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

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 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, 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 declared on October 9, 1970, the Khmer Republic was a right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak that took power in the March 18, 1970 coup against Prince Norodom Sihanouk, then the country's head of state.

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 Cisalpine Republic was an independent state allied with France, but the treaty of alliance established the effective subalternity of the new republic to France.

Formally a member of the country's collective head of state and, as president of parliament, holder of the third-highest office, he was left with little political influence.

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 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, a deterministic finite automaton may be defined by the tuple where is the set of states of the automaton, is the set of input symbols, is the transition function that takes a state and an input symbol to a new state, is the initial state of the automaton, and is the set of accepting or final states of the automaton.

Formally known as the Constitution of the Republic of Poland (), it replaced the temporary amendments put into place in 1992 designed to reverse the effects of Communism, establishing the nation as " a democratic state ruled by law and implementing the principles of social justice ".

Formally, it was owned by the PWS state aircraft manufacturer, in fact it was subordinated to the PZL.

Formally, a state is a set of conditions: a state is represented by the set of conditions that are true in it.

Formally, it remained a state of the Holy Roman Empire until its dissolution in 1806.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

Formally, the system is said to have memory.

Formally known as the " Six and A Half Point Pole " form, this is the second to last form of the system.

Formally, a generalised self reproducing system consists

Formally, HPGCC is a cross-compiler ; it compiles code for the ARM-based HP calculators, but runs on a PC rather than the target system.

Formally, an iterated function system is a finite set of contraction mappings on a complete metric space.

Formally, let G be a Coxeter group with reduced root system R and k < sub > v </ sub > a multiplicity function on R ( so k < sub > u </ sub > = k < sub > v </ sub > whenever the reflections σ < sub > u </ sub > and σ < sub > v </ sub > corresponding to the roots u and v are conjugate in G ).

Formally, a squeeze preserves the hyperbolic metric expressed in the form ; in a different coordinate system.

Formally, an Hamiltonian system is a dynamical system completely described by the scalar function, the Hamiltonian.

Formally, a graph rewriting system usually consists of a set of graph rewrite rules of the form, with being called pattern graph ( or left-hand side ) and being called replacement graph ( or right-hand side of the rule ).

Formally, Transnistria has a multi-party system and an unicameral parliament, called the Supreme Council.

Formally, a redistribution of all agents ’ initial endowments of goods among all agents in the system is a core allocation if no group of agents can redistribute their own initial endowments among themselves so as to improve the satisfaction of someone in the group without impairing that of any other in the group.

Formally known as the " Eastern Division of Surrey " or " Surrey Eastern ", it elected two MPs by the bloc vote system.

Formally, a Markov partition is used to provide a finite cover for the smooth system ; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one of the covering sets to another.

Formally system networks correspond to type lattices in formal lattice theory, although they are occasionally erroneously mistaken for flowcharts or directed decision trees.

Formally known as the Federal Reserve Wire Network, Fedwire is a Real Time Gross Settlement Funds Transfer system operated by the United States Federal Reserve Banks that enables financial institutions to electronically transfer funds between its more than 9, 289 participants ( as of March 19, 2009 ).

Formally organized vocational programs supported by federal funds allow high school students to gain experience in a field of work which is likely to lead to a full-time job on graduation.

Formally, a binary operation on a set S is called associative if it satisfies the associative law:

Formally, their designation is the letter Ž and the number.

Formally, a topological space X is called compact if each of its open covers has a finite subcover.

Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ).

Formally, the derivative of the function f at a is the limit

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, the base is known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).

Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.

Formally, a bifunctor is a functor whose domain is a product category.

Formally, a set S is called finite if there exists a bijection

Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map

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, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.

Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.

Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.

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, Φ = kx − ωt is the phase.