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Auxiliary function. In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions that appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value zero for many arguments, or having a zero of high order at some point. [1]
Markov decision process. In mathematics, a Markov decision process ( MDP) is a discrete-time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via ...
Proper convex function. In mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real -valued convex function with a non-empty domain, that never takes on the value and also is not identically equal to. In convex analysis and variational analysis, a point (in the domain ...
This is the polynomial functional calculus. It is a homomorphism from the ring of polynomials to the ring of n × n matrices. Extending slightly from the polynomials, if f : C → C is holomorphic everywhere, i.e. an entire function, with MacLaurin series. mimicking the polynomial case suggests we define.
Rademacher complexity. In computational learning theory ( machine learning and theory of computation ), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with respect to a probability distribution. The concept can also be extended to real valued functions.
Complex analytic variety. In mathematics, and in particular differential geometry and complex geometry, a complex analytic variety [note 1] or complex analytic space is a generalization of a complex manifold that allows the presence of singularities. Complex analytic varieties are locally ringed spaces that are locally isomorphic to local model ...
Polylogarithm. In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function.
Urban planning in Singapore is the direction of infrastructure development in Singapore. It is done through a three-tiered planning framework, consisting of a long-term plan to plot out Singapore's development over at least 50 years, a Master Plan for the medium term, and short-term plans, the first two of which are prepared by the Urban ...