The idea is based on simple principles of projective geometry: moving synchronously and in opposite directions the X-ray tube and the film, which are connected together by a rod whose pivot point is the focus ; the image created by the points on the focal plane appears sharper, while the images of the other points annihilate as noise.

The definition of elliptic curve from algebraic geometry is connected non-singular projective curve of genus 1 with a given rational point on it.

In 1953, Hidehiko Yamabe obtained the final answer to Hilbert ’ s Fifth Problem: a connected locally compact group is a projective limit of a sequence of Lie groups, and if " has no small subgroups " ( a condition defined below ), then G is a Lie group.

More generally, every locally compact, almost connected group is the projective limit of a Lie group.

The four finite volume manifolds with this geometry are: S < sup > 2 </ sup > × S < sup > 1 </ sup >, the mapping torus of the antipode map of S < sup > 2 </ sup >, the connected sum of two copies of 3 dimensional projective space, and the product of S < sup > 1 </ sup > with two-dimensional projective space.

* The connected sum of two projective 3-spaces has a S < sup > 2 </ sup >× R geometry, and is also the connected sum of two pieces with S < sup > 3 </ sup > geometry.

* a connected and projective algebraic group over k.

In particular, projective planes and generalized quadrangles form two classes of graphs studied in incidence geometry which satisfy the axioms of a building, but may not be connected with any group.

According to Kernberg, all ' the primitive defenses, such as splitting, and projective identification, are commonly connected with primitively organized personalities, such as ':

In many cases of interest it suffices to consider representations of covering groups ; for a connected Lie group G, this amounts to studying the representations of the Lie algebra of G. Notable cases of covering groups giving interesting projective representations:

These turn out to be maximal as connected solvable subgroups ( i. e., subgroups with composition series having as factors one-dimensional subgroups, all of which are groups of additive or multiplicative type ); and also minimal such that G / B is a projective variety.

In detail, let X and Y be smooth projective varieties, let be the decomposition of X into connected components, and let d < sub > i </ sub > := dim X < sub > i </ sub >.

The classification of closed surfaces, a foundational and historically significant result in topology, states that any closed surface can be expressed as the connected sum of a sphere with some number of tori and some number of real projective planes.

This generalizes to the notion of abelian scheme ; a group scheme G over a base S is abelian if the structural morphism from G to S is proper and smooth with geometrically connected fibers They are automatically projective, and they have many applications, e. g., in geometric class field theory and throughout algebraic geometry.

In the projective plane, we may no longer define arrangements using sides of lines ( a line in the projective plane does not separate the plane into two distinct sides ), but we may still define the cells of an arrangement to be the connected components of the points not belonging to any line, the edges to be the connected components of sets of points belonging to a single line, and the vertices to be points where two or more lines cross.

A rationally connected variety V is a projective algebraic variety over an algebraically closed field such that through every two points there passes the image of a regular map from the projective line into V. Equivalently, a variety is rationally connected if every two points are connected by a rational curve contained in the variety.

BIND 10 plans to make the data store modular, so that a variety of databases may be connected.

There were a variety of reasons for this failure, many connected to general weaknesses within the organization.

When neurons that are intrinsically rhythmic are connected to each other by excitatory or inhibitory synapses, the resulting networks are capable of a wide variety of dynamical behaviors, including attractor dynamics, periodicity, and even chaos.

This point is intimately connected with a variety of other themes in his later works, especially his investigations of " meaning ".

* ( c ) allows a variety of terminal types and subscriber networks, such as PBXs, local area networks ( LANs ), and controllers, to be connected to the network, and

At the same time, the provinces of Naples, Caserta and in part Salerno, have developed a variety of activities connected to advanced types of services.

Usually connected with Kition in Cyprus, but name appears in other texts with a variety of interpretations.

By the turn of the century the city Neosho was a thriving community connected by three rail lines and exporting a variety of products and agricultural produce.

There were three major grocery stores in Seymour — White's, which was connected with a general store, and owned by Charles White ; the MFA supermarket, which was part of the MFA complex ( feed and agriculture, hardware and groceries ); the MFA general manager was Sherman Eddings, and two of the ladies who worked in the office were Dorothy Herman and Lucille Brown ; and Williams ', which was owned by the Williams family, who also had a variety store.

During World War II, those methods employed earlier in the academic community in this field of research were brought to bear upon a variety of problems connected with the war effort.

Using these cartridge slots, a wide variety of peripherals could be connected.

In terms of international air links with Europe, the country is generally well connected, with daily flights from a variety of European cities, There are also direct flights operated from the main Scottish airports to destinations in North America such as New York, Philadelphia, Toronto, Vancouver and Calgary.

# Streets within the neighborhood form a connected network, which disperses traffic by providing a variety of pedestrian and vehicular routes to any destination.

With a variety of effects units connected to his mixer, Tubby was able to ' play ' the mixing desk like an instrument, bringing instruments and vocals in and out of the mix ( literally ' dubbing ' them ) to create an entirely new genre known as dub music.

While closed to the public the museum's building was used for a variety of purposes connected to the war effort, such as a repair garage for government motor vehicles, a centre for Air Raid Precautions civil defence lectures and a fire fighting training school.

The CRT unit contained the processor, and a large port on the back connected via heavy cable to a disk drive, allowing a wide variety of configurations.

Generally these are taken to be connected ( or irreducible as a variety ) as well.

These two pegs can be connected in two moves in a variety of ways, usually too many for the opponent to block them all.

According to Tibetan tradition, after death and before one's next birth, when one's consciousness is not connected with a physical body, one experiences a variety of phenomena.

The ancient part of the town is situated on a peninsula ( previously an island ) connected to the mainland by a narrow man-made isthmus, and it bears evidence of occupation by a variety of different civilisations over the course of its existence.

The main initial step in calculating étale cohomology groups of a variety is to calculate them for complete connected smooth algebraic curves X over algebraically closed fields k. The étale cohomology groups of arbitrary varieties can then be controlled using analogues of the usual machinery of algebraic topology, such as the spectral sequence of a fibration.

Voir dire is a legal phrase that refers to a variety of procedures connected with jury trials.

Furthermore, there are two special designations connected to a grape variety and a wine style, Vinho Verde Alvarinho and Vinho Verde Alvarinho Espumante.

It is the connected component of the identity in the Picard group of C, hence an abelian variety.

Common examples are the SATA ports in modern computers, which allow a number of hard drives to be connected without the need for a card.

Davidson adds that, on the other hand, various other examples of " certain supernatural women " connected with death are to be found in sources for Norse mythology, that they " seem to have been closely connected with the world of death, and were pictured as welcoming dead warriors ," and that the depiction of Hel " as a goddess " in Gylfaginning " might well owe something to these.

Mechanical examples include pendula ( with small angles of displacement ), masses connected to springs, and acoustical systems.

In the process, he discovered some interesting examples of simply connected non-compact 3-manifolds not homeomorphic to R < sup > 3 </ sup >, the prototype of which is now called the Whitehead manifold.

Most of his arguments were in the form of examples that were anecdotal or speculative in nature, and functioned as attempts to show how " exotic " grammatical traits were connected to what were apparently equally exotic worlds of thought.

It was applied to issues such as cutting-plane, with the paradoxical examples of connected components.

Common examples of an aggregated node in a food web might include parasites, microbes, decomposers, saprotrophs, consumers, or predators, each containing many species in a web that can otherwise be connected to other trophic species.

Connected cell complexes and connected manifolds are examples of " sufficiently good " spaces.

A particular and short-lived type of building, using the same basilican form, was the funerary hall, which was not a normal church, though the surviving examples long ago became regular churches, and they always offered funeral and memorial services, but a building erected in the Constantinian period as an indoor cemetery on a site connected with early Christian martyrs, such as a catacomb.

21st century had some examples of " live concerts " years ago died artists, which moving and image was created by power of computers, sometimes connected with 3d holography moving and walking models.

Built examples of such connected culs-de-sac can be found in the United States ( such as Radburn, New Jersey and Village Homes, California ), England ( such as Milton Keynes ) and Greece ( such as Papagou, a suburb of Athens ) ( see photo ).

The Yogic, Tantric and other systems of India, the Buddhist psychology of Tibet, as well as Chinese ( Taoist alchemy ) and Japanese ( Shingon ) esoterism are examples of doctrines that describe a subtle physiology having a number of focal points ( chakras, acupuncture points ) connected by a series of channels ( nadis, Acupuncture meridians ) that convey life-force ( prana, vayu, ch ' i, ki, lung ).

' These were quavers or semiquavers connected in pairs or series by one or two horizontal strokes at the end of their tails, the last note of the group retaining in the early examples the characteristic up-stroke.

When the 12-volt battery was connected to the system, they experienced one of the first examples of acoustic feedback.

In some examples, pairs of smaller burial chambers lead off from either side of the central rectangular burial chamber, itself connected to an ante-room.

A force-directed graph can involve forces other than mechanical springs and electrical repulsion ; examples include logarithmic springs ( as opposed to linear springs ), gravitational forces ( which aggregate connected components in graphs that are not singly connected ), magnetic fields ( so as to obtain good layouts for directed graphs ), and electrically charged springs ( in order to avoid overlap or near-overlap in the final drawing ).

The examples Aarseth gives include a diverse group of texts: wall inscriptions of the temples in ancient Egypt that are connected two-dimensionally ( on one wall ) or three dimensionally ( from wall to wall or room to room ); the I Ching ; Apollinaire ’ s Calligrammes in which the words of the poem “ are spread out in several directions to form a picture on the page, with no clear sequence in which to be read ”; Marc Saporta ’ s Composition No. 1, Roman, a novel with shuffleable pages ; Raymond Queneau ’ s One Hundred Thousand Billion Poems ; B. S. Johnson ’ s The Unfortunates ; Milorad Pavic ’ s Landscape Painted with Tea ; Joseph Weizenbaum ’ s ELIZA ; Ayn Rand ’ s play Night of January 16th, in which members of the audience form a jury and choose one of two endings ; William Chamberlain and Thomas Etter ’ s Racter ; Michael Joyce ’ s Afternoon: a story ; Roy Trubshaw and Richard Bartle ’ s Multi-User Dungeon ( aka MUD1 ); and James Aspnes ’ s TinyMUD.

Sculpted heads from the royal Abbey of St. Denis are rare surviving examples of portal sculptures that are directly connected with the origins of Gothic art in 12th-century France ( accession nos.

There are many examples of this ; the idea emphasises that the life and death of living things is intimately connected, not just with the physical environment, but with the life of other species.

They carry over 400 words but no examples of connected speech.

In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three obvious examples are Euclidean n-space, the n-dimensional sphere, and hyperbolic space, although a space form need not be simply connected.

Most examples have one or more drawers and four legs sometimes connected by stretchers.