Rebellion

Rebellion, uprising, or insurrection is a refusal of obedience or order. It may, therefore, be seen as encompassing a range of behaviors aimed at destroying or taking over the position of an established authority such as a government, governor, president, political leader, financial institution or boss. The methods can be peaceful, such as civil disobedience, civil resistance and nonviolent resistance, or violent, such as terrorism, sabotage and guerrila warfare. Those who participate in rebellions, especially if they are armed, are known as "rebels".

Throughout history, many different groups that opposed their governments have been called rebels. Over 450 peasant revolts erupted in southwestern France between 1590 and 1715. In the United States, the term was used for the Continentals by the British in the Revolutionary War, and for the Confederacy by the Union in the American Civil War. Most armed rebellions have not been against authority in general, but rather have sought to establish a new government in their place. For example, the Boxer Rebellion sought to implement a stronger government in China in place of the weak and divided government of the time. The Jacobite Risings (called "Jacobite Rebellions" by the government) attempted to restore the deposed Stuart kings to the thrones of England, Ireland and Scotland, rather than abolish the monarchy completely.

Uprising (2012 film)

Uprising is a 2012 documentary that traces the origins of the Egyptian Revolution of 2011 that began in January. It provides a first hand account of the early stages of revolution and follows various leaders and organizers of the movement. The film is directed and produced by Fredrik Stanton and is being distributed by Zeitgeist Films.

Synopsis

The documentary begins with coverage of the spontaneous marches against the 30 year oppressive military rule of president Hosni Mubarak. For the first time in history, organizers and activists turned to social media to voice their opinions and organize protests in Tahrir Square. Though initially a peaceful demonstration, the violence of the police charged with putting down the revolution inspired further violence on both sides as protesters continued to demand that Hosni Mubarak step down from the presidency. When the appointment of the former head of the Egyptian General Intelligence Directorate, Omar Suleiman, as Vice-President was not enough to end protests, Mubarak agreed to step down on February 11, 2011. It was decided that the military would rule for six months until elections could be held. While the film only covers the events leading up to and shortly following the end of the Mubarak regime, the revolution in Egypt continues to this day as new challenges are faced.

Uprising (Concord Dawn album)

Uprising is an album by New Zealand drum and bass group Concord Dawn, released in 2003. Classed as their most popular album, it features other New Zealand musicians such as Scribe and Salmonella Dub's front man Tiki and DJ Optiv.

Track listing

The song Tonite has been remixed by Australian drum and bass band Pendulum.

References

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 symbol

The degree symbol (°) is a typographical symbol that is used, among other things, to represent degrees of arc (e.g. in geographic coordinate systems), hours (in the medical field), degrees of temperature, alcohol proof, or diminished quality in musical harmony. The symbol consists of a small raised circle, historically a zero glyph.

In Unicode it is encoded at U+00B0 ° DEGREE SIGN (HTML ° · °).

History

The first known recorded modern use of the degree symbol in mathematics is from 1569 where the usage seems to show that the symbol is a small raised zero, to match the prime symbol notation of sexagesimal subdivisions of degree such as minute ′, second ″, and tertia ‴ which originates as small raised Roman numerals.

Typography

In the case of degrees of arc, the degree symbol follows the number without any intervening space.

Degree of a continuous mapping

In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the mapping. The degree is always an integer, but may be positive or negative depending on the orientations.

The degree of a map was first defined by Brouwer, who showed that the degree is homotopy invariant (invariant among homotopies), and used it to prove the Brouwer fixed point theorem. In modern mathematics, the degree of a map plays an important role in topology and geometry. In physics, the degree of a continuous map (for instance a map from space to some order parameter set) is one example of a topological quantum number.

Definitions of the degree

From Sⁿ to Sⁿ

The simplest and most important case is the degree of a continuous map from the -sphere to itself (in the case , this is called the winding number):

Let be a continuous map. Then induces a homomorphism , where is the th homology group. Considering the fact that , we see that must be of the form for some fixed . This is then called the degree of .