Dependent typeIn computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, and Idris, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations.
List of trigonometric identitiesIn trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified.
Vector calculus identitiesThe following are important identities involving derivatives and integrals in vector calculus. Gradient For a function in three-dimensional Cartesian coordinate variables, the gradient is the vector field: where i, j, k are the standard unit vectors for the x, y, z-axes. More generally, for a function of n variables , also called a scalar field, the gradient is the vector field: where are orthogonal unit vectors in arbitrary directions. As the name implies, the gradient is proportional to and points in the direction of the function's most rapid (positive) change.
Professional sportsIn professional sports, as opposed to amateur sports, participants receive payment for their performance. Professionalism in sport has come to the fore through a combination of developments. Mass media and increased leisure have brought larger audiences, so that sports organizations or teams can command large incomes. As a result, more sportspeople can afford to make sport their primary career, devoting the training time necessary to increase skills, physical condition, and experience to modern levels of achievement.
Women's sportsThe participation of women and girls in sports, physical fitness and exercise, has been recorded to have existed throughout history. However, participation rates and activities vary in accordance with nation, era, geography, and stage of economic development. While initially occurring informally, the modern era of organized sports did not begin to emerge either for men or women until the late industrial age. Until roughly 1870, women's activities tended to be informal and recreational in nature, lacked rules codes, and emphasized physical activity rather than competition.
