We begin with the abstract characterization of C *- algebras given in the 1943 paper by Gelfand and Naimark.

Instead of notating musical ideas on paper with the symbols of solfege and entrusting their realization to well-known instruments, the question was to collect concrete sounds, wherever they came from, and to abstract the musical values they were potentially containing " ( Reydellet 1996, 10 ).

Such articles begin with an abstract, which is a one-to-four-paragraph summary of the paper.

One innovative construction involved attaching a kaleidoscope made from a toilet paper roll to a camera lens with cardboard and tape and setting the resulting abstract images to music.

Jean Arp / Hans Arp ( 16 September 1886 – 7 June 1966 ) was a German-French, or Alsatian, sculptor, painter, poet and abstract artist in other media such as torn and pasted paper.

Illustrating S pneumoniaes plasticity, the abstract of Griffith's paper reports, " The S form of Type I has been produced from the R form of Type II, and the R form of Type I has been transformed into the S form of Type II ".

The paper is in Japanese only, except for the abstract.

" Closed Architectures for Content Distribution ," Japan Media Review ( University of Southern California, Annenberg School for Communication ); Yale University Conference ( 2004 ), " Reproduction in Modern Japan " -- paper abstract

Davison created abstract collages from torn and cut coloured paper which, Hirst said, " blew me away ", and which he modelled his own work on for the next two years.

* Transparent-Mode Control Procedures for Data Communication a paper from 1965 ; its abstract carries an early example of usage in IT field.

Its permanent collection contains primarily abstract expressionist paintings, works on paper, and an outdoor sculpture garden that began in 1966.

From the abstract: " This paper advances a ' pyramidal parametric ' prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images.

In Mémoire sur la résolution des équations ( 1771 ) he reported on symmetric functions and solution of cyclotomic polynomials ; this paper anticipated later Galois theory ( see also abstract algebra for the role of Vandermonde in the genesis of group theory ).

For each abstract returned, links are provided to other papers in the database which are referenced, and which cite the paper, and a link is provided to a preprint, where one exists.

When used, an abstract always appears at the beginning of a manuscript or typescript, acting as the point-of-entry for any given academic paper or patent application.

An abstract may act as a stand-alone entity instead of a full paper.

It is commonly surmised that one must not base reference citations on the abstract alone, but the entire merits of a paper.

Papers are usually submitted using an online abstract or paper management service.

Referring to a joint paper with Samuel Eilenberg that introduced the notion of a " category " in 1942, Saunders Mac Lane wrote the subject was ' then called " general abstract nonsense "'.

The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and A. Shapiro.

His paper " Artificial Evolution for Computer Graphics " described the application of genetic algorithms to generate abstract 2D images from complex mathematical formulae, evolved under the guidance of a human.

At first they stayed in the King's Hotel, Shanklin, and on 30 July Darwin began writing an " abstract " of his book on Natural Selection, planning a short paper in response to Hooker's urging to publish a scientific paper in the Linnean journal.

In July 2012, Slava Turyshev et al had a paper published in the Physical Review Letters that explained the anomaly ( abstract ) ( emphasis added ):

After a year in a studio on Sheridan Square, having married an American girl who was a native of Virginia, Helion moved to a village in the Blue Ridge mountains, where he produced some of the most imposing of his abstract canvases.

What I have observed time and time again is a process of integration, integration that begins as abstract design and gradually takes on recognizable form ; ;

Cubism, in its 1911-1912 phase ( which the French, with justice, call `` hermetic '' ) was on the verge of abstract art.

but he believed in the Jew-as-enemy in a kind of abstract, theological way, like a member of a cult speculating on the nature of things.

An abstract describes a chain of transfers from owner to owner and any agreements by former owners that are binding on later owners.

Van Emde Boas observes " even if we base complexity theory on abstract instead of concrete machines, arbitrariness of the choice of a model remains.

(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

An abstract data type is defined indirectly, only by the operations that may be performed on it and by mathematical constraints on the effects ( and possibly cost ) of those operations.

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.

An abstract data type is defined as a mathematical model of the data objects that make up a data type as well as the functions that operate on these objects.

Imperative ADT definitions often depend on the concept of an abstract variable, which may be regarded as the simplest non-trivial ADT.

The oldest known physical representations identified as symbols for abstract concepts are abstract engravings found on two pieces of ochre in Blombos Cave, South Africa, in 2001.

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.

An abstraction can be seen as a process of mapping multiple different pieces of constituent data to a single piece of abstract data based on similarities in the constituent data, for example many different physical cats map to the abstraction " CAT ".

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

I put abstract feelings on the same level as abstract thoughts.

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order ( the axiom of commutativity ).

The album features his interaction with students at Fresno State College ( now California State University, Fresno ) on such topics as " sensitivity training ," " humanitarianism ," " abstract art " ( Capp hated it ), and of course, " student protest.

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.

The differential operator must be understood to be an abstract operator, acting on kets, that has the effect of differentiating wavefunctions once the expression is projected into the position basis: