More formally, it is the theoretical temperature at which entropy reaches its minimum value.

More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language ( the sensitivity of complexity relative to the choice of description language is discussed below ).

More formally, a block cipher is specified by an encryption function

More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient

More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets ( sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers ).

More formally design has been defined as follows.

More formally, it is " the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.

More formally, such coordinates can be obtained from three-dimensional coordinates using the artifice of a map projection.

More formally, a " representation " means a homomorphism from the group to the automorphism group of an object.

More formally, case has been defined as " a system of marking dependent nouns for the type of relationship they bear to their heads.

More formally, if a, b, c, and d are all integers, then the fraction < sup > a </ sup >⁄< sub > b </ sub > is irreducible if and only if there is no other equal fraction < sup > c </ sup >⁄< sub > d </ sub > such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a.

More formally, the Klein bottle is the quotient space described as the square × with sides identified by the relations for and for:

More formally, a lexicon is a language's inventory of lexemes.

More formally, the environment is modeled as a Markov decision process ( MDP ) with states and actions with the following probability distributions: the instantaneous cost distribution, the observation distribution and the transition, while a policy is defined as conditional distribution over actions given the observations.

( More work is required to derive this result formally.

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution ; that is, the function can be stated before realization of the data.

More formally, # P is the class of function problems of the form " compute ƒ ( x )," where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time.

More formally, the output must satisfy two conditions:

More formally, we can state the Transfinite Recursion Theorem as follows.

More formally, ubiquitous computing is defined as " machines that fit the human environment instead of forcing humans to enter theirs.

More formally, complex systems often exhibit hysteresis.

More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i. e., a combination of translations, rotations and reflections.

More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

More formally, ( X, Σ, μ ) is complete if and only if

More formally, we can think of a truth condition as what makes for the truth of a sentence in an inductive definition of truth ( for details, see the semantic theory of truth ).

These include Word of God ( established in 1967 ), a charismatic inter-denominational movement ; and the Thomas More Law Center ( established in 1999 ), a religious-conservative advocacy group.

More compactly, an abelian group is a commutative group.

In the 1990s, Peter formed One More Time, a group that enjoyed European success with the ABBA-like " Highland " and, later, as Sweden's entry to the Eurovision Song Contest 1996.

* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.

More significantly, the jury also found that the leading anti-cult group known as the Cult Awareness Network was a co-conspirator in the crime and fined CAN $ 1, 000, 000 in punitive damages, forcing the group into bankruptcy.

More generally, the fundamental group of any graph is a free group.

* No More Drama ( group ), an American teen group where Howie Dorough was the manager

More recently, advocates for radical reform in justice systems have called for a public policy adoption of non-punitive, non-violent Restorative Justice methods, and many of those studying the success of these methods, including a United Nations working group on Restorative Justice, have attempted to re-define justice in terms related to peace.

Allmusic. com's Stephen Thomas Erlewine states that "... More than any other hip-hop group, Run-D. M. C.

More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H. This is usually represented notationally by H ≤ G, read as " H is a subgroup of G ".

More recently, House's music has influenced the blues rock group The White Stripes, who covered his song " Death Letter " ( also reworked by Skip James and Robert Johnson ) on their album De Stijl, and later performed it at the 2004 Grammy Awards.

This group includes Jan Baptist van Helmont ( 1618-1699 ), Robert Fludd ( 1574-1637 ), John Pordage ( 1608-1681 ), Jane Leade ( 1623-1704 ), Henry More ( 1614-1687 ), Pierre Poiret ( 1646-1719 ), and Antoinette Bourignon ( 1616-1680 ).

More precisely, if A is a finite set of generators for G then the word problem is the membership problem for the formal language of all words in A and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A to the group G. If B is another finite generating set for G, then the word problem over the generating set B is equivalent to the word problem over the generating set A.

More independent but clearly to the left of the political spectrum are the Centro de Investigaciones de Relaciones Internacionales y Desarrollo ( CIDOB ) founded in 1973 ; and the Fundación para las Relaciones Internacionales y el Diálogo Exterior ( FRIDE ) established in 1999 by Diego Hidalgo and main driving force behind projects such as the Club de Madrid, a group of democratic former heads of state and government, or the Foreign Policy Spanish Edition.

More generally, Euclidean n-space R < sup > n </ sup > with addition and standard topology is a topological group.

More recently, in 2009 Eric Scheid, also known as " Titus ," released a single called " What Do You Believe " featuring Bizzy Bone from the nationally known hip hop group Bone Thugs-n-Harmony.

Holbein also painted the Bavarian astronomer and mathematician Nicholas Kratzer, a tutor of the More family whose notes appear on Holbein's sketch for their group portrait.

In 1787, he came into contact with Thomas Clarkson and a group of anti-slave-trade activists, including Granville Sharp, Hannah More and Charles Middleton.