Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.

Formally, the system is said to have memory.

Formally, this means that the probability density functions or probability mass functions in this class have the form

Formally, according to the Constitution, citizens of Turkmenistan have the right to set up political parties and other public associations, acting within the framework of the Constitution and laws, and public associations and groups of citizens have the right to nominate their candidates in accordance with the election law.

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, the sequence of partial sums of some infinite summation converges if for every fixed power of X the coefficient stabilizes: there is a point beyond which all further partial sums have the same coefficient.

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.

Formally, we have for the approximation to the full solution A, a series in the small parameter ( here called ), like the following:

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.

Formally, for a countable set of events A < sub > 1 </ sub >, A < sub > 2 </ sub >, A < sub > 3 </ sub >, ..., we have

Formally, the principle of subsidiarity applies to those areas where the Community does not have exclusive competence, the principle delineating those areas where the Community should and should not act.

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.

Formally we have:

Formally, we have

Formally, Chrétien and Martin have remained publicly respectful of each other ; while much of the verbal sparring was between their supporters.

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, a production function is defined to have:

Formally, all members of the Ghelani family are Hindu Leuva Patel, although some have since chosen other religious beliefs.

Formally described, it alternates slow sections in a modal F with faster sections, " Neue Kraft fühlend " ( with renewed strength ), in D. The slow sections each have two elements, ( 1 ) a passage reminiscent of the opening of the first movement in which the instruments overlap each other with a brief motive ; ( 2 ) a chorale, the actual song.

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, they have always been considered Orthodox Christians, but most of them followed shamanism and animism as a part of their culture.

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 inaugurated in March 2004, the Global Leadership Foundation works to " promote good governance – democratic institutions, open markets, human rights and the rule of law – and to contribute to the prevention and resolution of conflict through mediation.

Formally, the Sachs – Hornbostel is modeled on the Dewey Decimal classification.

* Citibank Banamex USA – Formally California Commerce Bank, Banamex's U. S. banking division.

Formally designated as the Manhattan Engineer District, it refers specifically to the period of the project from 1941 – 1946 under the control of the U. S. Army Corps of Engineers, under the administration of General Leslie R. Groves.

Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows.

Formally, there are sixteen stages – or contemplations – of ānāpānasati.

Formally, Mbenga – Mbuti Pygmy music consists of at most only four parts, and can be described as an, " ostinato with variations ," or similar to a passacaglia, in that it is cyclical.

Formally, the complexity class MA is the set of decision problems that can be decided in polynomial time by an Arthur – Merlin protocol where Merlin's only move precedes any computation by Arthur.

Formally, he says, the piece consists of two parts of nearly equal length, the end of the first section being bars 24 – 28 ( p. 77 ).

Formally trained specialists recognized by the American Dental Association undergo a minimum of 2 – 3 years full-time rigorous education program after dental school graduation.

Formally, the issue is that interfertile " able to interbreed " is not a transitive relation – if A can breed with B, and B can breed with C, it does not follow that A can breed with C – and thus does not define an equivalence relation.

Formally, define the set of lines in the plane P as L ( P ); then a rigid motion of the plane takes lines to lines – the group of rigid motions acts on the set of lines – and one may ask which lines are unchanged by an action.

The Knight Foundation ( Formally the Foundation for Law and Government ), offers a possible solution – the " Knight 4000 ".

Formally the algorithm can be described as:

Formally, it is expected that information can not travel faster than the speed of light.

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, in the finite-dimensional case, if the linear map is represented as a multiplication by a matrix A and the translation as the addition of a vector, an affine map acting on a vector can be represented as

Formally, the theorem can be stated as follows:

Formally, a decision problem is P-complete ( complete for the complexity class P ) if it is in P and that every problem in P can be reduced to it by using an appropriate reduction.

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 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, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

Formally, a Menger sponge can be defined as follows:

Formally, a Coxeter group can be defined as a group with the presentation

Formally, the problem can be stated as follows: given a desired property, expressed as a temporal logic formula p, and a structure M with initial state s, decide if.

Formally, the poem can be understood as the combination of two sonnets, though the spacing of the stanzas is irregular.

Formally, the mutual information of two discrete random variables X and Y can be defined as:

Formally, a state space can be defined as a tuple where:

Formally, a system is said to be observable if, for any possible sequence of state and control vectors, the current state can be determined in finite time using only the outputs ( this definition is slanted towards the state space representation ).

Formally, the definition only requires some invertibility, so we can substitute for Q any matrix M whose eigenvalues do not include − 1.

Formally, the Calvinist position can be expressed this way:

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.