubidium is the chemical element with the symbol Rb and atomic number 37. It is a very soft, whitish-grey solid in the alkali metal group, similar to potassium and caesium. Rubidium is the first alkali metal in the group to have a density higher than water. On Earth, natural rubidium comprises two isotopes: 72% is a stable isotope 85Rb, and 28% is slightly radioactive 87Rb, with a half-life of 48.8 billion years—more than three times as long as the estimated age of the universe.
SodiumSodium is a chemical element with the symbol Na (from Latin natrium) and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table. Its only stable isotope is 23Na. The free metal does not occur in nature and must be prepared from compounds. Sodium is the sixth most abundant element in the Earth's crust and exists in numerous minerals such as feldspars, sodalite, and halite (NaCl).
StrontiumStrontium is the chemical element with the symbol Sr and atomic number 38. An alkaline earth metal, strontium is a soft silver-white yellowish metallic element that is highly chemically reactive. The metal forms a dark oxide layer when it is exposed to air. Strontium has physical and chemical properties similar to those of its two vertical neighbors in the periodic table, calcium and barium. It occurs naturally mainly in the minerals celestine and strontianite, and is mostly mined from these.
Strontium-90Strontium-90 () is a radioactive isotope of strontium produced by nuclear fission, with a half-life of 28.8 years. It undergoes β− decay into yttrium-90, with a decay energy of 0.546 MeV. Strontium-90 has applications in medicine and industry and is an isotope of concern in fallout from nuclear weapons, nuclear weapons testing, and nuclear accidents. Naturally occurring strontium is nonradioactive and nontoxic at levels normally found in the environment, but 90Sr is a radiation hazard.
Köppen climate classificationThe Köppen climate classification is one of the most widely used climate classification systems. It was first published by German-Russian climatologist Wladimir Köppen (1846–1940) in 1884, with several later modifications by Köppen, notably in 1918 and 1936. Later, German climatologist Rudolf Geiger (1894–1981) introduced some changes to the classification system, which is thus sometimes called the Köppen–Geiger climate classification.
