The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process, it is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, or 109 times that of Earth, its mass is about 330,000 times that of Earth. It accounts for about 99.86% of the total mass of the Solar System. Three quarters of the Sun's mass consists of hydrogen; the Sun is a G-type main-sequence star based on its spectral class. As such, it is informally and not accurately referred to as a yellow dwarf, it formed 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System; the central mass became so hot and dense that it initiated nuclear fusion in its core. It is thought that all stars form by this process.

The Sun fuses about 600 million tons of hydrogen into helium every second, converting 4 million tons of matter into energy every second as a result. This energy, which can take between 10,000 and 170,000 years to escape from its core, is the source of the Sun's light and heat; when hydrogen fusion in its core has diminished to the point at which the Sun is no longer in hydrostatic equilibrium, its core will undergo a marked increase in density and temperature while its outer layers expand transforming the Sun into a red giant. It is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury and Venus, render Earth uninhabitable – but not for about five billion years. After this, it will shed its outer layers and become a dense type of cooling star known as a white dwarf, no longer produce energy by fusion, but still glow and give off heat from its previous fusion; the enormous effect of the Sun on Earth has been recognized since prehistoric times, the Sun has been regarded by some cultures as a deity.

The synodic rotation of Earth and its orbit around the Sun are the basis of solar calendars, one of, the predominant calendar in use today. The English proper name Sun may be related to south. Cognates to English sun appear in other Germanic languages, including Old Frisian sunne, Old Saxon sunna, Middle Dutch sonne, modern Dutch zon, Old High German sunna, modern German Sonne, Old Norse sunna, Gothic sunnō. All Germanic terms for the Sun stem from Proto-Germanic *sunnōn; the Latin name for the Sun, Sol, is not used in everyday English. Sol is used by planetary astronomers to refer to the duration of a solar day on another planet, such as Mars; the related word solar is the usual adjectival term used, in terms such as solar day, solar eclipse, Solar System. The English weekday name Sunday stems from Old English and is a result of a Germanic interpretation of Latin dies solis, itself a translation of the Greek ἡμέρα ἡλίου; the Sun is a G-type main-sequence star. The Sun has an absolute magnitude of +4.83, estimated to be brighter than about 85% of the stars in the Milky Way, most of which are red dwarfs.

The Sun is heavy-element-rich, star. The formation of the Sun may have been triggered by shockwaves from more nearby supernovae; this is suggested by a high abundance of heavy elements in the Solar System, such as gold and uranium, relative to the abundances of these elements in so-called Population II, heavy-element-poor, stars. The heavy elements could most plausibly have been produced by endothermic nuclear reactions during a supernova, or by transmutation through neutron absorption within a massive second-generation star; the Sun is by far the brightest object in the Earth's sky, with an apparent magnitude of −26.74. This is about 13 billion times brighter than the next brightest star, which has an apparent magnitude of −1.46. 1 astronomical unit is defined as the mean distance of the Sun's center to Earth's center, though the distance varies as Earth moves from perihelion in January to aphelion in July. At this average distance, light travels from the Sun's horizon to Earth's horizon in about 8 minutes and 19 seconds, while light from the closest points of the Sun and Earth takes about two seconds less.

The energy of this sunlight supports all life on Earth by photosynthesis, drives Earth's climate and weather. The Sun does not have a definite boundary, but its density decreases exponentially with increasing height above the photosphere. For the purpose of measurement, the Sun's radius is considered to be the distance from its center to the edge of the photosphere, the apparent visible surface of the Sun. By this measure, the Sun is a near-perfect sphere with an oblateness estimated at about 9 millionths, which means that its polar diameter differs from its equatorial diameter by only 10 kilometres; the tidal effect of the planets is weak and does not affect the shape of the Sun. The Sun rotates faster at its equator than at its poles; this differential rotation is caused by convective motion due to heat transport and the Coriolis force due to the Sun's rotation. In a frame of reference defined by the stars, the rotational period is 25.6 days at the equator and 33.5 days at the poles. Viewed from Earth as it orbits the Sun, the apparent rotational period

Pickands–Balkema–de Haan theorem

The Pickands–Balkema–de Haan theorem is called the second theorem in extreme value theory. It gives the asymptotic tail distribution of a random variable X, when the true distribution F of X is unknown. Unlike for the first theorem in extreme value theory, the interest here is in the values above a threshold. If we consider an unknown distribution function F of a random variable X, we are interested in estimating the conditional distribution function F u of the variable X above a certain threshold u; this is the so-called conditional excess distribution function, defined as F u = P = F − F 1 − F for 0 ≤ y ≤ x F − u, where x F is either the finite or infinite right endpoint of the underlying distribution F. The function F u describes the distribution of the excess value over a threshold u, given that the threshold is exceeded. Let be a sequence of independent and identically-distributed random variables, let F u be their conditional excess distribution function. Pickands, Balkema and de Haan posed that for a large class of underlying distribution functions F, large u, F u is well approximated by the generalized Pareto distribution.

That is: F u → G k, σ, as u → ∞ where G k, σ = 1 − − 1 / k, if k ≠ 0 G k, σ = 1 − e − y / σ, if k = 0. Here σ > 0, y ≥ 0 when k ≥ 0 and 0 ≤ y ≤ −σ/k when k < 0. Since a special case of the generalized Pareto distribution is a power-law, the Pickands–Balkema–de Haan theorem is sometimes used to justify the use of a power-law for modeling extreme events. Still, many important distributions, such as the normal and log-normal distributions, do not have extreme-value tails that are asymptotically power-law. Exponential distribution with mean σ, if k = 0. Uniform distribution on, if k = -1. Pareto distribution, if k > 0. Stable distribution Balkema, A. and de Haan, L.. "Residual life time at great age", Annals of Probability, 2, 792–804. Pickands, J.. "Statistical inference using extreme order statistics", Annals of Statistics, 3, 119–131

Baron Athenry

Baron Athenry is one of the oldest titles in the Peerage of Ireland, but the date of its creation is uncertain. The title appears to have been given to the de Birmingham family of Birmingham, England as a reward for their help in the Norman invasion of Ireland in 1172. Both Sir William de Birmingham, his son Robert de Birmingham, are variously claimed to have been involved in the invasion, but it is probable that, after the invasion, William returned to his home in England and left Robert their new lands in Ireland. Peter Bermingham was fined for not attending Parliament in 1284, is enrolled as Lord Athenry in the Parliament of 1295; the title Earl of Louth was created in 1319 as a reward to John de Bermingham for his victory over Edward de Bruce in the Battle of Faughart in 1318. The last Baron was created Earl of Louth in the Peerage of Ireland in 1749, but died in 1799. Since he had three daughters, the Earldom of Louth became extinct at his death. Part of the problem has been whether the Barony properly can descend through the female line, in which case it is in abeyance between the heirs of his daughters.

A descendant of the younger brother of the Richard, Lord Athenry, who died in 1645, claimed the Barony as heir male in 1827, Thomas Denman, the Attorney General for England and Wales, agreed that he was heir male, but he was not recognized by the House of Lords. A claim by Thomas Sewell, son of the Earl of Louth's eldest daughter Elizabeth, failed on the ground that the title did not pass in the female line; the numbering follows the second edition of the Volume 1, pages 290ff. Robert de Bermingham Peter de Bermingham Meyler de Bermingham, fl. 1212–1262 Piers de Bermingham, died 1307 - 1st Baron Richard I de Bermingham, died 1322 - 2nd Baron Thomas de Bermingham, died 1374 - 3rd Baron Walter de Bermingham, died 1428 - 4th Baron Thomas II de Bermingham, died 1473 - 5th Baron Thomas III de Bermingham, died 1489 - 6th Baron Meiler de Bermingham, died 1529 - 7th Baron John de Bermingham, died 1547 - 8th Baron Richard II de Bermingham, died 1580 - 9th Baron Edmond I de Bermingham, 1540–1614 - 10th Baron Richard III de Bermingham, 1570–1645 - 11th Baron Edmond II de Bermingham, resigned 1641 in favour of his brother Francis de Bermingham, died 1677 - 12th Baron Edward de Bermingham, died 1709 - 13th Baron Francis II de Bermingham, 1692-1750 - 14th Baron Thomas IV de Bermingham, 1717–1799, created Earl of Louth in 1759 John de Bermingham, 1st Earl of Louth Richard de Bermingham, Lord Atherdee Thomas Bermingham, 1st Earl of Louth de Birmingham family Birmingham surname Bermingham Birmingham, England Complete Peerage, sub "Athenry".

Bermingham: Origins and History of the Family Name – 1060 to 1830, Douglas P. Bermingham, Kildare. 2012