But these are physical representations of the corresponding mathematical entities ; the line and the curve are idealized concepts whose width is 0 ( see Line ).

Most free verse, for example, self-evidently continues to observe a convention of the poetic line in some sense, at least in written representations, though retaining a potential degree of linkage, however nebulous, with more traditional forms.

There are more advanced representations such as Log Area Ratios ( LAR ), line spectral pairs ( LSP ) decomposition and reflection coefficients.

Following representations by the council in 1867 the Midland promised to build a through line within two years.

Some standards which introduce their own representations for line and paragraph control ( for example HTML ) and many programming languages treat carriage return and line feed as whitespace.

Alternative conventions to node-link diagrams include adjacency representations such as circle packings, in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions ; intersection representations in which vertices are represented by non-disjoint geometric objects and edges are represented by their intersections ; visibility representations in which vertices are represented by regions in the plane and edges are represented by regions that have an unobstructed line of sight to each other ; confluent drawings, in which edges are represented as smooth curves within mathematical train tracks ; and visualizations of the adjacency matrix of the graph.

London Transport ( later London Underground Ltd ) had made repeated representations to the government to close the line, but each was refused as there was no alternative mode of transport between Epping and Ongar.

* Constructing digitized representations of objects, with the emphasis on precision and efficiency ( either by means of synthesis, see, for example, Bresenham's line algorithm or digital disks, or by means of digitization and subsequent processing of digital images ).

Let us extend to compact Lie group and consider " integrable " orbits for which the symplectic structure comes from a line bundle then quantization leads to the irreducible representations of.

For example Anderson ( 1997 ) stated more generally: " diagrams are pictorial, yet abstract, representations of information, and maps, line graphs, bar charts, engineering blueprints, and architects ' sketches are all examples of diagrams, whereas photographs and video are not ".

According to some genealogies they had an only son, who inherited his mother's titles and / or representations and solely his father's Italian title, the one which could only be used through male line, named Manuel Luis.

Explicit representations for the cylinder sets can be gotten by noting that the string of values corresponds to a q-adic number, and thus, intuitively, the product topology resembles that of the real number line.

Smyth's book ' Milestones ' 1979 gives his version in which he relates that he had made representations to General Hutton 10 days previously recommending a withdrawal to the West bank of the Sittang River thus permitting a strong defence line to be established.

These representations are realized in the spaces of global sections of holomorphic line bundles on the flag manifold of the group.

Scan lines are important in representations of image data, because many image file formats have special rules for data at the end of a scan line.

Prior to opening day when the line was being inspected the mayor made representations for a new station some half mile to the north between Spring Road and Woodbridge Road.

By definition the representations are realised on L < sup > 2 </ sup > sections of line bundles on G / B = S < sup > 2 </ sup >, the Riemann sphere.

Menu bars are typically present in graphical user interfaces that display documents and representations of files in windows and windowing systems but menus can be used as well in command line interface programs like text editors or filemanagers where drop-down menu is activated with shortcut key or combination.

The next phase was from 1963 – 1967, when the rapido product line begins to swing toward scale representations of the trains.

The other representations are defined similar to how the projective Weierstrass curve follows from the affine.

In simple cases, it relates l-adic representations of the étale fundamental group of an algebraic curve to objects of the derived category of l-adic sheaves on the moduli stack of vector bundles over the curve.

In addition to the single-character representations U + 3031 VERTICAL KANA REPEAT MARK and U + 3032 VERTICAL KANA REPEAT WITH VOICED SOUND MARK, Unicode provides the half-character versions U + 3033 VERTICAL KANA REPEAT MARK UPPER HALF, U + 3034 VERTICAL KANA REPEAT WITH VOICED SOUND MARK UPPER HALF and U + 3035 VERTICAL KANA REPEAT MARK LOWER HALF, which can be stacked to render both voiced and unvoiced repeat marks:

Although scent trademarks ( also known as olfactory trademarks or smell trademarks ), are sometimes specifically mentioned in legislative definitions of " trademark ", it is often difficult to register such marks if consistent, non-arbitrary and meaningful graphic representations of the marks cannot be produced.

The case illustrates difficulties with the graphical representation of scent marks, as the ECJ held that these representations, whether individually or collectively, could not satisfy this requirement.

If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

These representations rely on presenting scenes directly to the eye for their own visible sake.

The fact that the name occurs on these gems in connection with representations of figures with the head of a cock, a lion, or an ass, and the tail of a serpent was formerly taken in the light of what Irenaeus says about the followers of Basilides:

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.

File: Mosaic2-plw. jpg | Room 49-Hinton St Mary Mosaic, Roman Britain, circa 4th century ( one of the earliest representations of Christ and the only such portrait on a mosaic floor from anywhere in the Roman Empire )

At the time, Skinner's behaviorist paradigm dominated psychology: Most psychologists focused on functional relations between stimulus and response, without positing internal representations.

In major modern economies such as those of the United States or the Euro Zone, most money is electronic, but the " currency " of these polities may, depending on context, include all money or just specie ( i. e., various physical representations of money ).

According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".

As various permanent representations evolved, usually on a treaty basis between two powers, they were frequently staffed by relatives of the sovereign or high-ranking nobles.

However, because the SEM image relies on surface processes rather than transmission, it is able to image bulk samples up to many centimetres in size and ( depending on instrument design and settings ) has a great depth of field, and so can produce images that are good representations of the three-dimensional shape of the sample.

In 1896, Munch moved to Paris, where he focused on graphic representations of his " Frieze of Life " themes.

This is then amplified by closer detailed live action representations of stations on " The Primrose Path ".

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

Manual alphabets based on the Arabic alphabet, the Ethiopian syllabary and the Korean hangul syllabary-alphabet use handshapes that are more or less iconic representations of the characters in the writing system.

Some manual representations of non-Roman scripts such as Chinese, Japanese, Devanagari, Hebrew, Greek, Thai and Russian alphabets are based to some extent on the one-handed Latin alphabet described above.

A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra ( which is specified by a coupling constant for each factor ), a Higgs sector consisting of a number of scalar fields taking on values within real / complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group.

Eckert's publication of Punched Card Methods in Scientific Computation in 1940, described punch card techniques sufficiently advanced to solve some differential equations or perform multiplication and division using floating point representations, all on punched cards and unit record machines.

There are early representations and reports of ice hockey-type games being played on ice in the Netherlands, and reports from Canada from the beginning of the nineteenth century, but the modern game was initially organized by students at McGill University, Montreal in 1875 who, by two years later, codified the first set of ice hockey rules and organized the first teams.

At the other end of the scale, there were representations from countries and areas where a detailed and sophisticated classification was irrelevant, but which nevertheless needed a classification based on the ICD in order to assess their progress in health care and in the control of disease.

Often artistic representations of female sexuality suggest trends or ideas on broad scales, giving historians clues as to how widespread or accepted erotic relationships between women were.

Weyl brought the early period of the development of the theory of Lie groups to fruition, for not only did he classify irreducible representations of semisimple Lie groups and connect the theory of groups with quantum mechanics, but he also put Lie's theory itself on firmer footing by clearly enunciating the distinction between Lie's infinitesimal groups ( i. e., Lie algebras ) and the Lie groups proper, and began investigations of topology of Lie groups ( Borel ( 2001 ), ).