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, 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 ).

More profound and more disturbing, however, is the moral isolation of Raymond Chandler's Philip Marlowe.

More important is the simple human point that all men suffer, and that it is a kind of anthropological-religious pride on the part of the Jew to believe that his suffering is more poignant than mine or anyone else's.

More than that, Sam Rayburn is the very living symbol of an iron-clad integrity so powerful in his nature and so constantly demonstrated that he can count some of his best friends in the opposition.

More than 50% of all lumber is unitized ; ;

More unitized lumber is being shipped on flat cars, and NLRDA studies show that flat cars loaded with the new Type 6-B floating-load method can be unloaded for as little as $.054/mbf.

More than anything, it is the therapist's intuitive sensing of these latent meanings in the stereotype which helps these meanings to become revealed, something like a spread-out deck of cards, on sporadic occasions over the passage of the patient's and his months of work together.

But to return to the main line of our inquiry, it is doubtful that Utopia is still widely read because More was medieval or even because he was a martyr -- indeed, it is likely that these days many who read Utopia with interest do not even know that its author was a martyr.

Utopia is still widely read because in a sense More stood on the margin of modernity.

we are concerned with Utopian communism -- that is, simply communism as it appears in the imaginary commonwealth of Utopia, as More conceived it.

More rarely, the hymen is so sturdy that it does not yield to penetration.

More typical is the case of a suburban Long Island housewife described by a marriage counselor.

More often, though, he is so accustomed to submitting to authority on the job without argument that he lives by the same rule at home.

More than 10 companies maintain facilities in Dallas and one large manufacturer is located to the north at Sherman.

More than 700 employees make gin machinery that's sold anywhere cotton is grown.

More than 200 are expected at the autumn event which is matched in the spring.

More than 300 teenagers last Sunday proved there is and as many more are expected to prove it again for Jim Kern and his wife Lynn from 4 to 8 p.m. Sunday at First Presbyterian Church.

More than a beautiful visualization of the illustrious adventures and escapades of the tragi-comic knight-errant and his squire, Sancho Panza, in seventeenth-century Spain, this inevitably abbreviated rendering of the classic satire on chivalry is an affectingly warm and human exposition of character.

More recently, Alasdair MacIntyre has attempted to reform what he calls the Aristotelian tradition in a way that is anti-elitist and capable of disputing the claims of both liberals and Nietzscheans.

More rarely, a script may have separate letters for tones, as is the case for Hmong and Zhuang.

More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

More explicitly, it is stating that for every indexed family of nonempty sets there exists an indexed family of elements such that for every.