reasons and in order to have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches...

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory...

In metalogic, mathematical logic, and computability theory, an effective method or effective procedure is a finite-time, deterministic procedure for solving...

compactness theorem Mahler measure Effective results in number theory Mahler's theorem Brun sieve Function field sieve General number field sieve Large sieve Larger...

fields with class number 1 (the 9 known ones, and at most one further). The result was ineffective (see effective results in number theory): it did not give...

In political science, the effective number of parties is a diversity index introduced by Laakso and Rein Taagepera (1979), which provides for an adjusted...

degree Effective results in number theory Diophantine set Matiyasevich's theorem Word problem for groups Arithmetical hierarchy Subrecursion theory Presburger...

significance". The result, proved by Alan Baker (1966, 1967a, 1967b), subsumed many earlier results in transcendental number theory. Baker used this to...

Teichmüller theory for number fields equipped with an elliptic curve". The theory was made public in a series of four preprints posted in 2012 to his...

theorem. Siegel's result was ineffective for g ≥ 2 {\displaystyle g\geq 2} (see effective results in number theory), since Thue's method in diophantine approximation...

an effective procedure. In group theory, a group element acts effectively (or faithfully) on a point, if that point is not fixed by the action. In physics...

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. Estimates of statistical...

field of elimination theory was motivated by the need of methods for solving systems of polynomial equations. One of the first results was Bézout's theorem...

The Excellence theory is a general theory of public relations that “specifies how public relations makes organizations more effective, how it is organized...

unique variable in the expression defining our function). By its nature, it was ineffective (see effective results in number theory); this is of particular...

contributions to a number of effective altruist organizations, but it was shut down in November 2022 when FTX collapsed. A number of books and articles...

supply" and developing a comprehensive theory of effective demand. According to Keynesian economics, weak demand results in unplanned accumulation of inventories...

and a constant d, in terms of the coupling g(M) at a reference scale M. Gell-Mann and Low realized in these results that the effective scale can be arbitrarily...

In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring...

In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic)...

Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate...

versions of string theory are subsumed in a single framework known as M-theory. Studies of string theory have also yielded a number of results on the nature...

In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus...

object s in S to its canonical form s*? Canonical forms are generally used to make operating with equivalence classes more effective. For example, in modular...

hyperarithmetical theory. In many cases, results of classical descriptive set theory have effective versions; in some cases, new results are obtained by...

In physics, M-theory is a theory that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory...

arithmetical hierarchy is important in computability theory, effective descriptive set theory, and the study of formal theories such as Peano arithmetic. The...

theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in...

set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory is...

suggests that an effective approach may be to provide criticism while avoiding such challenges. The widespread belief in conspiracy theories has become a...