Mix

Mix, mixes, mixture, or mixing may refer to:

In mathematics, science, and technology

In electronics and telecommunications

Other uses in mathematics, science, and technology

DJ mix

A DJ mix or DJ mixset is a sequence of musical tracks typically mixed together to appear as one continuous track. DJ mixes are usually performed using a DJ mixer and multiple sounds sources, such as turntables, CD players, digital audio players or computer sound cards, sometimes with the addition of samplers and effects units, although it's possible to create one using sound editing software.

DJ mixing is significantly different from live sound mixing. Remix services were offered beginning in the late 1970s in order to provide music which was more easily beatmixed by DJs for the dancefloor. One of the earliest DJs to refine their mixing skills was DJ Kool Herc.Francis Grasso was the first DJ to use headphones and a basic form of mixing at the New York nightclub Sanctuary. Upon its release in 2000, Paul Oakenfold's Perfecto Presents: Another World became the biggest selling dj mix album in the US.

Music

A DJ mix is often put together with music from genres that fit into the more general term electronic dance music. Other genres mixed by DJ includes hip hop, breakbeat and disco. Four on the floor disco beats can be used to create seamless mixes so as to keep dancers locked to the dancefloor. Two of main characteristics of music used in dj mixes is a dominant bassline and repetitive beats. Music mixed by djs usually has a tempo which ranges from 120 bpm up to 160 bpm.

MIX (XM)

MIX, often branded on-air as Today's Mix, was a channel on XM Satellite Radio playing the Hot Adult Contemporary format. It was located on XM 12 (previously 22) and plays a mix of hit songs from 1980-present day, except for urban music. MIX was one of 5 channels on XM's platform that plays commercial advertisements, which amount to about 3–4 minutes an hour, and are sold by Premiere Radio Networks. The channel was programmed by Clear Channel Communications, and was Clear Channel's most listened to channel on XM Radio, in both cume and AQH, according to the Fall 2007 Arbitron book.

Artists heard on MIX included Sheryl Crow, John Mayer, Lenny Kravitz, Jewel and Nelly Furtado; and groups like Maroon 5 and Blues Traveler. One can also hear top chart hits including songs from Train, Alanis Morissette, 3 Doors Down, Evanescence, Dave Matthews Band, No Doubt, Santana, Matchbox Twenty, and U2.

On June 8, 2011, this was replaced by a simulcast by WHTZ, licensed to Newark, New Jersey and serving the New York City area.

Degree

Degree may refer to:

As a unit of measurement

Field extension

In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x² = 2.

Definitions

Let L be a field. A subfield of L is a subset K of L that is closed under the field operations of L and under taking inverses in L. In other words, K is a field with respect to the field operations inherited from L. The larger field L is then said to be an extension field of K. To simplify notation and terminology, one says that L / K (read as "L over K") is a field extension to signify that L is an extension field of K.

If L is an extension of F which is in turn an extension of K, then F is said to be an intermediate field (or intermediate extension or subextension) of the field extension L / K.

Degree of an algebraic variety

The degree of an algebraic variety in mathematics is defined, for a projective variety V, by an elementary use of intersection theory.

Definition

For V embedded in a projective space Pⁿ and defined over some algebraically closed field K, the degree d of V is the number of points of intersection of V, defined over K, with a linear subspace L in general position, when

Here dim(V) is the dimension of V, and the codimension of L will be equal to that dimension. The degree d is an extrinsic quantity, and not intrinsic as a property of V. For example the projective line has an (essentially unique) embedding of degree n in Pⁿ.

Properties

The degree of a hypersurface F = 0 is the same as the total degree of the homogeneous polynomial F defining it (granted, in case F has repeated factors, that intersection theory is used to count intersections with multiplicity, as in Bézout's theorem).

Other approaches

For a more sophisticated approach, the linear system of divisors defining the embedding of V can be related to the line bundle or invertible sheaf defining the embedding by its space of sections. The tautological line bundle on Pⁿ pulls back to V. The degree determines the first Chern class. The degree can also be computed in the cohomology ring of Pⁿ, or Chow ring, with the class of a hyperplane intersecting the class of V an appropriate number of times.