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The definition works without any changes if instead of vector spaces over a field F, we use modules over a commutative ring R. It also can be easily generalized to n-ary functions, where the proper term is multilinear.
Some Related Sentences
definition and works
Philosophical aesthetics has not only to speak about art and to produce judgments about art works, but has also to give a definition of what art is.
This definition was proposed by Justus von Liebig circa 1838, based on his extensive works on the chemical composition of organic acids.
However, this definition only works well for substances that are composed of molecules, which is not true of many substances ( see below ).
While the specific definition has changed over time, modern usage refers to a typically non-realistic or semi-realistic drawing or painting intended for satire, caricature, or humor, or to the artistic style of such works.
The definition offered by the Oxford English Dictionary incorporates suffering as a necessary condition, with " the painless killing of a patient suffering from an incurable and painful disease or in an irreversible coma ", and this approach can be seen as a part of other works, such as Marvin Khol and Paul Kurtz's " a mode or act of inducing or permitting death painlessly as a relief from suffering ".
The term covers large paintings in oil on canvas or fresco produced between the Renaissance and the late 19th century, after which the term is generally not used even for the many works that still meet the basic definition.
This definition excludes any works that are the result of community creativity, for example Native American songs and stories ; current legislation does not recognize the uniqueness of indigenous cultural ' property ' and its ever-changing nature.
The absolute definition of morality in wuxia is understandably a reaction to the real world where it is not quite so clear what or who is purely good or otherwise, consider the context and the historicity of Hong Kong at the time of Louis Cha's works.
This is sometimes used as the definition of kurtosis in older works, but is not the definition used here.
In these contexts, libre encompasses the essential freedoms defined in the free software definition, and is used to describe works which may be used, modified, copied and shared without permission from the copyright holder.
The concept of libre works arose with Richard Stallman ’ s description of free software in 1985 and was codified in the 1986 free software definition.
Significantly, this definition of libre open access covered works for which any amount of permissions restrictions had been lifted.
However, the standard definition of libre requires that a work be free from a particular set of permission restrictions ; some works that qualify as libre open access would not qualify as libre ( for example, those with a Creative Commons NonCommercial or NoDerivatives licence term ).
We can solve both problems using a more abstract definition of the exponential map that works for all Lie groups, as follows.
The classical definition of probability works well for situations with only a finite number of equally-likely outcomes.
" However, most of the essential features of the modern definition are present in the works of Plato, Aristotle, and Polybius.
" If Kahnweiler considers Cubism as Picasso and Braque ," writes Daniel Robbins, " our only fault is in subjecting other Cubists ' works to the rigors of that limited definition.
Before the definition of the genre of fantasy, many works that would now be classified as fantasy were termed " fairy tales ", including Tolkien's The Hobbit, George Orwell's Animal Farm, and L. Frank Baum's The Wonderful Wizard of Oz.
This solution works even with definition 2, as long as we also know the being is essentially omnipotent rather than accidentally so.
It was Contarini who led to the stating of a definition in connection with the article of justification in which occurs the famous formula " by faith alone are we justified ," with which was combined, however, the Roman Catholic doctrine of good works.
definition and without
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.
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.
In some cases, one might like to have a direct definition of the cotangent space without reference to the tangent space.
Pope Paul VI spoke of it as " a profession of faith, ... a creed which, without being strictly speaking a dogmatic definition, repeats in substance, with some developments called for by the spiritual condition of our time, the creed of Nicea, the creed of the immortal tradition of the holy Church of God "
" is great enough to cast doubt on whether any strictly linguistic definition, without a socio-cultural approach, is possible.
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.
Rummel presents his definition without referencing any previous uses, but the term democide was defined and used in English more than 40 years earlier by Theodore Abel.
Therefore an ordination ceremony that concerns only the individual himself does not, they say, correspond to the definition of an ordination and is without effect.
The Roman Catholic Church does not consider the validity of an ecumenical council's teaching to be in any way dependent on where it is held or on the granting or withholding of prior authorization or legal status by any state, in line with the attitude of the 5th-century bishops who " saw the definition of the church's faith and canons as supremely their affair, with or without the leave of the Emperor " and who " needed no one to remind them that Synodical process pre-dated the Christianisation of the royal court by several centuries ".
The word " forest " comes from Middle English forest, from Old French forest ( also forès ) " forest, vast expanse covered by trees "; first introduced in English as the word for wild land set aside for hunting without the necessity in definition for the existence of trees ( James 1981 ; Muir 2000, 2008 ).
Some jurisdictions classify as violent certain property crimes involving a strong likelihood of psychological trauma to the property owner ; for example, Virginia treats both common-law burglary ( the breaking and entering of a dwelling house at night with the intent to commit larceny, assault and battery, or any felony therein ) and statutory burglary ( breaking and entering with further criminal intent but without the dwelling-house or time elements, such that the definition applies to break-ins at any time and of businesses as well as of dwelling houses ) as felonies.
The FileMan utilities allow the definition of data structures, menus and security, reports, and forms, allowing someone to set up applications without tremendous experience in the MUMPS programming language.
A group action is an extension to the definition of a symmetry group in which every element of the group " acts " like a bijective transformation ( or " symmetry ") of some set, without being identified with that transformation.
Determining the presence of both parts of this definition is not always straightforward, as hypoglycemic symptoms and effects are vague and can be produced by other conditions ; people with recurrently low glucose levels can lose their threshold symptoms so that severe neuroglycopenic impairment can occur without much warning, and many measurement methods ( especially glucose meters ) are imprecise at low levels.
In fact, a successful definition of the hawala system that is used is ‘ money transfer without money movement ’.
In this definition, references to the way or ways in which an offence is triable are to be construed without regard to the effect, if any, of section 22 of the Magistrates ' Courts Act 1980 on the mode of trial in a particular case.
Controversy has arisen over whether the usage of the term jihad without further explanation refers to military combat, and whether some have used confusion over the definition of the term to their advantage.
The Canon of the New Testament, like that of the Old, is the result of a development, of a process at once stimulated by disputes with doubters, both within and without the Church, and retarded by certain obscurities and natural hesitations, and which did not reach its final term until the dogmatic definition of the Tridentine Council.
The definition of convergence via nets is important in topology, where preorders cannot be replaced by partially ordered sets without losing important features.
Wittgenstein's point is not that it is impossible to define " game ", but that we don't have a definition, and we don't need one, because even without the definition, we use the word successfully.