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 ).

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 sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory.

* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.

More advanced statistical methods employed by some I – O psychologists include logistic regression, multivariate analysis of variance, structural equation modeling, and hierarchical linear modeling ( HLM ; also known as multilevel modeling ).

More generally, a parabola is a curve in the Cartesian plane defined by an irreducible equation — one that does not factor as a product of two not necessarily distinct linear equations — of the general conic form

More generally, if a linear operator on a vector space ( possibly infinite-dimensional ) has finite-dimensional range ( e. g., a finite-rank operator ), then the rank of the operator is defined as the dimension of the range.

( More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?

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 generally, it can be in any state, corresponding to linear, circular, or elliptical polarization.

More precisely, defining two linear functions: and, the graph of the functions will be perpendicular and will make four right angles where the lines intersect if and only if.

More advanced designs use baffles and expansion chambers to slow down the escaping gases ; this is the basic principle behind a linear compensator.

More generally, the general linear group of degree n over any field F ( such as the complex numbers ), or a ring R ( such as the ring of integers ), is the set of n × n invertible matrices with entries from F ( or R ), again with matrix multiplication as the group operation.

More generally still, the general linear group of a vector space GL ( V ) is the abstract automorphism group, not necessarily written as matrices.

More precisely, this is an infinite list of simultaneous linear equations, one for each n > d − 1.

More abstractly, the symplectic group can be defined as the set of linear transformations of a 2n-dimensional vector space over F that preserve a nondegenerate, skew-symmetric, bilinear form.

More generally, a partially defined linear operator A from a topological vector space E into its continuous dual space E < sup >∗</ sup > is said to be symmetric if

More than one element per linear foot is common, and an array of these elements is required to heat a griddle plate of any given width.

More generally, the cokernel of a morphism f: X → Y in some category ( e. g. a homomorphism between groups or a bounded linear operator between Hilbert spaces ) is an object Q and a morphism q: Y → Q such that the composition q f is the zero morphism of the category, and furthermore q is universal with respect to this property.

More accurately, any linear functional applied to the sample function X < sub > t </ sub > will give a normally distributed result.

More generally, one can consider the image, kernel, coimage, and cokernel, which are related by the fundamental theorem of linear algebra.