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Formally and has
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally, one has an implication, not an equivalence, so the solution set may get larger.
Formally the " head of state " can also personally be the " head of government " ( ex officio or by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over the Head of Government and other ministers, whether he is their actual political superior ( absolute monarch, executive president ) or rather theoretical or ceremonial in character.
Formally described as " Truck, Cargo: 10-Ton, 8x8 ", it has been nicknamed the " Dragon Wagon ".
Formally, we start with a category C with finite products ( i. e. C has a terminal object 1 and any two objects of C have a product ).
Formally it is a part of Novosibirsk city, and has never been a closed city.
Formally, DFS is an uninformed search that progresses by expanding the first child node of the search tree that appears and thus going deeper and deeper until a goal node is found, or until it hits a node that has no children.
Informally, G has the above presentation if it is the " freest group " generated by S subject only to the relations R. Formally, the group G is said to have the above presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R.
It has been leased from the National Trust since 1974 by the Somerset Wildlife Trust ( Formally Somerset Trust for Nature Conservation ) and is run as a nature reserve and visitor centre.
Formally known as trilina, the armónico has seven strings, two of which form a doubled string.
Formally known as Bootle-cum-Linacre, the town is < span style =" white-space: nowrap "> 4 miles ( 6. 4 km )</ span > to the north of Liverpool city centre, and has a total resident population of 77, 640.
Formally, this means that, for some function f, the image f ( D ) of a directed set D ( i. e. the set of the images of each element of D ) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say that f preserves directed suprema.
Following a merger with the Furnishing Industry Trust ( Formally The Furnishing Trades Benevolent Association ) in 2011, the Company has become the most significant charity in the sector, supporting the needy and promoting welfare and education of those entering and working within the industry, as well as the wider support of the charitable work of the Mayoralty and the Corporation of the City of London.
Formally established in 1475, though in fact much older, it has 75, 000 codices from throughout history.
Formally, the situation has the characteristics of a prisoner's dilemma game that is played repeatedly between the same partners, and in this case " defection "-jumping the queue-would not be advantageous.
Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.
* Formally real field, an algebraic field that has the so-called " real " property
Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any given input, and the algorithm is a process that produces this particular value as output.
Formally, an antihomomorphism between X and Y is a homomorphism, where equals Y as a set, but has multiplication reversed: denoting the multiplication on Y as and the multiplication on as, we have.
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 described in Stephen Gilligan's article: The relational self: the expanding of love beyond desire ( 1996 ), and expanded on in his book: The Courage to Love ( 1997 ), it has become a major new approach in psychotherapy and healing.
Formally launched in 2004, the network currently has 16 members in nine states.
Enbridge currently has offices in Enbridge Place ( Formally ING Tower ), Manulife Place, and Royal Bank Building.
Formally, given a finite set X, a collection C of subsets of X, all of size n, has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.
Formally named " Olallie ", it has usually been marketed as olallieberry, just as " Marion " is sold as marionberry.

Formally and been
Formally, the case where only a subset of parameters is defined is still a composite hypothesis ; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters whose values have not been specified under the point null hypothesis.
By 1912, the Social Democrats, with an explicitly anti-antisemitic program, were the largest party in the German Reichstag, and the Progressives ran very strongly as well ... Formally, at least, the Jews had been fully emancipated with the establishment of the German Empire, although they were kept out of certain influential occupations, enjoyed extraordinary prosperity ... Germans intermarried with Jews: in the 1930s some 50, 000 Jews were living in mixed German-Jewish marriages, so at least 50, 000 Germans, and presumably parts of their families, had familial contact with the Jews.
Formally the neutral is called the “ grounded conductor ”; as of the 2008 NEC, the terms “ neutral conductor ” and “ neutral point ” have been defined in the Code to record what had been common usage.
Dick Smith Electronics has also long been known for its " home brand " range of electronics which fall under the brand name " Dick Smith " ( Formally called DSE, a commonly used abbreviation of Dick Smith Electronics ).
Formally, it has been defined as:
Formally introduced in 1991, Gut Recordings was founded by Guy Holmes, who had been Head of Promotions at Island Records.
Formally the Airframe Reconditioning Squadron RNZAF, the unit was commercialised in 1998 and is now managed by SAFE Air Ltd. No. 1 Repair Depot was also active at the base for a number of years, though during the war it appears to have been stationed at Hamilton.
Formally this mission was declared to be only in pursuit of the Russian vessels and ammunition taken to Anzali by the White Russian counter-revolutionary General Denikin, who had been given asylum by British forces in Anzali.
Formally, they have always been considered Orthodox Christians, but most of them followed shamanism and animism as a part of their culture.
Formally launched in November 2004 The Economic Times Chandigarh edition has been immensely successful.
Formally, the minimum age for front line fighter is eighteen, but apparently rear line fighters below that age limit have been captured by the Colombian Army or occasionally have deserted.

Formally and defined
Formally, as per the 2002 Memorandum of Understanding between the BSI and the United Kingdom Government, British Standards are defined as:
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 ).
More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,
Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies
Formally, a frame is defined to be a lattice L in which finite meets distribute over arbitrary joins, i. e. every ( even infinite ) subset
Formally, these reside in a complex separable Hilbert space-variously called the " state space " or the " associated Hilbert space " of the system-that is well defined up to a complex number of norm 1 ( the phase factor ).
Formally it is defined by the equation
Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:
Formally, the convex hull may be defined as the intersection of all convex sets containing X or as the set of all convex combinations of points in X.
Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u:
Formally, a transductive support vector machine is defined by the following primal optimization problem:
Formally, powers with positive integer exponents may be defined by the initial condition
Formally, bending modulus is defined as the energy required to deform a membrane from its intrinsic curvature to some other curvature.
Formally, a Menger sponge can be defined as follows:
Formally, a constraint satisfaction problem is defined as a triple, where is a set of variables, is a domain of values, and is a set of constraints.
Formally, the index of H in G is defined as the number of cosets of H in G. ( The number of left cosets of H in G is always equal to the number of right cosets.
Formally, the subhypergraph induced by a subset of is defined as
Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.
Formally, a cardinal κ is defined to be weakly compact if it is uncountable and for every function f: < sup > 2 </ sup > →
Formally, a Coxeter group can be defined as a group with the presentation
Formally, the Cantor function c: → is defined as follows:
Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows.
Formally, the mutual information of two discrete random variables X and Y can be defined as:
Formally, an absolute coequalizer of a pair in a category C is a coequalizer as defined above but with the added property that given any functor F ( Q ) together with F ( q ) is the coequalizer of F ( f ) and F ( g ) in the category D. Split coequalizers are examples of absolute coequalizers.

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