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 likely, you simply told yourself, as you handed us the book, that it mattered little what we incanted providing we underwent the discipline of incantation.

The same sort of thinking plays so large a part in both Babbitt and More, that we must examine it in some detail.

More recently, the chairman of the Atomic Energy Commission, Dr. Glenn T. Seaborg, `` admitted '' to a news conference in Las Vegas, Nevada, that the US might fall behind Russia ( he apparently meant in weapons development ) if the Soviets continue to test in the atmosphere while we abstain.

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

More than half of the sorghum and barley seeds we produce and most of the byproducts of the milling of cereals and the crushing of oilseeds are fed to livestock.

More broadly, philosophers who do not accept the possibility of zombies generally believe that consciousness is reflected in behavior ( including verbal behavior ), and that we attribute consciousness on the basis of behavior.

More recently, Peter Singer has argued that it is unreasonable that we do not give equal consideration to the interests of animals as to those of human beings when we choose the way we are to treat them.

Violence occurred at a small town called Patzicia, where about one thousand Indians rose in spontaneous outbursts: “ in honor of our General Ponce ,” and “ we want land .” More than twenty ladinos were killed during this demonstration.

More abstractly, Campbell's idea that myths are how we shape our lives deeply informs the picture of life in Glorantha throughout the game world's publication history.

More work was published in 1909 by Geiger and Marsden and further greatly expanded work was published in 1910 by Geiger, In 1911-2 Rutherford went before the Royal Society to explain the experiments and propound the new theory of the atomic nucleus as we now understand it.

" More recent comparisons of well-known recommendations on fluid intake have revealed large discrepancies in the volumes of water we need to consume for good health.

More generally, any collection of events — possibly more than just two of them — are mutually independent if and only if for every finite subset A < sub > 1 </ sub >, ..., A < sub > n </ sub > of the collection we have

More recent scholarship, such as that of Yaakov Elman, concludes that since the Tosefta, as we know it, must be dated linguistically as an example of Middle Hebrew 1, it was most likely compiled in early Amoraic times from oral transmission of baraitot., Professor Shamma Friedman, has found that the Tosefta draws on relatively early Tannaitic source material and that parts of the Tosefta predate the Mishnah.

Historian Hugh Trevor-Roper said in 1977 that More was " the first great Englishman whom we feel that we know, the most saintly of humanists, the most human of saints, the universal man of our cool northern renaissance.

As Marius writes in his biography of More: " To stand before a man at an inquisition, knowing that he will rejoice when we die, knowing that he will commit us to the stake and its horrors without a moment's hesitation or remorse if we do not satisfy him, is not an experience much less cruel because our inquisitor does not whip us or rack us or shout at us.

More geographically correct were Icelandic texts from about the same time, which presented a clear picture of the northern countries as experienced by Norse explorers: north of Iceland a vast, barren plain ( which we now know to be the Polar ice-cap ) extended from Biarmeland ( northern Russia ) east of the White Sea, to Greenland, then further west and south were, in succession, Helluland, Markland and Vinland.

' More than a century later, we continue to bestow diplomas upon individuals of outstanding capabilities and great talent.

More in general, in presence of time variation of the geometrical reflection conditions, this impulse response is time varying, and as such we have