Arc (projective geometry)

A (simple) arc in finite projective geometry is a set of points which satisfies, in an intuitive way, a feature of curved figures in continuous geometries. Loosely speaking, they are sets of points that are far from "line-like" in a plane or far from "plane-like" in a three-dimensional space. In this finite setting it is typical to include the number of points in the set in the name, so these simple arcs are called k-arcs. An important generalization of the k-arc concept, also referred to as arcs in the literature, are the (k, d)-arcs.

k-arcs in a projective plane

In a finite projective plane π (not necessarily Desarguesian) a set A of k (k ≥ 3) points such that no three points of A are collinear (on a line) is called a k - arc. If the plane π has order q then k ≤ q + 2, however the maximum value of k can only be achieved if q is even. In a plane of order q, a (q + 1)-arc is called an oval and, if q is even, a (q + 2)-arc is called a hyperoval.

Every conic in the Desarguesian projective plane PG(2,q), i.e., the set of zeros of an irreducible homogeneous quadratic equation, is an oval. A celebrated result of Beniamino Segre states that when q is odd, every (q + 1)-arc in PG(2,q) is a conic. This is one of the pioneering results in finite geometry.

Arc (protein)

Arc, for activity-regulated cytoskeleton-associated protein (also known as Arg3.1), is a plasticity protein first characterized in 1995. Arc is a member of the immediate-early gene (IEG) family, a rapidly activated class of genes functionally defined by their ability to be transcribed in the presence of protein synthesis inhibitors. Arc mRNA is localized to activated synaptic sites in an NMDA receptor-dependent manner, where the newly translated protein is believed to play a critical role in learning and memory-related molecular processes. Arc is widely considered to be an important protein in neurobiology because of its activity regulation, localization, and utility as a marker for plastic changes in the brain. Dysfunctions in the production of Arc protein has been implicated as an important factor in understanding of various neurological conditions including: Amnesia;Alzheimer's disease; Autism spectrum disorders; and, Fragile X syndrome. Along with other IEGs such as zif268 and Homer 1a, Arc is also a significant tool for systems neuroscience as illustrated by the development of the cellular compartment analysis of temporal activity by fluorescence in situ hybridization, or catFISH technique (see fluorescent in situ hybridization).

Arc (geometry)

In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve. A common example in the plane (a two-dimensional manifold), is a segment of a circle called a circular arc. In space, if the arc is part of a great circle (or great ellipse), it is called a great arc.

Every pair of distinct points on a circle determines two arcs. If the two points are not directly opposite each other, one of these arcs, the minor arc, will subtend an angle at the centre of the circle that is less than π radians (180 degrees), and the other arc, the major arc, will subtend an angle greater than π radians.

Circular arcs

Length of an arc of a circle

The length (more precisely, arc length), L, of an arc of a circle with radius and subtending an angle (measured in radians) with the circle center — i.e., the central angle — equals . This is because

Substituting in the circumference

and, with being the same angle measured in degrees, since the arc length equals

A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement:

Ice

Ice is water frozen into a solid state. Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaque bluish-white color.

In the Solar System, ice is abundant and occurs naturally from as close to the Sun as Mercury to as far as the Oort cloud. Beyond the Solar System, it occurs as interstellar ice. It is abundant on Earth's surface – particularly in the polar regions and above the snow line – and, as a common form of precipitation and deposition, plays a key role in Earth's water cycle and climate. It falls as snowflakes and hail or occurs as frost, icicles or ice spikes.

Ice molecules can exhibit up to sixteen different phases (packing geometries) that depend on temperature and pressure. When water is cooled rapidly (quenching), up to three different types of amorphous ice can form depending on the history of its pressure and temperature. When cooled slowly correlated proton tunneling occurs below 20 K giving rise to macroscopic quantum phenomena. Virtually all the ice on Earth's surface and in its atmosphere is of a hexagonal crystalline structure denoted as ice Ih (spoken as "ice one h") with minute traces of cubic ice denoted as ice Ic. The most common phase transition to ice Ih occurs when liquid water is cooled below 0°C (273.15K, 32°F) at standard atmospheric pressure. It may also be deposited directly by water vapor, as happens in the formation of frost. The transition from ice to water is melting and from ice directly to water vapor is sublimation.

Ice (1998 film)

Ice is a 1998 television disaster film starring Grant Show, Udo Kier, and Eva La Rue. The film has a similar premise as The Day After Tomorrow, a science fiction disaster film released six years later. Though completely in English, it first premiered in Germany in 1998 before being aired on ABC in the United States in 2000.

Plot

A small meteor hits the sun, causing disastrous consequences for the Earth. Los Angeles is, just as the rest of the world, covered with a layer of ice and snow. The government has collapsed and everyone is on their own. Chaos and crime prevails. Together with scientist Dr. Kistler and a small group of survivors, L.A. cop Robert Drake leaves in the direction of Long Beach Harbor to meet with a government ship which will take them to Guam, where it is warmer.

Cast

Ice (band)

Ice is an industrial music band formed by guitarist Justin Broadrick and saxophonist/vocalist Kevin Martin.

History

Keeping to a similar vein as their other musical project Techno Animal, Justin Broadrick and Kevin Martin opted for Ice to be a studio-based project. Drummer John Jobaggy and bassist Dave Cochrane were recruited to aid them in the recording process. Their debut album, Under the Skin, is comparable to Pure-era Godflesh and Martin's free jazz and dub work with God. The group went on hiatus for several years and Jobaggy was replaced by Laika drummer Lou Ciccotelli. By their second album, Bad Blood, the band had absorbed hip hop influences and nearly all the songs featured contributions from recognizable names in the underground rap scene. Blixa Bargeld, of Einsturzende Neubauten, also contributed his vocals to the music.

Band members

Discography