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Formally and one
Formally, one has an implication, not an equivalence, so the solution set may get larger.
Formally one defines
Formally, a detailed balanced process is the one on which the probability to be in the state x and transit to x ' must be the same as to be in the state x ' and transit to x.
Formally, a function ƒ is real analytic on an open set D in the real line if for any x < sub > 0 </ sub > in D one can write
Formally, two variables are inversely proportional ( or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion ) if one of the variables is directly proportional with the multiplicative inverse ( reciprocal ) of the other, or equivalently if their product is a constant.
Formally, the appointment remains a royal one made on the advice of the Lord Chancellor, but he / she no longer comments on individual applications, and merely supervises the process and reviews the panel's recommendations in general terms ( satisfying himself / herself that the process as operated is fair and efficient ).
Formally, they are partial derivatives of the option price with respect to the independent variables ( technically, one Greek, gamma, is a partial derivative of another Greek, called delta ).
Formally known as the Kingfisher Pier, the Pier at Garden City is one of the most renowned attractions in Garden City, SC.
Formally, the process is one of progressive development, divided into three stages of increasingly complexity.
Formally, the word is applied to persons who are publicly accepted in a recognised capacity, such as professional employment, graduation from a course of study, etc., to give critical commentaries in one or any of a number of specific fields of public or private achievement or endeavour.
Formally speaking, the strategy pattern defines a family of algorithms, encapsulates each one, and makes them interchangeable.
Formally, the symphony is one of Mahler's most outwardly conventional.
Formally, however, there is an examination board consisting of a candidate's teachers / examiners, the headmaster / headmistress and one external Vorsitzende ( r ) ( head ), usually a high-ranking school official or the head of another school.
Formally, one may connect the kernel and the cokernel by the exact sequence
Formally, one inserts under the trace for each degree of freedom
Formally, an nth order approximation is one where the order of magnitude of the error is at most, or in terms of big O notation, the error is
Formally a congruence subgroup is one that contains Γ ( N ) for some N, and the least such N is the level or Stufe of the subgroup.
Formally, a rigged Hilbert space consists of a Hilbert space H, together with a subspace Φ which carries a finer topology, that is one for which the natural inclusion
Formally, a generative grammar is defined as one that is fully explicit.
Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.
Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.
Formally, a vertex cover of a graph G is a set C of vertices such that each edge of G is incident to at least one vertex in C. The set C is said to cover the edges of G. The following figure shows examples of vertex covers in two graphs ( and the set C is marked with red ).
Formally, given complex-valued functions f and g of a natural number variable n, one writes
Formally dedicated " as a memorial to the boys that were " on October 30, 1915, Alumni Field and its distinctive " maroon goal-posts on a field of green " were hailed in that evening's edition of the Boston Saturday Evening Transcript as " one of the sights in Boston.
Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has

Formally and defines
Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ).
Formally, the International Vocabulary of Metrology, 3rd edition ( VIM3 ) defines quantity as:
Formally, the equation above defines the macroscopic neutron cross-section ( for reaction x ) as the proportionality constant between a neutron flux incident on a ( thin ) piece of material and the number of reactions that occur ( per unit volume ) in that material.
Formally, each of the following definitions defines a concrete category, and every pair of these categories can be shown to be concretely isomorphic.

one and defines
For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms ( usually called a small category ), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets.
Another view defines anxiety as " a future-oriented mood state in which one is ready or prepared to attempt to cope with upcoming negative events ," suggesting that it is a distinction between future and present dangers which divides anxiety and fear.
" The book Plea Bargaining's Triumph: A History of Plea Bargaining in America published by Stanford University Press defines the plea as one in " which the defendant adheres to his / her claim of innocence even while allowing that the government has enough evidence to prove his / her guilt beyond a reasonable doubt ".
On September 21, 1996, barely three years after the " Don't Ask, Don't Tell " imbroglio, and further straining relations with the LGBT community, Clinton signed into law the Defense of Marriage Act ( DOMA ), which defines marriage as the legal union of one man and one woman.
Scholars recognize that classification ultimately depends on how one defines religion.
The Definition defines that Christ is ' acknowledged in two natures ', which ' come together into one person and hypostasis '.
It defines that Christ is ' acknowledged in two natures ', which ' come together into one person and hypostasis '.
In the same way one defines a Cartesian space of any dimension n, whose points can be identified with the tuples ( lists ) of n real numbers, that is, with.
A recursive definition, sometimes also called an inductive definition, is one that defines a word in terms of itself, so to speak, albeit in a useful way.
The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.
In the same way, one defines the binary operation of division ÷ in terms of the assumed binary operation of multiplication and the implicitly defined operation of " reciprocal " ( multiplicative inverse ).</ ref >
::* Statistical self-similarity: repeats a pattern stochastically so numerical or statistical measures are preserved across scales ; e. g., randomly generated fractals ; the well-known example of the coastline of Britain, for which one would not expect to find a segment scaled and repeated as neatly as the repeated unit that defines, for example, the Koch snowflake
In the United States, where the felony / misdemeanor distinction is still widely applied, the federal government defines a felony as a crime punishable by death or imprisonment in excess of one year.
Another way to describe G-sets is the functor category, where is the groupoid ( category ) with one element and isomorphic to the group G. Indeed, every functor F of this category defines a set X = F and for every g in G ( i. e. for every morphism in ) induces a bijection F < sub > g </ sub >: X → X.
The main feature that defines a galliard step is the last two beats consist of a large jump, landing with one leg ahead of the other.
Nelson defines transclusion as " the same content knowably in more than one place ", setting it apart from more special cases such as the inclusion of content stored in a different location ( which he calls " transdelivery ") or " explicit quotation which remains connected to its origins " ( which he calls " transquotation ").
Since one cannot logically consider these subjects to be both " at the same moment " and " away in time ", an exclusive choice has to be made that defines these two separate domains, B and C. Our reality or domain B is created by the complex, but consistent transformation of A by our biological and mental makeup.
ANSI standard ANSI Z535. 6-2006 defines an optional accompanying text in one or more languages.
Biochemistry professor Michael Behe, the originator of the term irreducible complexity, defines an irreducibly complex system as one " composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning ".
The meandering red path defines one course, the path of the yarn through the fabric.
If g is the metric on this manifold, one defines the action S ( g ) as
The MIME standard defines various multipart-message subtypes, which specify the nature of the message parts and their relationship to one another.

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