This wider definition of Anatolia has gained widespread currency outside of Turkey and has, for instance, been adopted by Encyclopedia Britannica and other encyclopedic and general reference publications.

The 1976 definition of the astronomical unit was incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and " vigorous debate " ensued until in August 2012 the International Astronomical Union adopted the current definition of 1 astronomical unit = 149597870700 meters.

Heschel then goes on to explore the problems of doubts and faith ; what Judaism means by teaching that God is one ; the essence of humanity and the problem of human needs ; the definition of religion in general and of Judaism in particular ; and human yearning for spirituality.

More recent IUPAC recommendations now suggest the newer term " hydronium " be used in favor of the older accepted term " oxonium " to illustrate reaction mechanisms such as those defined in the Brønsted – Lowry and solvent system definitions more clearly, with the Arrhenius definition serving as a simple general outline of acid – base character.

Whenever a confusion between the two kinds of definitions might arise it can be avoided by referring to the more general definition and by reintroducing the erased parameter: writing B < sub > m </ sub >( 0 ) in the first case and B < sub > m </ sub >( 1 ) in the second will unambiguously denote the value in question.

The most basic definition he used to describe a constitution in general terms was " the arrangement of the offices in a state ".

In addition, this article discusses the definition for the more general case of functions between two metric spaces.

Omnivores also consume both animal and non-animal food, and apart from the more general definition, there is no clearly defined ratio of plant to animal material that would distinguish a facultative carnivore from an omnivore, or an omnivore from a facultative herbivore, for that matter.

However, the general definition of a file does not require that its instant size has any real meaning, unless the data within the file happens to correspond to data within a pool of persistent storage.

In theory, general dictionaries are supposed to be semasiological, mapping word to definition, while specialized dictionaries are supposed to be onomasiological, first identifying concepts and then establishing the terms used to designate them.

A definition may be descriptive of the general use meaning, or stipulative of the speaker's immediate intentional meaning.

A descriptive definition can be shown to be " right " or " wrong " by comparison to general usage, but a stipulative definition can only be disproved by showing a logical contradiction.

The four definitions given above are special cases of a more general definition.

There has never been general agreement on the definition of the term.

If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.

This general definition is still in common use.

This definition originally referred to martial courage or excellence but extended to more general moral excellence.

In a more general definition, an acid can be any chemical species capable of binding to electron pairs is called a Lewis acid ; conversely any molecule that tends to donate an electron pair is referred to as a Lewis base.

Then a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.

Spearman named it g for " general factor " and labelled the smaller, specific factors or abilities for specific areas s. In any collection of IQ tests, by definition the test that best measures g is the one that has the highest correlations with all the others.

If the term has nonetheless retained a certain consistency in its use across these fields and would-be movements, it perhaps reflects the word ’ s position in general English usage: though the standard dictionary definition of irreal gives it the same meaning as unreal, irreal is very rarely used in comparison with unreal.

The definition in general is somewhat technical, but in the case of real matrix groups, it can be formulated via the exponential map, or the matrix exponent.

Then is a derivation and is linear, i. e., and, and a Lie algebra homomorphism, i. e.,, but it is not always an algebra homomorphism, i. e. the identity does not hold in general.

This gives a rather large number of different cases to check: there are not only 26 sporadic groups and 16 families of groups of Lie type and the alternating groups, but also many of the groups of small rank or over small fields behave differently from the general case and have to be treated separately, and the groups of Lie type of even and odd characteristic are also quite different.

The general higher rank case consists mostly of the groups of Lie type over fields of characteristic 2 of rank at least 3 or 4.

* Linear algebraic groups ( or more generally affine group schemes ) — These are the analogues of Lie groups, but over more general fields than just R or C. Although linear algebraic groups have a classification that is very similar to that of Lie groups, and give rise to the same families of Lie algebras, their representations are rather different ( and much less well understood ).

The general theory for Lie groups deals with semidirect products of the two types, by means of general results called Mackey theory, which is a generalization of Wigner's classification methods.

Once this geometrical interpretation is understood, it is relatively straightforward to replace U ( 1 ) by a general Lie group.

The above development generalizes in a more-or-less straightforward fashion to general principal G-bundles for some arbitrary Lie group G taking the place of U ( 1 ).

( Lie groups corresponding to a Lie algebra is not unique in general.

In particular, the associative algebra of n × n matrices over a field F gives rise to the general linear Lie algebra The associative algebra A is called an enveloping algebra of the Lie algebra L ( A ).

The Lie bracket is not an associative operation in general, meaning that need not equal.

* The subspace of the general linear Lie algebra consisting of matrices of trace zero is a subalgebra, the special linear Lie algebra, denoted

Lie groups are smooth manifolds and, therefore, can be studied using differential calculus, in contrast with the case of more general topological groups.

* The group GL < sub > n </ sub >( R ) of invertible matrices ( under matrix multiplication ) is a Lie group of dimension n < sup > 2 </ sup >, called the general linear group.

In general, only topological groups having similar local properties to R < sup > n </ sup > for some positive integer n can be Lie groups ( of course they must also have a differentiable structure )

( In general the Lie bracket of a connected Lie group is always 0 if and only if the Lie group is abelian.

* The Lie algebra of the general linear group GL < sub > n </ sub >( R ) of invertible matrices is the vector space M < sub > n </ sub >( R ) of square matrices with the Lie bracket given by

This reduction has been accomplished by the general methods of linear algebra, i.e., by the primary decomposition theorem.

* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).

The eleventh century Persian mathematician Omar Khayyám saw a strong relationship between geometry and algebra, and was moving in the right direction when he helped to close the gap between numerical and geometric algebra with his geometric solution of the general cubic equations, but the decisive step came later with Descartes.

: Without doubt this is the most important work on general algebra that the Annalen has ever published.

Elementary algebra builds on and extends arithmetic by introducing letters called variables to represent general ( non-specified ) numbers.

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

He left school at 15 after an unsuccessful attempt to master algebra ; he then worked at the local general store.

The exponential map from the Lie algebra M < sub > n </ sub >( R ) of the general linear group GL < sub > n </ sub >( R ) to GL < sub > n </ sub >( R ) is defined by the usual power series:

Although Descartes did not pursue the subject, he preceded Leibniz in envisioning a more general science of algebra or " universal mathematics ," as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.

The Stone – Weierstrass theorem generalizes the Weierstrass approximation theorem in two directions: instead of the real interval, an arbitrary compact Hausdorff space X is considered, and instead of the algebra of polynomial functions, approximation with elements from more general subalgebras of C ( X ) is investigated.

Their algebra is formally understood but their general significance is mysterious.