Santo Domingo Santo Domingo de Guzmán, is the capital and largest city in the Dominican Republic and the largest metropolitan area in the Caribbean by population. As of 2010, the city had a total population of 2,908,607; the city is coterminous with the boundaries of the Distrito Nacional, itself bordered on three sides by Santo Domingo Province. Founded by Bartholomew Columbus in 1496, on the east bank of the Ozama River and moved by Nicolás de Ovando in 1502 to the west bank of the river, the city is the oldest continuously inhabited European settlement in the Americas, was the first seat of the Spanish colonial rule in the New World. Santo Domingo is the site of the first university, castle and fortress in the New World; the city's Colonial Zone was declared as a World Heritage Site by UNESCO. Santo Domingo was called Ciudad Trujillo, from 1936 to 1961, after the Dominican Republic's dictator, Rafael Trujillo, named the capital after himself. Following his assassination, the city resumed its original designation.

Santo Domingo is the cultural, political and industrial center of the Dominican Republic, with the country's most important industries being located within the city. Santo Domingo serves as the chief seaport of the country; the city's harbor at the mouth of the Ozama River accommodates the largest vessels, the port handles both heavy passenger and freight traffic. Temperatures are high year round, with cooler breezes in the winter time. Prior to the arrival of Christopher Columbus in 1492, the native Taíno people populated the island which they called Quisqueya and Ayiti, which Columbus named Hispaniola, including the territory of today's Republic of Haiti. At the time, the island's territory consisted of five chiefdoms: Marién, Maguá, Maguana and Higüey; these were ruled by caciques Guacanagarix, Caonabo, Bohechío, Cayacoa. Dating from 1493, when the Spanish settled on the island, from 5 August 1498, Santo Domingo became the oldest European city in the Americas. Bartholomew Columbus founded the settlement and named it La Nueva Isabela, after an earlier settlement in the north named after the Queen of Spain Isabella I.

In 1495 it was renamed "Santo Domingo", in honor of Saint Dominic. Santo Domingo came to be known as the "Gateway to the Caribbean" and the chief town in Hispaniola from on. Expeditions which led to Ponce de León's colonization of Puerto Rico, Diego Velázquez de Cuéllar's colonization of Cuba, Hernando Cortes' conquest of Mexico, Vasco Núñez de Balboa's sighting of the Pacific Ocean were all launched from Santo Domingo. In June 1502, Santo Domingo was destroyed by a major hurricane, the new Governor Nicolás de Ovando had it rebuilt on a different site on the other side of the Ozama River; the original layout of the city and a large portion of its defensive wall can still be appreciated today throughout the Colonial Zone, declared a World Heritage Site by UNESCO. Diego Colon arrived in 1509, assuming the powers of admiral. In 1512, Ferdinand established a Real Audiencia with Juan Ortiz de Matienzo, Marcelo de Villalobos, Lucas Vazquez de Ayllon appointed as judges of appeal. In 1514, Pedro Ibanez de Ibarra arrived with the Laws of Burgos.

Rodrigo de Alburquerque was named repartidor de indios and soon named visitadores to enforce the laws. The first major slave revolt in the Americas occurred in Santo Domingo during 1522, when slaves led an uprising in the sugar plantation of Diego Columbus, son of Christopher Columbus. In 1586, Francis Drake of England held it for ransom. A report which reached England in May 1586 states that from Santo Domingo he took away 1,200 Englishmen, Flemings, "Provincials out of prison, besides 800 of the countrey people." Drake's invasion signaled the decline of Spanish dominion over Hispaniola, accentuated in the early 17th century by policies that resulted in the depopulation of most of the island outside of the capital. An expedition sent by Oliver Cromwell in 1655 attacked the city of Santo Domingo, but the English were repulsed by mulatto and mestizo militiamen. Santo Domingo suffered only 25 dead. In 1697, the Treaty of Ryswick included the acknowledgement by Spain of France's dominion over the Western third of the island, now Haiti.

During the 18th century, privateers from Santo Domingo trolled the Caribbean Sea, attacking slave ships. This activity proved beneficial to the Dominican privateers, as evidenced by the fact that Captain Lorenzo Daniel, aka Lorencin, captured more than 70 ships from Britain during the Anglo-Spanish War of 1762–1763; the French imported slaves to work on plantations in their colonies in Saint-Domingue, they were exploited until the French Revolution of 1789. Former plantation slave Toussaint L'ouverture led an uprising of slaves in 1791, arming them with French weapons, they allied with Spain and raided the colony from Santo Domingo, but in 1794 the French revolutionary government capitulated to Toussaint and made him a Brigadier-General. The Haitian rebels fought not only against the Dominicans, but the French, rival rebel groups, the British. From 1795 to 1822 the city changed hands several times along with the colony it headed, it was ceded to France in 1795 after years of struggles. However, the French failed to consolidate this cession because of the continued presence of British troops in Saint-Domingue.

As the news of Santo Domingo's cession became known on the island, many Dominicans had s

Fr. Caseys GAA Club is an Irish Gaelic Athletic Association club based in Abbeyfeale on the border of Kerry and Limerick. Gaelic football is the club's main sport. Established in 1884 by Father William Casey, Fr. Caseys GAA Club has been one of the most successful clubs in the history of Limerick Gaelic Games. Fr. Caseys GAA Club have won the Limerick Senior Football Championship on 8 occasions and contributed many players to the Limerick county teams over the years. In addition to their Senior triumphs Fr. Caseys have enjoyed numerous Intermediate, Junior, U21, Minor and Underage successes during their history. Rugby internationals Phil Danaher and Séamus Dennison both played football for the club. Father Casey's most recent Limerick senior title came in 2006, when the team defeated St. Senan's by two points in the final at the Gaelic Grounds. Fr. William Casey was born in 1840 in the parish of Co.. Limerick. Ordained as a priest in 1868, Fr. Casey was appointed permanently as a curate to Abbeyfeale on November 18, 1871.

Fr. Casey was appointed parish priest of Abbeyfeale, a position he held until his death in 1907; as a follower of Michael Davitt, Fr. Casey became a leader in Abbeyfeale and its surrounding areas in the land league and the fight against landlordism. In addition to forming the GAA Club, Fr. Casey was responsible for organising the building of a local community hall and forming a brass and reed band. Between 1904 and 1906 Fr. Casey was appointed chairman of the Limerick County Board. Limerick Senior Football Championship Winners 1914, 1915, 1932, 1941, 1942, 1947, 2000, 2006 Limerick Under-21 Football Championship Winners 2009, 2010, 2011 Fr. Caseys GAA Grounds & Pavilion are situated on the Kerry side of the River Feale on the outskirts of Abbeyfeale. Official Fr. Caseys GAA Club website

In mathematics, an antiunitary transformation, is a bijective antilinear map U: H 1 → H 2 between two complex Hilbert spaces such that ⟨ U x, U y ⟩ = ⟨ x, y ⟩ ¯ for all x and y in H 1, where the horizontal bar represents the complex conjugate. If additionally one has H 1 = H 2 U is called an antiunitary operator. Antiunitary operators are important in quantum theory because they are used to represent certain symmetries, such as time-reversal symmetry, their fundamental importance in quantum physics is further demonstrated by Wigner's theorem. In quantum mechanics, the invariance transformations of complex Hilbert space H leave the absolute value of scalar product invariant: | ⟨ T x, T y ⟩ | = | ⟨ x, y ⟩ | for all x and y in H. Due to Wigner's theorem these transformations fall into two categories, they can be unitary or antiunitary. Congruences of the plane form two distinct classes; the first is generated by translations and rotations. The second does not conserve the orientation and is obtained from the first class by applying a reflection.

On the complex plane these two classes corresponds to antiunitaries, respectively. ⟨ U x, U y ⟩ = ⟨ x, y ⟩ ¯ = ⟨ y, x ⟩ holds for all elements x, y of the Hilbert space and an antiunitary U. When U is antiunitary U 2 is unitary; this follows from ⟨ U 2 x, U 2 y ⟩ = ⟨ U x, U y ⟩ ¯ = ⟨ x, y ⟩. For unitary operator V the operator V K, where K is complex conjugate operator, is antiunitary; the reverse is true, for antiunitary U the operator U K is unitary. For antiunitary U the definition of the adjoint operator U ∗ is changed to compensate the complex conjugation, becoming ⟨ U x, y ⟩ = ⟨ x, U ∗ y ⟩ ¯; the adjoint of an antiunitary U is antiunitary and U U ∗ = U ∗ U = 1. An antiunitary operator on a finite-dimensional space may be decomposed as a direct sum of elementary Wigner antiunitaries W θ, 0 ≤ θ ≤ π; the operator W 0: C → C is just simple complex conjugation on C W 0 = z ¯ For 0 < θ ≤ π, the operator W θ acts on two-dimensional complex Hilbert space. It is defined by W θ =. {\displaystyle W_\left=\left(e^{\overline {z_