Metric

Metric or metrical may refer to:

Mathematics

Science

Metric (vector bundle)

In differential geometry, the notion of a metric tensor can be extended to an arbitrary vector bundle. Specifically, if M is a topological manifold and E → M a vector bundle on M, then a metric (sometimes called a bundle metric, or fibre metric) on E is a bundle map g : E ×_ME → M × R from the fiber product of E with itself to the trivial bundle with fiber R such that the restriction of g to each fibre over M is a nondegenerate bilinear map of vector spaces.

References

Metric (mathematics)

In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.

In differential geometry, the word "metric" may refer to a bilinear form that may be defined from the tangent vectors of a differentiable manifold onto a scalar, allowing distances along curves to be determined through integration. It is more properly termed a metric tensor.

Definition

A metric on a set X is a function (called the distance function or simply distance)

where [0,∞) is the set of non-negative real numbers (because distance can't be negative so we can't use R), and for all x, y, z in X, the following conditions are satisfied:

Conditions 1 and 2 together define a positive-definite function. The first condition is implied by the others.

Mumps

Mumps, also known as epidemic parotitis, is a viral disease caused by the mumps virus. Initial signs and symptoms often include fever, muscle pain, headache, and feeling tired. This is then usually followed by painful swelling of one or both parotid glands. Symptoms typically occur 16 to 18 days after exposure and resolve after 7 to 10 days. Symptoms in adults are often more severe than in children. About a third of people have mild or no symptoms. Complications may include infections of the covering of the brain (15%), pancreatitis (4%), permanent deafness, and painful testicular swelling which uncommonly results in infertility. Women may develop ovarian swelling but this does not increase the risk of infertility.

Mumps is highly contagious and spreads rapidly among people living in close quarters. The virus is transmitted by respiratory droplets or direct contact with an infected person. Only humans get and spread the disease. People are infectious to each other from a few days before the start of symptoms to four days after. After an infection a person is typically immune for life. Reinfection is possible but tends to be mild. Diagnosis is usually suspected due to parotid swelling and can be confirmed by isolating the virus on a swab of the parotid duct. Testing for IgM antibodies in the blood is simple and may be useful; however, can be falsely negative in those who have been immunized.

Mumps (disambiguation)

Mumps is a viral disease.

Mumps or MUMPS may also refer to:

Mumps (rock band)

Mumps (sometimes credited as The Mumps) were an American punk band fronted by Lance Loud.

Other members of the band included Kristian Hoffman, Rob Duprey, Jay Dee Daugherty and Aaron Kiley. Kiley and Daugherty were replaced with Kevin Kiely and Paul Rutner.

Their first 45 RPM single was "I Like To Be Clean". Their second was "Rock & Roll This & That" with a double side B of "Muscleboys" and "That Fatal Charm". The recorded version of the song "Rock & Roll This & That" interpolated a short guitar riff from the Rolling Stones' "I Can't Get No Satisfaction", but in live performances they would interpolate other riffs such as David Bowie's "Rebel Rebel".

Mumps concerts were lively and featured energetic, expressive performances from Lance Loud and other band members on songs like "We're Americans", "I Believe In Anyone But You", "Strange Seed", "Brain Massage", "Scream and Scream Again".

Mumps were a popular band at clubs such as Max's Kansas City and CBGB. They also performed at Irving Plaza and Maxwell's (Hoboken, New Jersey), and opened for the Ramones at Hurrah (nightclub) in August 1978.