Part 1, below describes this abstract model by spelling out its assumptions.

The term " applied mathematics " also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract.

It describes the relationship between the fundamental objects of physical reality and those of everyday experience as well as those of a more abstract social nature.

While the first factor, which describes the bulk of the variation in a set of data, is more likely to represent something objectively real, subsequent factors become more and more abstract.

Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds, e. g., in the Hamiltonian formulation of classical mechanics, which provides one of the major motivations for the field: The set of all possible configurations of a system is modelled as a manifold, and this manifold's cotangent bundle describes the phase space of the system.

In optics, shot noise describes the fluctuations of the number of photons detected ( or simply counted in the abstract ) due to their occurrence independent of each other.

The abstract of a U. S. report describes what happened:

Thus, unlike, for example, Dungeons and Dragons, Rolemaster describes wounds not only in the number of points of damage dealt ( which are then subtracted from an abstract pool of ' Hit Points '), but with specific details of the injury inflicted.

Market systems are more abstract than their application to any one use, and typically a ' system ' describes a protocol of offering or requesting things for sale.

It almost inevitably describes conduct in the abstract, not by reference to the character of the persons performing it.

* Mathematics describes abstract structures: on the other hand, there are areas of pure mathematics which deal with abstract structures, which have no known physical counterparts at all.

When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences ( microscopy ) or theories ( microphysics, statistical physics ) considering objects of geometric lengths smaller than one millimeter.

Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi about whether the celestial spheres are real, concrete physical bodies or " merely the abstract circles in the heavens traced out … by the various stars and planets.

In A House of Her Own, her 1997 biography of Sage, Judith Suther describes these works as “ experimental abstract compositions .”

The abstract superclass of all metaclasses is, which describes the general nature of classes.

* Relational data model ( if applicable ): A data model is an abstract model that describes how data is represented and used.

; as an abstract form that describes perfectly the properties of the physical world.

' feel smart " generally hosts a " Cocktail Conversations " article which describes a definite difference between terms, objects, persons and abstract views which are normally considered to be the same.

Although the objectives are expressed in somewhat abstract terms, they are underpinned by actions which concentrate on the creation of links between people, institutions and countries in education and training – what the programme describes as the " European Dimension " of education and training.

The term " abstract of judgment " may be used in a generic sense to describe a condensed summary of a court case, but it is chiefly used in a technical sense to describe a document produced by a court which describes the judgment rendered in a case.

Critic Alex Henderson describes the band's music as a " mildly avant-garde blend of jazz, rock and funk draws on a wide variety of influences ... Often quirky, eccentric and abstract, JFJO favors an inside / outside approach but is usually more inside than outside.

In 2008, the lighthouse was replaced with what the university describes as an ' abstract, timeless image ' of water lillies.

In this article he describes the difference between the figurative art he was making and the more fashionable abstract art or representational art.

Details of these invasions are abstract, as it is nearly impossible to reconstruct the happenings, due to the chain of conflicts initiated by the Herulians in 268.

More generally, homological algebra includes the study of chain complexes in the abstract, without any reference to an underlying space.

Applications of chain complexes usually define and apply their homology groups ( cohomology groups for cochain complexes ); in more abstract settings various equivalence relations are applied to complexes ( for example starting with the chain homotopy idea ).

In other cases, the chain of title is established by an abstract of title, sometimes, although not always, certified by an attorney.

In abstract algebra, an Artinian ring is a ring that satisfies the descending chain condition on ideals.

In abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules.

In abstract algebra, an Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially ordered by inclusion.

Gordon was born in, the son of Marjorie Minkin, an abstract painter, and Robert Gordon, founder and former President and CEO of New England convenience store chain Store 24.

In abstract algebra, especially in the area of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a stabilizer chain.

As one of the 2011 Artists in Residence, she utilized fallen logs, in a variety of species, and a chain saw to create these abstract sculptures.

In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded algebra with an added chain complex structure that respects the algebra structure.

Prisoners of a chain gang move powerfully across the stage creating an expressive narrative through abstract movements of physical labor.

And, he added: `` During the many months in prison camp, all abstract images vanished from my mind ''.

In much the same way, we recognize the importance of Shakespeare's familarity with Plutarch and Montaigne, of Shelley's study of Plato's dialogues, and of Coleridge's enthusiastic plundering of the writings of many philosophers and theologians from Plato to Schelling and William Godwin, through which so many abstract ideas were brought to the attention of English men of letters.

( We abstract here from technological progress and assume that prices of all other products change proportionately.

In this model, we abstract from all non-wage sources of cost changes, so that the `` public-limit price '' only rises as the wage rate rises.

The union vigorously demands wage increases from productivity increases, and wage increases to offset cost-of-living increases, but we abstract from these forces here.

One of these days, I'm going to organize a gigantic exhibition that will span everything that's being painted these days, from extreme abstract expressionism to extreme photorealism, and then you'll be able to see at a glance how much artists have in common with each other.

Sculpture and performance art are prominent, and abstract and partially abstracted forms are valued, and were valued long before influence from the Western tradition began in earnest.

For example, an abstract stack data structure could be defined by three operations:, that inserts some data item onto the structure,, that extracts an item from it ( with the constraint that each pop always returns the most recently pushed item that has not been popped yet ), and, that allows data on top of the structure to be examined without removal.

xiii, " Cum ad Sacrosanctae Romanae Ecclesiae ") prescribes their work, determines how much they may charge for their labour, fixes a certain tax for an abstract or abridgment of twenty-five words, or their equivalent, 150 letters, forbids them to charge more, even though the abstract goes over twenty-five words but less than fifty words, enacts that the basis of the tax is the labour employed in writing, expediting, etc., the Bulls, and by no means the emoluments accruing to the recipient of the favour or benefice conferred by the Bull, and declares that whoever shall charge more than the tax fixed by him shall be suspended for six months from office, and upon a second violation of the law, shall be deprived of it altogether, and if the delinquent be an abbreviator, he shall be excommunicated.

Although the description sitting-on ( graph 1 ) is more abstract than the graphic image of a cat sitting on a mat ( picture 1 ), the delineation of abstract things from concrete things is somewhat ambiguous ; this ambiguity or vagueness is characteristic of abstraction.

Thus something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach ( 1979 ):

This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between " abstract " and " concrete ".

Artwork that reshapes the natural world for expressive purposes is called abstract ; that which derives from, but does not imitate a recognizable subject is called nonobjective abstraction.

Bayesian probability interprets the concept of probability as " an abstract concept, a quantity that we assign theoretically, for the purpose of representing a state of knowledge, or that we calculate from previously assigned probabilities ," in contrast to interpreting it as a frequency or " propensity " of some phenomenon.

This realization led Beck to begin viewing emotional reactions as resulting from cognitions, rather than understanding emotion within the abstract psychoanalytic framework.

A term dating from the 1940s, " general abstract nonsense ", refers to its high level of abstraction, compared to more classical branches of mathematics.

Such a pair of adjoint functors typically arises from a construction defined by a universal property ; this can be seen as a more abstract and powerful view on universal properties.

In cognitive linguistics, abstract concepts are transformations of concrete concepts derived from embodied experience.

The abstract concepts are now considered to be totally autonomous, even though they originated from the process of abstracting or taking away qualities from perceptions until only the common, essential attributes remained.