The Anglo-Saxon Chronicle makes no mention of Offa for the years between 757—777. No Mercian chronicles from this time period have survived. Charters are the only records that give any idea of Offa's power outside of Mercia. But he proved to be ruthless, bold and creative in bringing Kent, Sussex and Essex under his control. Aethelbert the king of Kent was apparently under Offa's influence before he died in 762. In 794 another Aethelbert, a king in East Anglia was beheaded at Offa's command. When Egbert of Wessex made a bid for the throne of Wessex in 786 Offa had him banished from England. He made Beorhtric king of Wessex instead. Egbert was welcomed at the court of Charlemagne for at least three years. In charters Offa issued in Kent, East Anglia, Sussex and Middlesex he simply used the style "Rex Merciorum" (Latin for king of Mercia). Only in three church charters does he expand his title to indicate he is overlord of all of England.
Offa had diplomatic relations with Charlemagne. He was one of the few Anglo-Saxon monarchs to have dealings with continental rulers. Letters and presents were exchanged. But when Offa sought a marriage of his son to one of Charlemagne's daughters, relations were quickly cut off. Charlemagne had all Frankish ports closed to British ships. Offa, very involved in church affairs, presided over church councils personally in 786-7. In 787 he convinced the pope to create the position of archbishop of Lichfield in Mercia. He wanted his own archbishop who was closer at hand than the Archbishop of Canterbury. He reorganized the defenses of his kingdom. One of these defenses, Offa's Dyke was a massive earthworks between Mercia and the Welsh kingdoms to the west. Offa died in 796. His son, Ecgfrith, lasted only 141 days as king. Mercia was never again as powerful as it was during Offa's reign.
Higgs boson
The Higgs boson (or Higgs particle) is a particle in the Standard Model of physics. In the 1960s Peter Higgs was the first person to suggest that this particle might exist. On 14 March 2013, scientists at CERN confirmed for the time that they had found a Higgs particle.
The Higgs particle is one of the 17 particles in the Standard Model, the model of physics which describes all known basic particles. The Higgs particle is a boson. Bosons are thought to be particles which are responsible for all physical forces. Other known bosons are the photon, the W and Z bosons, and the gluon. Scientists do not yet know how to combine gravity with the Standard Model.
The Higgs field is a fundamental field of crucial importance to particle physics theory. Unlike other known fields such as the electromagnetic field, the Higgs field takes the same non-zero value almost everywhere. The question of the Higgs field's existence was the last unverified part of the Standard Model of particle physics and, according to some, was "the central problem in particle physics".
It is difficult to detect the Higgs boson. The Higgs boson is very massive compared to other particles, so it does not last very long. There are usually no Higgs bosons around because it takes so much energy to make one. The Large Hadron Collider at CERN was built mainly for this reason. It speeds up two bunches of particles to almost light speed (travelling in opposite directions), before setting them on a path to collide with each other.
Each collision produces a flurry of new particles which are detected by detectors around the point where they collide. There is still only a very small chance, one in 10 billion, of a Higgs boson appearing and being detected. To find the few collisions with evidence of the Higgs boson, the LHC smashes together trillions of particles, and supercomputers sift through a massive amount of data.
Higgs bosons obey the conservation of energy law, which states that no energy is created or destroyed, but instead can be transferred or change form. First, the energy starts out in the gauge boson that interacts with the Higgs field. This energy is in the form of kinetic energy as movement. After the gauge boson interacts with the Higgs field, it slows down. This slowing down reduces the amount of kinetic energy in the gauge boson. However, this energy is not destroyed. Instead, the energy from the motion goes into the field and is converted into mass-energy, which is the energy stored in mass. The mass created can become what we call a Higgs boson. The amount of mass created comes from Einstein's famous equation E=mc, which states that mass is equal to a large amount of energy (for example, 1 kg of mass is equivalent to almost 90 quadrillion joules of energy—the same amount of energy used by the entire world in roughly an hour and a quarter in 2008). Since the amount of mass-energy created by the Higgs field is equal to the amount of kinetic energy that the gauge boson lost by slowing down, energy is conserved.
Higgs bosons are used in a variety of science fiction stories. The physicist Leon Lederman called it the "God particle" in 1993.
On 12 December 2011, the two teams at the Large Hadron Collider looking for the Higgs boson, ATLAS and CMS, announced that they had finally seen results which could suggest the Higgs boson existed; however, they did not know for certain if this was true.
On 4 July 2012, the teams at the Large Hadron Collider declared that they had discovered a particle which they think is the Higgs boson.
On 14 March 2013 the teams had done much more testing, and announced that they now think the new particle is a Higgs boson.
Taylor series
A Taylor series is an idea used in computer science, calculus, chemistry, physics and other kinds of higher-level mathematics. It is a series that is used to create an estimate (guess) of what a function looks like. There is also a special kind of Taylor series called a Maclaurin series.
The theory behind the Taylor series is that if a point is chosen on the coordinate plane (x- and y-axes), then it is possible to guess what a function will look like in the area around that point. This is done by taking the derivatives of the function and adding them all together. The idea is that it is possible to add the infinite number of derivatives and come up with a single finite sum.
In mathematics, a Taylor series shows a function as the sum of an . The sum's terms are taken from the function's derivatives. Taylor series come from Taylor's theorem.
The Ancient Greek philosopher Zeno of Elea first came up with the idea of this series. The paradox called "zeno's parodox' is the result. He believed that it would be impossible to add an infinite number of values and get a single finite value as a result.
Another Greek philosopher, Aristotle, came up with an answer to the philosophical question. It was Archimedes, however, who came up with a mathematical solution using his method of exhaustion. He was able to prove that when something is split up into an infinite number of tiny pieces, they will still add up to a single whole when all of them are added back together. The ancient Chinese mathematician Liu Hui proved the same thing several hundred years later.
The earliest known examples of the Taylor series are the work of Mādhava of Sañgamāgrama in India in the 1300s. Later Indian mathematicians wrote about his work with the trigonometric functions of sine, cosine, tangent, and arctangent. None of Mādhava's writings or records still exists today. Other mathematicians based their work on Mādhava's discoveries and worked more with these series until the 1500s.
James Gregory, a Scottish mathematician, worked in this area in the 1600s. Gregory studied the Taylor series and published several Maclaurin series. In 1715, Brook Taylor discovered a general method for applying the series to all functions. (All of the previous research showed how to apply the method to only specific functions.) published a special case of the Taylor series in the 1700s. This series, which is based around zero, is called the "Maclaurin series".