An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare their lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths because interferometer errors were eliminated.

The structural definition of the word skyscraper was refined later by architectural historians, based on engineering developments of the 1880s that had enabled construction of tall multi-storey buildings.

This standard has enabled wide scale deployment of high definition desktop videoconferencing and made possible new architectures, which reduces latency between the transmitting sources and receivers, resulting in more fluid communication without pauses.

The Charter and its definition of crimes against peace was also the basis of the Finnish law, approved by the Finnish parliament on 11 September 1945, that enabled the war-responsibility trials in Finland.

Van Grembergen and De Haes ( 2009 ) focus on enterprise governance of IT and define this as " an integral part of corporate governance and addresses the definition and implementation of processes, structures and relational mechanisms in the organization that enable both business and IT people to execute their responsibilities in support of business / IT alignment and the creation of business value from IT enabled investments ".

This shuffle also enabled 36. 1 to eventually air programming in high definition beginning February 7, 2011, a move delayed by budget concerns.

The practical definition may lead to confusion with the definition of a coulomb ( i. e., 1 amp-second ), but in practical terms this means that measures of a constant current ( e. g., the nominal flow of charge per second through a simple circuit ) will be defined in amperes ( e. g., " a 20 mA circuit ") and the flow of charge through a circuit over a period of time will be defined in coulombs ( e. g., " a variable-current circuit that flows a total of 10 coulombs over 5 seconds ").

William Camden provided a definition of " Anagrammatisme " as " a dissolution of a name truly written into his letters, as his elements, and a new connection of it by artificial transposition, without addition, subtraction or change of any letter, into different words, making some perfect sense applyable ( i. e., applicable ) to the person named.

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Meteorologists ( and most of the temperate countries in the southern hemisphere ) use a definition based on months, with autumn being September, October and November in the northern hemisphere, According to United States tradition, autumn runs from the day after Labor Day ( i. e. the Tuesday following the first Monday of September ) through Thanksgiving ( i. e. the fourth Thursday in November ), after which the holiday season that demarcates the unofficial beginning of winter begins.

A more abstract definition, which is equivalent but more easily generalized to infinite-dimensional spaces, is to say that bras are linear functionals on kets, i. e. operators that input a ket and output a complex number.

This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power one temporarily labels the term X with an index i ( running from 1 to n ), then each subset of k indices gives after expansion a contribution X < sup > k </ sup >, and the coefficient of that monomial in the result will be the number of such subsets.

These categories surely have some objects that are " special " in a certain way, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered to be atomic, i. e., we do not know whether an object A is a set, a topology, or any other abstract concept – hence, the challenge is to define special objects without referring to the internal structure of those objects.

Was the notion of " effective calculability " to be ( i ) an " axiom or axioms " in an axiomatic system, or ( ii ) merely a definition that " identified " two or more propositions, or ( iii ) an empirical hypothesis to be verified by observation of natural events, or ( iv ) or just a proposal for the sake of argument ( i. e. a " thesis ").

: Turing's thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i. e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.

The same definition is used for any consistent norm, i. e. one that satisfies

The law primarily uses the notion of the consumer in relation to consumer protection laws, and the definition of consumer is often restricted to living persons ( i. e. not corporations or businesses ) and excludes commercial users.

According to the logical positivists, unless a statement could be verified by experience, or else was true or false by definition ( i. e. either tautological or contradictory ), then it was meaningless ( this is a summary statement of their verification principle ).

A nominal definition is the definition explaining what a word means, i. e. which says what the ' nominal essence ' is, and is definition in the classical sense as given above.

However, whether this is possible depends on how the field of complex numbers is derived in the first place: it may not be possible to distinguish a complex number from its conjugate ( say, 3 + i from 3-i ), since it is impossible to find a property of one that is not also a property of the other, without falling back on the underlying set-theoretic definition.

( Form of Content, that Louis Hjelmslev distinguished from Form of Expression ) than how the word " house " may be tied to a certain image of a traditional house ( i. e. the relationship between signifier and signified ) with each term being established in reciprocal determination with the other terms than by an ostensive description or definition: when can we talk about a " house " or a " mansion " or a " shed "?

The main concept, however, common to all idealist epistemologies is the centrality of Reason: ( i. e.: ' Reason ' with a capital ' R '): a priori Reason: Knowledge can only be, ultimately, a product of the mind and is therefore, by definition, ' ideal '.

There are two related definitions of entropy: the thermodynamic definition and the statistical mechanics definition.

The thermodynamic definition was developed in the early 1850s by Rudolf Clausius and essentially describes how to measure the entropy of an isolated system in thermodynamic equilibrium.

Boltzmann showed that this definition of entropy was equivalent to the thermodynamic entropy to within a constant number which has since been known as Boltzmann's constant.

In summary, the thermodynamic definition of entropy provides the experimental definition of entropy, while the statistical definition of entropy extends the concept, providing an explanation and a deeper understanding of its nature.

The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and pV work in fluids for open systems:

Lastly, and most importantly, the formal definition of entropy of a thermodynamic system from a statistical perspective is called statistical entropy, and is defined as:

For a thermodynamic account of a process in terms of the entropies of small local regions, the definition of entropy should be such as to ensure that the second law of thermodynamics applies in each small local region.

In thermodynamic equilibrium, a system's properties are, by definition, unchanging in time.

James Clerk Maxwell | Maxwell's sketch of the lines of constant temperature and pressure, made in preparation for his construction of a Maxwell's thermodynamic surface | solid model based on Gibbs's definition of a thermodynamic surface for water

However a more theoretical thermodynamic definition of an ideal solution is one in which the chemical potential of each component is given by the above formula.

The thermodynamic definition of temperature, due to Nicolas Léonard Sadi Carnot, refers to heat " flowing " between " infinite reservoirs ".

When comparing the performance of heat pumps, it is best to avoid the word " efficiency " which has a very specific thermodynamic definition.

The first law of thermodynamics provides the basic definition of thermodynamic energy, also called internal energy, associated with all thermodynamic systems, but unknown in mechanics, and states the rule of conservation of energy in nature.

However, based on the entropy, the second law permits a definition of the absolute, thermodynamic temperature, which has its null point at absolute zero.

Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation, aka " master equation " ( always true for reversible or irreversible processes ):

Prigogine is best known for his definition of dissipative structures and their role in thermodynamic systems far from equilibrium, a discovery that won him the Nobel Prize in Chemistry in 1977.

The paradox is resolved by understanding temperature through its more rigorous definition as the tradeoff between energy and entropy, with the reciprocal of the temperature, thermodynamic beta, as the more fundamental quantity.

Milne ( 1928 ), thinking about stars, gave a definition of ' local thermodynamic equilibrium ' in terms of the thermal radiation of the matter in each small local ' cell '.

Another definition of the Bessel function, for integer values of, is possible using an integral representation:

Their principal claim relates to the definition of who is a citizen of Ivory Coast ( and so who can stand for election as president ), voting rights and their representation in government in Abidjan.

For the mathematical definition, see Decimal representation.

The ( unique ) representable functor F: → is the Cayley representation of G. In fact, this functor is isomorphic to and so sends to the set which is by definition the " set " G and the morphism g of ( i. e. the element g of G ) to the permutation F < sub > g </ sub > of the set G. We deduce from the Yoneda embedding that the group G is isomorphic to the group

In typography, a glyph has a slightly different definition: it is " the specific shape, design, or representation of a character ".

The concrete definition given above is easy to work with, but has some minor problems: to use it we first need to represent a Lie group as a group of matrices, but not all Lie groups can be represented in this way, and it is not obvious that the Lie algebra is independent of the representation we use.

The definition above is easy to use, but it is not defined for Lie groups that are not matrix groups, and it is not clear that the exponential map of a Lie group does not depend on its representation as a matrix group.

Under this definition, a simple representation of the real number e is:

IEEE 754 NaNs are represented with the exponential field filled with ones ( like infinity values ), and some non-zero number in the significand ( to make them distinct from infinity values ); this representation allows the definition of multiple distinct NaN values, depending on which bits are set in the significand, but also on the value of the leading sign bit ( not all applications are required to provide distinct semantics for those distinct NaN values ).

For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e. g., the closed graph theorem in functional analysis.

Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory:

Identifiable examples become numerous in the late Middle Ages, but if the definition is extended the first was by the Egyptian Pharaoh Akhenaten's sculptor Bak, who carved a representation of himself and his wife Taheri c. 1365 BC.

By choosing a = 0, this formula gives both an integral and a series representation for a function that interpolates the harmonic numbers and extends a definition to the complex plane.

Under this definition, encapsulation means that the internal representation of an object is generally hidden from view outside of the object's definition.

It represents a midpoint between what he sees as the two " great discontinuities " in art history, the classical and the modern: " Perhaps there exists, in this painting by Velázquez, the representation as it were of Classical representation, and the definition of the space it opens up to us ... representation, freed finally from the relation that was impeding it, can offer itself as representation in its pure form.

First, to prove that x is strictly positive, we insert the above series representation of e into the definition of x and obtain

A categorical definition of a quiver representation can also be given.

Now by applying the Riesz representation theorem we can identify H < sup >*</ sup > with H. Therefore the definition of rigged Hilbert space is in terms of a sandwich:

This definition takes the representation of the sentence into account, but it is problematic for several reasons.

Some have gone so far as to suggest that images are best understood to be, by definition, a form of inner, mental or neural representation ; in the case of hypnagogic and hypnapompic imagery, it is not representational at all.