The Florida Reef is the only living coral barrier reef in the continental United States. It is the third largest coral barrier reef system in the world, it lies a few miles seaward of the Florida Keys, is about 4 miles wide and extends 270 km from Fowey Rocks just east of Soldier Key to just south of the Marquesas Keys. The barrier reef tract forms a great arc, concentric with the Florida Keys, with the northern end, in Biscayne National Park, oriented north-south and the western end, south of the Marquesas Keys, oriented east-west; the rest of the reef outside Biscayne National Park lies within John Pennekamp Coral Reef State Park and the Florida Keys National Marine Sanctuary. Isolated coral patch reefs occur northward from Biscayne National Park as far north as Stuart, in Martin County. Coral reefs are found in Dry Tortugas National Park west of the Marquesas Keys. There are more than 6,000 individual reefs in the system; the reefs are 5,000 to 7,000 years old, having developed since sea levels rose following the Wisconsinan glaciation.

The densest and most spectacular reefs, along with the highest water clarity, are found to the seaward of Key Largo and Elliott Key where the two long keys help protect the reefs from the effects of water exchange with Florida Bay, Biscayne Bay, Card Sound and Barnes Sound. The bays and sounds tend to have lower salinity, higher turbidity and wider temperature variations than the water in the open ocean. Channels between the Keys allow brackish water from the bays to flow onto the reefs, limiting their growth; the Florida Reef consists of two ridges separated from the Florida Keys by the Hawk Channel. Closest to the Keys is a sand ridge called White Bank, covered by large beds of sea grass, with patch reefs scattered across it. Further out to sea on the edge of the Florida Straits is the second ridge forming the outer reefs, covered by reefs and hard banks composed of coral rubble and sand. 1,400 species of marine plants and animals, including more than 40 species of stony corals and 500 species of fish, live on the Florida Reef.

The Florida Reef lies close to the northern limit for tropical corals, but the species diversity on the reef is comparable to that of reef systems in the Caribbean Sea. The Florida Museum of Natural History defines three communities on the Florida reefs; the hardbottom community lies closest to the Florida Keys and consists of algae, sea fans and stony corals growing on limestone rock that has a thin covering of sand. The stony corals in hardbottom communities include Smooth Starlet coral, Mustard Hill Coral, Golfball coral, Elliptical Star coral and Common Brain coral. Hardbottom provides habitat for anemones, crabs, spiny lobsters, sea cucumbers and various fish, including grunts, groupers, Ocean surgeon and Great barracuda. Second is the patch reef community. Patch reefs form in shallow water, some in Hawk Channel and some on the outer reef, but on White Bank between Hawk Channel and the outer reefs. Patch reefs start from corals growing on a hard bottom, but grow upward as new corals establish themselves on the skeletons of dead corals.

Most of the structure of patch reefs is formed from brain corals. Other corals attach. Patch reefs may grow up to the surface of the water, spread outwards. Dome-type patch reefs, found in Hawk Channel and on White Bank, are round or elliptical, are less than three meters high, but may reach up to nine meters high. Dome-type patch reefs are surrounded by sand, kept clear due to browsing by long-spined sea urchins and grass-eating fish. Linear-type patch reefs are found on the outer reefs, are linear or curved, they occur in single or multiple rows, trending the same direction as the bank reefs on the outer reefs. Linear-type patch reefs include Elkhorn coral, rare on the dome-type patch reefs; as dead coral skeletons age and are weakened by the activities of boring sponges and mollusks and by wave action, parts of a patch reef may collapse. Patch reefs provide habitat for spiny lobsters and for many species of fish, including Bluehead wrasse, Ocean surgeon and Queen angelfish, White and Spanish grunts and other snappers and Stoplight parrotfish, Sergeant major, Trumpetfish, groupers, Bar jack, Great barracuda, squirrelfish and green morays.

Third is the bank reef community. Bank reefs are found on the outer reefs. Bank reefs consist of three zones; the reef flat is closest to the keys, consists of coralline algae growing on fragments of coral skeletons. Further out to sea are the spur and groove formations, low ridges of coral separated by channels with sand bottoms; the shallowest parts of the spurs support fire zoanthids. Starting at five or six feet deep, star, br

In quantum field theory, the Gupta–Bleuler formalism is a way of quantizing the electromagnetic field. The formulation is due to theoretical physicists Suraj N. Konrad Bleuler. Firstly, consider a single photon. A basis of the one-photon vector space is given by the eigenstates | k, ϵ μ ⟩ where k, the 4-momentum is null and the k 0 component, the energy, is positive and ϵ μ is the unit polarization vector and the index μ ranges from 0 to 3. So, k is uniquely determined by the spatial momentum k →. Using the bra–ket notation, this space is equipped with a sesquilinear form defined by ⟨ k → a; the metric signature used here is +−−−. However, this sesquilinear form gives positive norms for spatial polarizations but negative norms for time-like polarizations. Negative probabilities are unphysical, not to mention a physical photon only has two transverse polarizations, not four. If one includes gauge covariance, one realizes; this is given by the restriction k ⋅ ϵ = 0. However, the longitudinal component is an unphysical gauge.

While it would be nice to define a stricter restriction than the one given above which only leaves the two transverse components, it is easy to check that this can't be defined in a Lorentz covariant manner because what is transverse in one frame of reference isn't transverse anymore in another. To resolve this difficulty, first look at the subspace with three polarizations; the sesquilinear form restricted to it is semidefinite, better than indefinite. In addition, the subspace with zero norm turns out to be none other than the gauge degrees of freedom. So, define the physical Hilbert space to be the quotient space of the three polarization subspace by its zero norm subspace; this space has a positive definite form. This technique can be extended to the bosonic Fock space of multiparticle photons. Using the standard trick of adjoint creation and annihilation operators, but with this quotient trick, one can formulate free field vector potential operator valued distribution A satisfying ∂ μ ∂ μ A = 0 with the condition ⟨ χ | ∂ μ A μ | ψ ⟩ = 0 for physical states | χ ⟩ and | ψ ⟩ in the Fock space.

This is not the same thing as ∂ μ A μ = 0. Note that if O is any gauge invariant operator, ⟨ χ | O | ψ ⟩ does not depend upon the choice of the representatives of the equivalence classes, so, this quantity is well-defined; this is not true for non-gauge-invariant operators in general because the Lorenz gauge still leaves residual gauge degrees of freedom. In an interacting theory of quantum electrodynamics, the Lorenz gauge condition still applies, but A no longer satisfies the free wave equation. BRST formalism Quantum gauge theory Quantum electrodynamics ξ gauge Bleuler, K. "Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen", Helv. Phys. Acta, 23: 567–586, doi:10.5169/seals-112124 Gupta, S. "Theory of Longitudinal Photons in Quantum Electrodynamics", Proc. Phys. Soc. 63A: 681–691, Bibcode:1950PPSA...63..681G, doi:10.1088/0370-1298/63/7/301

Kerelaw House was part of the former Kerelaw Estate situated on the west coast of Ayrshire, Scotland, in the town of Stevenston. The house was built in the neo-Palladian style in 1787 by Lieut.-Col. Alexander Hamilton. Hamilton left considerable debts. Captain Logan Neely was forced to sell the mansion house to Gavin Fullarton, Esq.. A retired West Indies merchant, in 1838 along with the rest of the Kerelaw Estate including Kerelaw Castle; the Fullarton family were a cadet branch of the ancient family of the Fullartons of Kirkmichael, in Arran, who held their charter from the days of Robert the Bruce. The family were hereditary Crowners in the island of Arran, their family motto was Lux in tenebris. The light shineth in darkness. In 1919 the house was bought by James Campbell, WS. Campbell and his family were the last family to live at Kerelaw; the house was instead demolished. Built in the Adam style, Kerelaw House was a tall, three-storey ashlar building of five bays with a wide projecting central bay.

A long driveway leads up to the house from the nearby road, is still in existence, having latterly been used as an entrance to Kerelaw Residential School. There is, however, no other trace of the house. Mayville HouseDavis refers to this property as an exceptionally attractive and delightful little mansion, built around 1720 for Robert Baillie, father of Lesley Baillie, Burns's'Bonnie Lesley'; the property became part of the Kerelaw Estate until sold by Mr James Campbell in 1914. Hullerhirst HouseThis small 18th-century dwelling was a dower house for Kerelaw House. Clements, James. Stevenston; the Kernel of Cunninghame. Glasgow: Gilmour and Lawrence. Davis, Michael; the Castles and Mansions of Ayrshire. Ardrishaig, Argyll M. C. Davis, 1991. McSherry, R & M. Old Stevenston. Catrine: Stenlake Publishing. OCLC 39876063. McLatchie, Alexander. Kerelaw House. A History of the Ayrshire Mansion and the American Connection. Stevenston: Alexander McLatchie. Paterson, James. History of the counties of Ayr and Wigton, Vol. 3.

Edinburgh: James Stillie. OCLC 4352073. Robertson, George. A genealogical account of the principal families in Ayrshire... Irvine: Cunninghame P. sold by A. Constable, Edinburgh. OCLC 181661431. Kerelaw Glen, YouTube Video

The Carlebach Movement is an Orthodox Jewish movement inspired by the legacy of Rabbi Shlomo Carlebach. The Carlebach Movement has promoted a form of Jewish worship, colloquially known as "Carlebach nusach". One of the centers of the movement is Mevo Modi'im in Israel; the movement originates with the founding of The House of Love and Prayer, a synagogue founded by Rabbi Carlebach, inspired by the counterculture of the 1960s. Rabbi Carlebach called his followers "holy hippielech". Many of Carlebach's followers soon began practicing Judaism according to the Orthodox tradition. Carlebach founded a Moshav settlement in Israel. A number of his followers continue to live there today; the Moshav is referred to as the "Carlebach Moshav". Following Rabbi Carlebach's death, his followers organized a number of commemorative events, paying tribute to their deceased leader; these events included both traditional Jewish mourning events, as well as concerts and Friday night services incorporating songs composed by Rabbi Carlebach.

Carlebach's legacy inspired the creation of a musical presented by the National Yiddish Theatre titled "The House of Love and Prayer". Carlebach's daughter, Neshama Carlebach was among the production's collaborators, and a Broadway musical, titled Soul Doctor: Journey of a Rockstar Rabbi ran in New Orleans and New York City. The Carlebach movement does not have a centralized leadership, no legal entity represents the movement at large; the movement is not homogenous. Carlebach followers are located around the world near existing Orthodox communities. Since Carlebach's death, a number of Orthodox Synagogues have adapted their liturgical style to incorporate Carlebach tunes and customs. In some cases, synagogues are formed for this purpose, have attracted Jews from non-Carlebach communities. There are believed to be over 100 Carlebach synagogues around the world. Shlomo Carlebach Carlebach minyan The Carlebach Shul Official Website

Karmelyukove Podillya is a national park in southwest Ukraine on the forested southern slopes of the Ukrainian Shield. It is located in the Chechelnyk districts of the Ukraine's Vinnytsia region, its area is 16518 hectares and it was founded on 16 December 2009. The national nature park was created in accordance with the decree of the President of Ukraine Viktor Yushchenko at December 16, 2009 for the purpose of conservation and sustainable using of its unique natural and historical-cultural complexes of Southern Podillya that have important environmental, historical, aesthetic and curative value. In the National Nature Park, Karmelyukove Podillya, agreed in due including 20203,4 hectares of state-owned land, including 16,518 hectares of land that are excluded from the state enterprise "Chechelnitsky forestry" and granted National Nature Park in constant use, 3685, 4 acres of land included in its composition, without exception. Media related to Karmelyukove Podillya at Wikimedia Commons

Los Pepes, a name derived from the Spanish phrase "Perseguidos por Pablo Escobar", was a vigilante group composed of enemies of Pablo Escobar. They waged a small-scale war against the Medellín Cartel in the early 1990s, which ended in 1993 following the death of Escobar. There are reports that Los Pepes had ties to some members of the Colombian National Police the Search Bloc, with whom they exchanged information in order to execute their activities against Escobar. According to documents released to the public by the U. S. Central Intelligence Agency in 2008, "Colombian National Police director general Miguel Antonio Gómez Padilla said'that he had directed a senior CNP intelligence officer to maintain contact with Fidel Castaño, paramilitary leader of Los Pepes, for the purposes of intelligence collection'." Given that the main objective of Los Pepes was to assassinate Escobar, they acted in the same way that the Medellín Cartel acted against their enemies: killing anyone who had any allegiance with Escobar, such as their guards, accountants or lawyers, in addition to directly threatening friends and family of Pablo Escobar.

They were involved in the destruction of two haciendas. They were characterized by the frequent use of explosives in their attacks. After Escobar was shot and killed when fighting against the Search Bloc in 1993, several of their leaders went on to become leaders of a national paramilitary alliance in Colombia, the United Self-Defense Forces of Colombia, a paramilitary death squad, formed not only for the purpose of fighting the Cartel but the Revolutionary Armed Forces of Colombia, a Marxist guerrilla group; the Castaño Brothers were founders of several paramilitary groups and the driving force behind the AUC's creation. Another member of Los Pepes, Diego Murillo Bejarano aka "Don Berna" became Inspector General of the AUC as well as an important drug trafficker with The Office of Envigado; the Institute for Policy Studies is searching for details of what connections the CIA and DEA had to Los Pepes. They have launched a lawsuit under the Freedom of Information Act against the CIA; that suit has resulted in the declassification of thousands of documents from the CIA as well as other U.

S. agencies including the Department of State, Drug Enforcement Administration, Defense Intelligence Agency and the U. S Coast Guard; these documents have been made public at the website Pepes Project. Mark Bowden's book Killing Pablo highlights some of the operations of Los Pepes and describes some of the forms of cooperation and support that the group received from members of the Colombian National Police. Los Pepes are featured in the second season of the Netflix television series Narcos. Diego Murillo Bejarano Carlos Castaño Fidel Castaño Peasant Self-Defenders of Córdoba and Urabá United Self-Defense Forces of Colombia Bowden, Mark. Killing Pablo: The Hunt for the World's Greatest Outlaw Information paper on Los Pepes Pepes Project