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, 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 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.

More importantly, several of the more advanced of the less developed countries have found through experience that they must plan their own complex investment programs for at least 5 years forward and tentatively for considerably more than that if they are to be sure that the various interdependent activities involved are all to take place in the proper sequence.

More technically, the law is concerned with the speedup achievable from an improvement to a computation that affects a proportion P of that computation where the improvement has a speedup of S. ( For example, if an improvement can speed up 30 % of the computation, P will be 0. 3 ; if the improvement makes the portion affected twice as fast, S will be 2.

More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.

More controversially, officials of the Federal Reserve assisted in the negotiations that led to this bail-out, on the grounds that so many companies and deals were intertwined with LTCM that if LTCM actually failed, they would as well, causing a collapse in confidence in the economic system.

More precisely, if S

More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.

More generally, if ƒ has a branch-point near the origin of such a nature that then

More direct government involvement can lead to specific areas of crony capitalism, even if the economy as a whole may be healthy.

More often than not, a second light will be mounted to the helmet for quick transition if the primary fails.

More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.

More often than not a cross-examiner will also attempt to undermine the credibility of a witness if he will not be perceived to be a bully ( such as discrediting a very elderly person or young child ).

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 total output and utility thereby results from specializing in production and trading than if each country produced its own high-tech and low-tech products.

More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b.

More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b.

More generally, if the numbers are, the geometric mean satisfies

More severe withdrawal symptoms which occur can include seizures ( some of which can be fatal ), visual and auditory hallucinations, suicidal ideation, extremely severe panic attacks, depersonalization, tremors, delirium, delirium tremens and if not treated as an emergency by a proper medical staff death from a seizure can occur.

More generally, the direct product of two cyclic groups Z < sub > m </ sub > and Z < sub > n </ sub > is isomorphic to Z < sub > mn </ sub > if and only if m and n are coprime.

More generally, if C is an arbitrary abelian category that has enough injectives, then so does C < sup > I </ sup >, and the right derived functors of the inverse limit functor can thus be defined.