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 ).

Among the teachings of Jesus Christ in the Gospel of Luke and the Gospel of Matthew, the message to his followers that one should " Turn the other cheek " and his example in the story Pericope Adulterae, in which Jesus intervenes in the stoning of an adulteress, are generally accepted as his condemnation of physical retaliation ( though most scholars agree that the latter passage was " certainly not part of the original text of St John's Gospel ") More militant Christians consider Romans 13: 3 – 4 to support the death penalty.

More often, the support and the catalyst interact, affecting the catalytic reaction.

More recently, both Elms and librarian Lee Weinstein have gathered circumstantial evidence to support the case for Linebarger's being " Allen ," but both concede there is no direct proof that Linebarger was ever a patient of Lindner's or that he suffered from a disorder similar to that of " Kirk Allen.

More than anything else, the caddy is there to make the player's round enjoyable by taking care of menial tasks, speeding up play, and providing mental support if asked.

More recent Gopher revisions and graphical clients added support for multimedia.

More recently, Hindu nationalists have created a version of history for the schools to support their demands for " Hindutva " (" Hinduness ") in Indian society.

More striking, however, was the level of support for Hezbollah's resistance from non-Shiite communities.

More significantly, an informal defence arrangement with Britain reassured Kenyatta that he could rely on direct British military support in the event of an army mutiny or attempted coup.

More advanced implementations may support more complicated operations, such as pull_lowest_priority_element, inspecting the first few highest-or lowest-priority elements ( peeking at the highest priority element can be made O ( 1 ) time in nearly all implementations ), clearing the queue, clearing subsets of the queue, performing a batch insert, merging two or more queues into one, incrementing priority of any element, etc.

More trusting in the power of rhetoric to support a republic, the Roman orator Cicero argued that art required something more than eloquence.

More important, the pope forbade ecclesiastical officials under pain of excommunication to support Henry as they had so freely done in the past.

More than 12, 000 volunteers and rescue workers took part in the rescue, recovery and support operations following the bombing.

More difficulties struck in 1083, when his eldest son Robert rebelled once more with support from the French king.

More recently, IWW members were involved in the Liverpool dockers ' strike that took place between 1995 and 1998, and numerous other events and struggles throughout the 1990s and 2000s ( decade ), including the successful unionising of several workplaces, such as support workers for the Scottish Socialist Party.

More importantly for French – and English – history would be his support for Thomas Becket, Archbishop of Canterbury, whom he tried to reconcile with Henry II.

More recently, a Quinnipiac poll from June 2009 finds that 55 % of Americans feel that affirmative action should be discontinued, yet 55 % support affirmative action for disabled people.

More recently the server has been enhanced to support data warehouse workloads.

More than 2, 000 of Cadbury's male employees joined the Armed Forces and to support the war effort, Cadbury provided clothing, books and chocolate to soldiers.

More recent historians, such as Donald Kagan and R. J. Buck, have tended to support this analysis, pointing to the role that Thrasybulus played in crafting Athenian strategy in all these battles, and specifically to the decisive action he took at Cyzicus, which saved Alcibiades's force from being swamped, and turned a potential Athenian defeat into a stunning victory.

More than 442, 000 signatures in support of the move were collected within three months, but the initiators had underestimated the conservatism of the Supreme Soviet.

More specifically pilgrims spent money and would leave gifts for the support of the cathedral.

More rarely, some systems support having the extra bit of color depth on the red or blue channel, usually in applications where that color is more prevalent ( photographing of skin tones or skies, for example ).

More recently, decentralized IP-based CCTV cameras, some equipped with megapixel sensors, support recording directly to network-attached storage devices, or internal flash for completely stand-alone operation.

More and more Fortune 500 companies are embracing LGBT / gay community consumers to include " domestic partner benefits, non-discrimination policies, and financial support for organizations working to promote equality.