Form

Form is the shape, visual appearance, constitution or configuration of an object. In a wider sense, the form is the way something is or happens.

Form may also refer to the following:

Mathematics

One-form

In linear algebra, a one-form on a vector space is the same as a linear functional on the space. The usage of one-form in this context usually distinguishes the one-forms from higher-degree multilinear functionals on the space. For details, see linear functional.

In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold M is a smooth mapping of the total space of the tangent bundle of M to whose restriction to each fibre is a linear functional on the tangent space. Symbolically,

where α_x is linear.

Often one-forms are described locally, particularly in local coordinates. In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates:

where the f_i are smooth functions. From this perspective, a one-form has a covariant transformation law on passing from one coordinate system to another. Thus a one-form is an order 1 covariant tensor field.

Examples

Nerve (upcoming film)

Nerve is an upcoming American drama thriller film directed by Henry Joost and Ariel Schulman and written by Jessica Sharzer, based on the novel Nerve by Jeanne Ryan. The film stars Dave Franco, Emma Roberts, Kimiko Glenn, Juliette Lewis, Emily Meade and Marc John Jefferies. Principal photography began on April 13, 2015 in New York City.

Cast

Production

In February 2014, it was announced that Henry Joost and Ariel Schulman would be directing the film, from a screenplay by Jessica Sharzer, based on the novel of the same name by Jeanne Ryan. In January 2015, it was announced that Emma Roberts and Dave Franco had joined the cast of the film. In April 2015, it was announced that Kimiko Glenn had joined the cast of the film, portraying the role of Emma Robert's characters worried friend. That same day, it was announced that rapper Richard "MGK" Baker had joined the cast of the film.

Nerve (disambiguation)

A nerve is a part of the peripheral nervous system.

Nerve or Nerves may also refer to:

Mathematics

Film and television

Books

Computing

Music

See also

Nerve (category theory)

In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory.

Motivation

The nerve of a category is often used to construct topological versions of moduli spaces. If X is an object of C, its moduli space should somehow encode all objects isomorphic to X and keep track of the various isomorphisms between all of these objects in that category. This can become rather complicated, especially if the objects have many non-identity automorphisms. The nerve provides a combinatorial way of organizing this data. Since simplicial sets have a good homotopy theory, one can ask questions about the meaning of the various homotopy groups π_n(N(C)). One hopes that the answers to such questions provide interesting information about the original category C, or about related categories.

Liquid

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.

The density of a liquid is usually close to that of a solid, and much higher than in a gas. Therefore, liquid and solid are both termed condensed matter. On the other hand, as liquids and gases share the ability to flow, they are both called fluids. Although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is in gaseous form (with traces of detectable solid matter) as interstellar clouds or in plasma form within stars.

Liquid consonant

In phonetics, liquids or liquid consonants are a class of consonants consisting of lateral consonants together with rhotics.

Distribution

Liquids as a class often behave in a similar way in the phonotactics of a language: for example, they often have the greatest freedom in occurring in consonant clusters. In many languages, such as Japanese and Korean, there is a single liquid phoneme that has both lateral and rhotic allophones.

English has two liquid phonemes, one lateral, /l/ and one rhotic, /ɹ/, exemplified in the words led and red.

Many other European languages have one lateral and one rhotic phoneme. Some, such as Greek, Italian and Serbo-Croatian, have more than two liquid phonemes. All three languages have the set /l/ /ʎ/ /r/, with two laterals and one rhotic. Similarly, the Iberian languages contrast four liquid phonemes. /l/, /ʎ/, /ɾ/, and a fourth phoneme that is an alveolar trill in all but some varieties of Portuguese, where it is a uvular trill or fricative. Some European languages, like Russian and Irish, contrast a palatalized lateral–rhotic pair with an unpalatalized (or velarized) set (e.g. /lʲ/ /rʲ/ /l/ /r/ in Russian).