Stochastic matrixIn mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics.
Zeroth law of thermodynamicsThe zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws had been widely recognized. The zeroth law states that if two thermodynamic systems are in thermal equilibrium with each other, and also separately in thermal equilibrium with a third system, then the three systems are in thermal equilibrium with each other.
Residue (complex analysis)In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.) Residues can be computed quite easily and, once known, allow the determination of general contour integrals via the residue theorem.
An Essay towards solving a Problem in the Doctrine of ChancesAn Essay towards solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by Thomas Bayes, published in 1763, two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price. The title comes from the contemporary use of the phrase "doctrine of chances" to mean the theory of probability, which had been introduced via the title of a book by Abraham de Moivre.
