Factor

Factor, a Latin word meaning "who/which acts", may refer to:

Commerce

Science and technology

Biology

Computer science and information technology

Factoring (finance)

Factoring is a financial transaction and a type of debtor finance in which a business sells its accounts receivable (i.e., invoices) to a third party (called a factor) at a discount. A business will sometimes factor its receivable assets to meet its present and immediate cash needs.Forfaiting is a factoring arrangement used in international trade finance by exporters who wish to sell their receivables to a forfaiter. Factoring is commonly referred to as accounts receivable factoring, invoice factoring, and sometimes accounts receivable financing. Accounts receivable financing is a term more accurately used to describe a form of asset based lending against accounts receivable.

Factoring is not the same as invoice discounting (which is called an "Assignment of Accounts Receivable" in American accounting – as propagated by FASB within GAAP). Factoring is the sale of receivables, whereas invoice discounting ("assignment of accounts receivable" in American accounting) is a borrowing that involves the use of the accounts receivable assets as collateral for the loan. However, in some other markets, such as the UK, invoice discounting is considered to be a form of factoring, involving the "assignment of receivables", that is included in official factoring statistics. It is therefore also not considered to be borrowing in the UK. In the UK the arrangement is usually confidential in that the debtor is not notified of the assignment of the receivable and the seller of the receivable collects the debt on behalf of the factor. In the UK, the main difference between factoring and invoice discounting is confidentiality.

Von Neumann algebra

In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries.

Two basic examples of von Neumann algebras are as follows. The ring L^∞(R) of essentially bounded measurable functions on the real line is a commutative von Neumann algebra, which acts by pointwise multiplication on the Hilbert space L²(R) of square integrable functions. The algebra B(H) of all bounded operators on a Hilbert space H is a von Neumann algebra, non-commutative if the Hilbert space has dimension at least 2.

Von Neumann algebras were first studied by von Neumann (1930) in 1929; he and Francis Murray developed the basic theory, under the original name of rings of operators, in a series of papers written in the 1930s and 1940s (F.J. Murray & J. von Neumann 1936, 1937, 1943; J. von Neumann 1938, 1940, 1943, 1949), reprinted in the collected works of von Neumann (1961).

Official (ice hockey)

In ice hockey, an official is a person who has some responsibility in enforcing the rules and maintaining the order of the game. There are two categories of officials, on-ice officials, who are the referees and linesmen that enforce the rules during game play, and off-ice officials, who have an administrative role rather than an enforcement role.

On-ice officials

As the name implies, on-ice officials do their job on the hockey rink. They are traditionally clad in a black hockey helmet, black trousers, and a black-and-white striped shirt. They wear standard hockey skates and carry a finger whistle, which they use to stop play. They communicate with players, coaches, off-ice officials, both verbally and via hand signals. Starting in 1955 with the introduction of the black-and-white jersey, NHL on-ice officials wore numbers on their back for identification. In 1977, NHL officials removed the number and had their surnames on the back of their jerseys for identification, normally in a single row across the shoulders. (Some officials with long names would have their name in two rows, the most notable example being Andy Van Hellemond.) Starting in 1994, however, NHL officials returned to wearing numbers on their shirts, a procedure adopted by other leagues.

Referee

A referee is the person of authority in a variety of sports who is responsible for presiding over the game from a neutral point of view and making on-the-fly decisions that enforce the rules of the sport, including sportsmanship decisions such as ejection. The official tasked with this job may be known, in addition to referee, by a variety of other titles as well (often depending on the sport), including umpire, judge, arbiter, arbitrator, linesman, commissaire, timekeeper, touch judge or Technical Official (by the International Olympic Committee).

Origin

The term referee originated in association football. Originally the team captains would consult with each other in order to resolve any dispute on the pitch. Eventually this role was delegated to an umpire. Each team would bring their own partisan umpire allowing the team captains to concentrate on the game. Later, the referee, a third "neutral" official was added, this referee would be "referred to" if the umpires could not resolve a dispute. The referee did not take his place on the pitch until 1891, when the umpires became linesmen (now assistant referees). Today, in many amateur football matches, each side will still supply their own partisan assistant referees (still commonly called club linesmen) to assist the neutral referee appointed by the governing football association if one or both assistant referees are not provided. In this case, the role of the linesmen is limited to indicating out of play and cannot decide off side.

Official (American football)

In American football, an official is a person who has responsibility in enforcing the rules and maintaining the order of the game.

During professional and most college football games, seven officials operate on the field. Beginning in 2015, Division I college football conferences are using eight game officials. College games outside the Division I level use six or seven officials. Arena football, high school football, and other levels of football have other officiating systems. High school football played under the National Federation of State High School Associations (NFHS) rules typically use five officials for varsity and 3, 4, or 5 for non-varsity games.

Football officials are commonly, but incorrectly, referred to as referees, but each position has specific duties and a specific name: referee, umpire, head linesman, line judge, back judge, side judge, center judge (in Division I college football) and field judge. Because the referee is responsible for the general supervision of the game, the position is sometimes referred to as head referee or crew chief.