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

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 ).

More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.

More recently, with the progress of computer technology, other representations were introduced and specialized computer languages were developed, since with the explosive growth of the complexity of electronic circuits, traditional schematics are becoming less practical.

More simple outfits may be compensated for their lack of complexity by paying attention to material choice, and overall excellent quality.

More recent scholarship has revealed the historical errors in the poem and the complexity of the Expulsion and those involved, which the poem ignores.

More recent scholarship has revealed the historical errors in the poem and the complexity of the Expulsion and those involved, which the poem obscures.

More specifically, it has been seen by Batson as comprising a willingness to view religious doubts in a positive manner, acceptance that religious orientation can change and existential complexity, the belief that one's religious beliefs should be shaped from personal crises that one has experienced in one's life.

More generally, the total complexity of the cells of a line arrangement that are intersected by any convex curve is O ( n α ( n )), where α denotes the inverse Ackermann function, as may be shown using Davenport – Schinzel sequences.

More formally, a problem p is called hard for a complexity class C under a given type of reduction, if there exists a reduction ( of the given type ) from any problem in C to p. If a problem is both hard for the class and a member of the class, it is complete for that class ( for that type of reduction ).

More recent projects include the lemmatization of the Greek corpus ( 2006 )-- a substantial undertaking, given the highly inflectional nature of the Greek language and the complexity of the corpus, covering more than two millennia of literary development -- and the Online LSJ ( released in February 2011 ).

More generally, the label includes such disparate lay, professional, and academic groups as visionaries, foresight consultants, corporate strategists, policy analysts, cultural critics, planners, marketers, forecasters, prediction market developers, roadmappers, operations researchers, investment managers, actuaries and other risk analyzers, and future-oriented individuals educated in every academic discipline, including anthropology, complexity studies, computer science, economics, engineering, evolutionary biology, history, management, mathematics, philosophy, physical sciences, political science, psychology, sociology, systems theory, technology studies, and other disciplines.

More in general functional decomposition in computer science is a technique for mastering the complexity of the function of a model.

More obviously influential was his moral philosophy, not primarily because of his casuistry – an approach acknowledging the complexity of individual cases.

More than one string orchestra can be utilized.

More subtle is the slight over-representation of string operations, which is largely language-related: both Ada and Pascal have strings as normal variables in the language, whereas C does not, so what was simple variable assignment in reference benchmarks became buffer copy operations in the C library.

Following that came More Than Idle Chatter, the six compositions of which focus on processings of the human voice using linear predictive coding, granular synthesis, and plucked string synthesis ; its three highlights are granular synth pieces called " Idle Chatter ," " Just_more_idle_chatter ," and " Notjustmoreidlechatter ," which look at the same thing from multiple perspectives.

More recent work has suggested the problem may be indirect evidence of a cyclic universe possibly as allowed by string theory.

More recently, theoretical interest in varying constants ( not just α ) has been motivated by string theory and other such proposals for going beyond the Standard Model of particle physics.

More weight towards the rim will make the yo-yo more stable for string tricks ; more weight towards the center will make the yo-yo easier to turn and therefore better for looping tricks.

Over the following years, Summer followed this success with a string of other disco hits, such as " I Feel Love ", " MacArthur Park ", " Hot Stuff " and " No More Tears ( Enough is Enough )".

More recently, notable string trios have been written by Murray Adaskin, Alain Bancquart, Robert Carl, Pascal Dusapin, Donald Erb, Karlheinz Essl, Brian Ferneyhough, Berthold Goldschmidt, Sofia Gubaidulina, Bertold Hummel, Talivaldis Kenins, Ernst Krenek, Helmut Lachenmann, Paul Lansky, Ljubica Marić, Krzysztof Meyer, Krzysztof Penderecki, Wayne Peterson, Wolfgang Rihm, Bogusław Schaeffer, Alfred Schnittke, Karlheinz Stockhausen, Graham Waterhouse, Charles Wuorinen, La Monte Young, Iannis Xenakis, and Ellen Taaffe Zwilich.

The group had a string of international hit singles including " I Ran ( So Far Away )", " Space Age Love Song ," " Wishing ( If I Had a Photograph of You )" and " The More You Live, the More You Love ", and became notable in the 1980s for their MTV video for the song " I Ran ( So Far Away )".

More sophisticated tops are spun by holding the axis firmly while pulling a string or twisting a stick or pushing an auger.

She performed three tracks solo (" Love Me No More ", " Stay With Me Till Dawn " and " If ( When You Go )") accompanied by a string quartet.

More generally, in a system with radix b ( b > 1 ), a string of digits denotes the decimal number.

In 1981, he made his first appearance at the Reggae Sunsplash festival ( returning annually until 1991 ), and he moved on to the Charisma Records offshoot Pre, who released his The Lonely Lover ( another nickname that stuck ) and More Gregory albums along with a string of increasingly successful singles including " Tune In ", " Permanent Lover ", " Wailing Rudy " and " Tribute to Waddy ".

Diamond Rio has been one of few self-contained country bands to have followed the " rock band " route, each member playing their own instruments and singing their own vocals on all their albums themselves without any additional input from outside musicians ; starting with the One More Day album, however, some of their songs have occasionally featured accompaniment from a string section, but the actual band members still perform their own parts nonetheless.

On February 23, 2009, it was announced as part of a press release by Mike Patton that Faith No More would be reuniting for a string of European tour dates., On February 25, shortly after Patton's press release, Bill Gould announced a Faith No More reunion tour and identified the line-up, which excluded Martin.

( More advanced players and professionals prefer synthetic or gut core strings wound with metal, and an all-metal E string.

More typical systems incorporate a digital telephone dialer unit that will dial a central station ( or some other location ) via the Public Switched Telephone Network ( PSTN ) and raise the alarm, either with a synthesized voice or increasingly via an encoded message string that the central station decodes.

More generally, the pickup operation can be described using the concept of a magnetic circuit, in which the motion of the string varies the magnetic reluctance in the circuit created by the permanent magnet.