title: Giovanni Boccaccio

text: Boccaccio, together with Dante Alighieri and Francesco Petrarca, is part of the so-called "Three Crowns" of Italian literature. He is remembered for being one of the precursors of humanism, of which he helped lay the foundations in the city of Florence, in conjunction with the activity of his friend and teacher Petrarch. He was the one who initiated Dante's criticism and philology: Boccaccio devoted himself to copying codices of the "Divine Comedy" and was a promoter of Dante's work and figure.


title: Giovanni Boccaccio

text: In the twentieth century, Boccaccio was the subject of critical-philological studies by Vittore Branca and Giuseppe Billanovich, and his "Decameron" was transposed to the big screen by the director and writer Pier Paolo Pasolini.


title: Giovanni Boccaccio

text: The details of Boccaccio's birth are uncertain. He was born in Florence or in a village near Certaldo where his family was from. He was the son of Florentine merchant Boccaccino di Chellino and an unknown woman; he was likely born out of wedlock. Boccaccio's stepmother was called Margherita de' Mardoli.


title: Giovanni Boccaccio

text: Boccaccio grew up in Florence. His father worked for the Compagnia dei Bardi and, in the 1320s, married Margherita dei Mardoli, who was of a well-to-do family. Boccaccio may have been tutored by Giovanni Mazzuoli and received from him an early introduction to the works of Dante. In 1326, his father was appointed head of a bank and moved with his family to Naples. Boccaccio was an apprentice at the bank but disliked the banking profession. He persuaded his father to let him study law at the "Studium" (the present-day University of Naples), where he studied canon law for the next six years. He also pursued his interest in scientific and literary studies.


title: Giovanni Boccaccio

text: His father introduced him to the Neapolitan nobility and the French-influenced court of Robert the Wise (the king of Naples) in the 1330s. At this time, he fell in love with a married daughter of the king, who is portrayed as "Fiammetta" in many of Boccaccio's prose romances, including "Il Filocolo" (1338). Boccaccio became a friend of fellow Florentine Niccolò Acciaioli, and benefited from his influence as the administrator, and perhaps the lover, of Catherine of Valois-Courtenay, widow of Philip I of Taranto. Acciaioli later became counselor to Queen Joanna I of Naples and, eventually, her "Grand Seneschal".


title: Giovanni Boccaccio

text: It seems that Boccaccio enjoyed law no more than banking, but his studies allowed him the opportunity to study widely and make good contacts with fellow scholars. His early influences included Paolo da Perugia (a curator and author of a collection of myths called the "Collectiones"), humanists Barbato da Sulmona and Giovanni Barrili, and theologian Dionigi di Borgo San Sepolcro.


title: Giovanni Boccaccio

text: In Naples, Boccaccio began what he considered his true vocation of poetry. Works produced in this period include "Il Filostrato" and "Teseida" (the sources for Chaucer's "Troilus and Criseyde" and "The Knight's Tale", respectively), "The Filocolo" (a prose version of an existing French romance), and "La caccia di Diana" (a poem in "terza rima" listing Neapolitan women). The period featured considerable formal innovation, including possibly the introduction of the Sicilian octave, where it influenced Petrarch.


title: Giovanni Boccaccio

text: Boccaccio returned to Florence in early 1341, avoiding the plague of 1340 in that city, but also missing the visit of Petrarch to Naples in 1341. He had left Naples due to tensions between the Angevin king and Florence. His father had returned to Florence in 1338, where he had gone bankrupt. His mother died shortly afterward (possibly, as she was unknown – see above). Boccaccio continued to work, although dissatisfied with his return to Florence, producing "Comedia delle ninfe fiorentine" in 1341 (also known as "Ameto"), a mix of prose and poems, completing the fifty-canto allegorical poem "Amorosa visione" in 1342, and "Fiammetta" in 1343. The pastoral piece "Ninfale fiesolano" probably dates from this time, also. In 1343, Boccaccio's father remarried to Bice del Bostichi. His other children by his first marriage had all died, but he had another son named Iacopo in 1344.


title: Giovanni Boccaccio

text: In Florence, the overthrow of Walter of Brienne brought about the government of "popolo minuto" ("small people", workers). It diminished the influence of the nobility and the wealthier merchant classes and assisted in the relative decline of Florence. The city was hurt further in 1348 by the Black Death, which killed some three-quarters of the city's population, later represented in the "Decameron".


title: Giovanni Boccaccio

text: From 1347, Boccaccio spent much time in Ravenna, seeking new patronage and, despite his claims, it is not certain whether he was present in plague-ravaged Florence. His stepmother died during the epidemic and his father was closely associated with the government efforts as minister of supply in the city. His father died in 1349 and Boccaccio was forced into a more active role as head of the family.


title: Giovanni Boccaccio

text: Boccaccio began work on "The Decameron" around 1349. It is probable that the structures of many of the tales date from earlier in his career, but the choice of a hundred tales and the frame-story "lieta brigata" of three men and seven women dates from this time. The work was largely complete by 1352. It was Boccaccio's final effort in literature and one of his last works in Tuscan vernacular; the only other substantial work was "Corbaccio" (dated to either 1355 or 1365). Boccaccio revised and rewrote "The Decameron" in 1370–1371. This manuscript has survived to the present day.


title: Giovanni Boccaccio

text: From 1350, Boccaccio became closely involved with Italian humanism (although less of a scholar) and also with the Florentine government. His first official mission was to Romagna in late 1350. He revisited that city-state twice and also was sent to Brandenburg, Milan and Avignon. He also pushed for the study of Greek, housing Barlaam of Calabria, and encouraging his tentative translations of works by Homer, Euripides, and Aristotle. In these years, he also took minor orders.


title: Giovanni Boccaccio

text: In October 1350, he was delegated to greet Francesco Petrarch as he entered Florence and also to have Petrarch as a guest at Boccaccio's home, during his stay. The meeting between the two was extremely fruitful and they were friends from then on, Boccaccio calling Petrarch his teacher and "magister". Petrarch at that time encouraged Boccaccio to study classical Greek and Latin literature. They met again in Padua in 1351, Boccaccio on an official mission to invite Petrarch to take a chair at the university in Florence. Although unsuccessful, the discussions between the two were instrumental in Boccaccio writing the "Genealogia deorum gentilium"; the first edition was completed in 1360 and this remained one of the key reference works on classical mythology for over 400 years. It served as an extended defense for the studies of ancient literature and thought. Despite the Pagan beliefs at its core, Boccaccio believed that much could be learned from antiquity. Thus, he challenged the arguments of clerical intellectuals who wanted to limit access to classical sources to prevent any moral harm to Christian readers. The revival of classical antiquity became a foundation of the Renaissance, and his defense of the importance of ancient literature was an essential requirement for its development. The discussions also formalized Boccaccio's poetic ideas. Certain sources also see a conversion of Boccaccio by Petrarch from the open humanist of the "Decameron" to a more ascetic style, closer to the dominant fourteenth century ethos. For example, he followed Petrarch (and Dante) in the unsuccessful championing of an archaic and deeply allusive form of Latin poetry. In 1359, following a meeting with Pope Innocent VI and further meetings with Petrarch, it is probable that Boccaccio took some kind of religious mantle. There is a persistent (but unsupported) tale that he repudiated his earlier works as profane in 1362, including "The Decameron".


title: Giovanni Boccaccio

text: In 1360, Boccaccio began work on "De mulieribus claris", a book offering biographies of 106 famous women, that he completed in 1374.


title: Giovanni Boccaccio

text: A number of Boccaccio's close friends and other acquaintances were executed or exiled in the purge following the failed coup of 1361. It was in this year that Boccaccio left Florence to reside in Certaldo, although not directly linked to the conspiracy, where he became less involved in government affairs. He did not undertake further missions for Florence until 1365, and traveled to Naples and then on to Padua and Venice, where he met up with Petrarch in grand style at Palazzo Molina, Petrarch's residence as well as the place of Petrarch's library. He later returned to Certaldo. He met Petrarch only once again in Padua in 1368. Upon hearing of the death of Petrarch (19 July 1374), Boccaccio wrote a commemorative poem, including it in his collection of lyric poems, the "Rime".


title: Giovanni Boccaccio

text: He returned to work for the Florentine government in 1365, undertaking a mission to Pope Urban V. The papacy returned to Rome from Avignon in 1367, and Boccaccio was again sent to Urban, offering congratulations. He also undertook diplomatic missions to Venice and Naples.


title: Giovanni Boccaccio

text: Of his later works, the moralistic biographies gathered as "De casibus virorum illustrium" (1355–74) and "De mulieribus claris" (1361–1375) were most significant. Other works include a dictionary of geographical allusions in classical literature, "De montibus, silvis, fontibus, lacubus, fluminibus, stagnis seu paludibus, et de nominibus maris liber". He gave a series of lectures on Dante at the Santo Stefano church in 1373 and these resulted in his final major work, the detailed "Esposizioni sopra la Commedia di Dante". Boccaccio and Petrarch were also two of the most educated people in early Renaissance in the field of archaeology.


title: Giovanni Boccaccio

text: Boccaccio's change in writing style in the 1350s was due in part to meeting with Petrarch, but it was mostly due to poor health and a premature weakening of his physical strength. It also was due to disappointments in love. Some such disappointment could explain why Boccaccio came suddenly to write in a bitter "Corbaccio" style, having previously written mostly in praise of women and love, though elements of misogyny are present in "Il Teseida". Petrarch describes how Pietro Petrone (a Carthusian monk) on his death bed in 1362 sent another Carthusian (Gioacchino Ciani) to urge him to renounce his worldly studies. Petrarch then dissuaded Boccaccio from burning his own works and selling off his personal library, letters, books, and manuscripts. Petrarch even offered to purchase Boccaccio's library, so that it would become part of Petrarch's library. However, upon Boccaccio's death, his entire collection was given to the monastery of Santo Spirito, in Florence, where it still resides.


title: Giovanni Boccaccio

text: His final years were troubled by illnesses, some relating to obesity and what often is described as dropsy, severe edema that would be described today as congestive heart failure. He died on 21 December 1375 in Certaldo, where he is buried.


title: Square number

text: In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .


title: Square number

text: The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name "square" number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by "n" points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of "n"; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers).


title: Square number

text: Square numbers are non-negative. A non-negative integer is a square number when its square root is again an integer. For example, formula_1 so 9 is a square number.


title: Square number

text: For a non-negative integer , the th square number is , with being the zeroth one. The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square, for example,


title: Square number

text: Starting with 1, there are formula_3 square numbers up to and including , where the expression formula_4 represents the floor of the number .


title: Square number

text: The difference between any perfect square and its predecessor is given by the identity . Equivalently, it is possible to count square numbers by adding together the last square, the last square's root, and the current root, that is, .


title: Square number

text: The expression for the th square number is . This is also equal to the sum of the first odd numbers as can be seen in the above pictures, where a square results from the previous one by adding an odd number of points (shown in magenta). The formula follows:


title: Square number

text: There are several recursive methods for computing square numbers. For example, the th square number can be computed from the previous square by . Alternatively, the th square number can be calculated from the previous two by doubling the th square, subtracting the th square number, and adding 2, because . For example,


title: Square number

text: For example, since formula_9 one has formula_10 It follows that is the only prime number one less than a square (). More generally, the difference of the squares of two numbers is the product of their sum and their difference. That is,


title: Square number

text: (this is the difference-of-squares formula). This can be useful for mental arithmetic: for example, can be easily computed as .


title: Square number

text: A square number is also the sum of two consecutive triangular numbers. The sum of two consecutive square numbers is a centered square number. Every odd square is also a centered octagonal number.


title: Square number

text: Another property of a square number is that (except 0) it has an odd number of positive divisors, while other natural numbers have an even number of positive divisors. An integer root is the only divisor that pairs up with itself to yield the square number, while other divisors come in pairs.


title: Square number

text: Lagrange's four-square theorem states that any positive integer can be written as the sum of four or fewer perfect squares. Three squares are not sufficient for numbers of the form . A positive integer can be represented as a sum of two squares precisely if its prime factorization contains no odd powers of primes of the form . This is generalized by Waring's problem.


title: Square number

text: In base 12, a square number can end only with square digits (like in base 12, a prime number can end only with prime digits or 1), that is, 0, 1, 4 or 9, as follows:


title: Square number

text: Similar rules can be given for other bases, or for earlier digits (the tens instead of the units digit, for example). All such rules can be proved by checking a fixed number of cases and using modular arithmetic.


title: Square number

text: In general, if a prime  divides a square number  then the square of must also divide ; if fails to divide , then is definitely not square. Repeating the divisions of the previous sentence, one concludes that every prime must divide a given perfect square an even number of times (including possibly 0 times). Thus, the number is a square number if and only if, in its canonical representation, all exponents are even.


title: Square number

text: Squarity testing can be used as alternative way in factorization of large numbers. Instead of testing for divisibility, test for squarity: for given and some number , if is the square of an integer  then divides . (This is an application of the factorization of a difference of two squares.) For example, is the square of 3, so consequently divides 9991. This test is deterministic for odd divisors in the range from to where covers some range of natural numbers formula_12


title: Square number

text: 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201...


title: Square number

text: The sum of the first odd integers, beginning with one, is a perfect square: 1, 1 + 3, 1 + 3 + 5, 1 + 3 + 5 + 7, etc. This explains Galileo's law of odd numbers: if a body falling from rest covers one unit of distance in the first arbitrary time interval, it covers 3, 5, 7, etc., units of distance in subsequent time intervals of the same length. From "s" = "ut" + "at", for "u" = 0 and constant "a" (acceleration due to gravity without air resistance); so "s" is proportional to "t", and the distance from the starting point are consecutive squares for integer values of time elapsed.


title: Square number

text: The sum of the "n" first cubes is the square of the sum of the "n" first positive integers; this is Nicomachus's theorem.


title: Square number

text: Squares of even numbers are even, and are divisible by 4, since (2"n") = 4"n". Squares of odd numbers are odd, and are congruent to 1 modulo 8, since (2"n" + 1) = 4"n"("n" + 1) + 1, and "n"("n" + 1) is always even. In other words, all odd square numbers have a remainder of 1 when divided by 8.


title: Square number

text: Every odd perfect square is a centered octagonal number. The difference between any two odd perfect squares is a multiple of 8. The difference between 1 and any higher odd perfect square always is eight times a triangular number, while the difference between 9 and any higher odd perfect square is eight times a triangular number minus eight. Since all triangular numbers have an odd factor, but no two values of differ by an amount containing an odd factor, the only perfect square of the form is 1, and the only perfect square of the form is 9.


title: .410 bore

text: The .410 bore is one of the smallest caliber of shotgun shell commonly available (along with the 9mm Flobert rimfire cartridge, and the less common .22 rimfire shot shell). A .410 bore shotgun loaded with shot shells is well suited for small game hunting and pest control. The .410 started off in the UK as a garden gun along with the .360 and the No. 3 bore (9 mm) rimfire, No. 2 bore (7 mm) rimfire, and No. 1 bore (6 mm) rimfire. .410 shells have similar base dimensions to the .45 Colt cartridge, allowing many single-shot firearms, as well as some derringers chambered in that caliber, to fire .410 shot shells without any modifications.


title: .410 bore

text: Lancaster's pattern centerfire and pinfire .410 shot cartridges first appeared in Eley Brothers Ltd. flysheets in 1857. By 1874, Eleys were advertising modern centerfire .410 cartridges. It appears to have become popular around 1900, although it was recommended as "suited to the requirements of naturalists, garden guns and for such weapons as walking-stick guns", presumably for self-defense, in 1892 by W. W. Greener. The first ammunition was 2.0 inches (50.8 mm) long, compared with the modern 2.5 (63.5 mm) and sizes. Aluminum shells are available but are not reloadable, as are paper or plastic shells. Full length brass shells can be found and are reloadable. Brass shells can be made from .444 Marlin rifle cartridges, and these are reloadable .


title: .410 bore

text: Shotguns in .410 loaded with shot shells are well suited for small game hunting and pest control; including rabbits, squirrels, snakes, rats, and birds. A .410 loaded with 1/4 ounce slugs is effective against larger animals such as coyotes and deer.


title: .410 bore

text: While a .410 is inferior to the traditional 12-gauge shotshell for defensive use, a number of companies market defensive guns chambered in .410, such as the Mossberg 500 Home Security Model shotgun, the Smith & Wesson Governor revolver, and the Taurus Judge revolver. Defensive ammunition such as buckshot, slugs and combination loads are common. American Derringer and Winchester market ammunition loaded with five 000 buckshot pellets in shells and three pellets in shells. Combination shells such as Winchester Supreme Elite .410 shells are loaded with three 71 grain disks and twelve BB pellets.


title: .410 bore

text: The small size of the .410 bore makes it popular for use in compact firearms carried for emergency use. These are often combination guns, with a .22 Hornet or .22 rimfire rifle barrel mounted over a .410 bore shotgun barrel.


title: .410 bore

text: The Snake Charmer is a .410 gauge, stainless steel, single shot, break-action shotgun, with an exposed hammer, an , black molded plastic furniture and a short thumb-hole butt-stock that holds four additional shotgun shells. These light-weight guns have an overall length of . They are commonly used by gardeners and farmers for pest control. It originally sold for $89.95 and was marketed as a general purpose utility shotgun "perfect" for "fishing - hunting - camping - back packing - survival - home defense - truck or Jeep gun".


title: .410 bore

text: The Savage Model 24 is an American-made, over and under, combination gun, manufactured by Savage Arms. The basic .22LR over .410 gauge model weighs , has barrels, and an overall length of . It may also be disassembled for ease of stowage. Its predecessor was made by Stevens and sported a tenite stock and forearm. In WWII, 15,000 were ordered and issued in air crew survival kits for Army Air Force bomber crews to be used as survival arms in the event they were shot down.


title: .410 bore

text: The M6 aircrew survival weapon was made for the US Air Force, with a .22 Hornet rifle barrel mounted over a .410 bore shotgun barrel and was first issued in the Korean War. The military also lists an aluminum .410 shell, with a rifle primer, as standard issue under the ammunition inventory name M-35. The civilian version Springfield Armory M6 Scout has a .22 rimfire or .22 Hornet over a .410 bore shotgun barrel. The original M6 has a barrel, the same length as the stock, and folds in half for storage, making a compact package. With the short barrel, this is legally classified as an "any other weapon" in the United States, so the M6 Scout is made with barrels for civilian sales. Special flare cartridges in .410 were issued with the USAF model.


title: .410 bore

text: The fact that the .410 bore shell fits in a .45 Colt chamber has resulted in some unusual applications. While shotguns are often limited in minimum length, a firearm chambered in .45 Colt, such as the Contender pistol, is not defined as a shotgun even though it can chamber shotgun shells. In the UK .410 shot-pistols are used around pheasant pens to kill rats where a full-length shotgun would be inappropriate.


title: .410 bore

text: The Thompson Center Arms Contender pistols are commonly encountered with a special .45 Colt/.410 bore barrel. The barrel is rifled for the .45 Colt, but has a special choke and vent rib to make it function as a shotgun. Due to the rifled barrel, the assembled firearm is considered a rifle or pistol (depending on barrel length) and thus is not subject to the National Firearms Act's minimum barrel length. Nonetheless, possession of a Thompson Center Arms .45/.410 pistol barrel is illegal in California, for both dealers and individuals, and such a barrel may not legally be shipped into the state, or even taken into California for a hunting trip, by reason of it being classified as a short barreled shotgun (SBSG) when used with a Contender receiver.


title: .410 bore

text: Bond Arms also offers various Derringer models which chamber both .45 Colt cartridges and .410 shotshell.


title: .410 bore

text: Also, Taurus, Magnum Research, and Smith & Wesson offer revolvers with extended cylinders, long enough to hold .410 shells as well. Magnum Research offers a single-action revolver in their BFR (big frame revolver) line, while the Taurus Judge is similar in price to their other double-action revolvers, with the Raging Judge model capable of chambering and firing the .454 Casull cartridge. The Smith & Wesson Governor is a double-action revolver also capable of firing .45 Colt as well as .45 ACP cartridges with the aid of moon clips. The discontinued MIL Thunder 5 is also chambered in .410-bore. Over the years, a large number of devices have been made that will convert larger-gauge shotguns to accept .410 shotgun shells.


title: .410 bore

text: Most shotgun cartridges are measured in terms of "shotgun gauge". Shotgun gauge is determined by the weight of a round lead ball that is sized to fit into its barrel. For example, the barrel of a 12-gauge shotgun is equal to the diameter of a one-twelfth/pound lead ball (0.729 in) and a 20-gauge can fit a one-twentieth/pound lead ball (0.615 in). Using this method a .410 bore is equivalent to a (hypothetical) 67-gauge.


title: Battle of Kadesh

text: The Battle of Kadesh or Battle of Qadesh took place between the forces of the New Kingdom of Egypt under Ramesses II and the Hittite Empire under Muwatalli II at the city of Kadesh on the Orontes River, just upstream of Lake Homs near the modern Lebanon–Syria border.


title: Battle of Kadesh

text: The battle is generally dated to 1274 BC from the Egyptian chronology, and is the earliest pitched battle in recorded history for which details of tactics and formations are known. It is believed to have been the largest chariot battle ever fought, involving between 5,000 and 6,000 chariots in total.


title: Battle of Kadesh

text: As a result of discovery of multiple Kadesh inscriptions and the Egyptian–Hittite peace treaty, it is the best documented battle in all of ancient history.


title: Battle of Kadesh

text: After expelling the Hyksos' 15th Dynasty around 1550 BC, the Egyptian New Kingdom rulers became more aggressive in reclaiming control of their state's borders. Thutmose I, Thutmose III and his son and coregent Amenhotep II fought battles from Megiddo north to the Orontes River, including conflict with Kadesh.


title: Battle of Kadesh

text: Many of the Egyptian campaign accounts between c. 1400 and 1300 BC reflect the general destabilization of the Djahy region (southern Canaan). The reigns of Thutmose IV and Amenhotep III were undistinguished, except that Egypt continued to lose territory to the Mitanni in northern Syria.


title: Battle of Kadesh

text: During the late Eighteenth Dynasty, the Amarna letters tell the story of the decline of Egyptian influence in the region. The Egyptians showed flagging interest here until almost the end of the dynasty. Horemheb (d. 1292 BC), the last ruler of this dynasty, campaigned in this region, finally beginning to turn Egyptian interest back to the area.


title: Battle of Kadesh

text: This process continued in the Nineteenth Dynasty. Like his father Ramesses I, Seti I was a military commander who set out to restore Egypt's empire to the days of the Tuthmosid kings almost a century before. Inscriptions on the Karnak walls record the details of his campaigns into Canaan and ancient Syria. He took 20,000 men and reoccupied abandoned Egyptian posts and garrisoned cities. He made an informal peace with the Hittites, took control of coastal areas along the Mediterranean Sea and continued to campaign in Canaan. A second campaign led to his capture of Kadesh (where a stela commemorated his victory) and the Amurru kingdom. His son and heir Ramesses II campaigned with him. There are historical records that record a large weapons order by Ramesses II in the year before the expedition he led to Kadesh in his fifth regnal year.


title: Battle of Kadesh

text: However, at some point both regions may have lapsed back under Hittite control. What exactly happened to Amurru is disputed. Hittitologist Trevor R. Bryce suggests that although it may have fallen once again under Hittite control, it is more likely Amurru remained a Hittite vassal state.


title: Battle of Kadesh

text: The immediate antecedents to the Battle of Kadesh were the early campaigns of Ramesses II into Canaan. In the fourth year of his reign, he marched north into Syria, either to recapture Amurru or, as a probing effort, to confirm his vassals' loyalty and explore the terrain of possible battles. In the spring of the fifth year of his reign, in May 1274 BC, Ramesses II launched a campaign from his capital Pi-Ramesses (modern Qantir). The army moved beyond the fortress of Tjel and along the coast leading to Gaza.


title: Battle of Kadesh

text: The recovery of Amurru was Muwatalli II's stated motivation for marching south to confront the Egyptians.


title: Battle of Kadesh

text: Ramesses led an army of four divisions: Amun, Re (pRe), Set, and the apparently newly-formed Ptah division.


title: Battle of Kadesh

text: There was also a poorly documented troop called the "nrrn" (Ne'arin or Nearin), possibly Canaanite military mercenaries with Egyptian allegiance or even Egyptians, that Ramesses II had left in Amurru, apparently in order to secure the port of Sumur. This division would come to play a critical role in the battle. Also significant was the presence of Sherden troops within the Egyptian army. This is the first time they appear as Egyptian mercenaries, and they would play an increasingly significant role in Late Bronze Age history, ultimately appearing among the Sea Peoples that ravaged the east Mediterranean at the end of the Bronze Age. Healy in "Armies of the Pharaohs" observes:


title: Battle of Kadesh

text: On the Hittite side, King Muwatalli II had mustered several of his allies, among them Rimisharrinaa, the king of Aleppo. Ramesses II recorded a long list of 19 Hittite allies brought to Kadesh by Muwatalli. This list is of considerable interest to Hittitologists, as it reflects the extent of Hittite influence at the time.


title: Battle of Kadesh

text: Muwatalli had positioned his troops behind "Old Kadesh", but Ramesses was misled by two spies whom the Egyptians had captured to think that the Hittite forces were still far off, at Aleppo, and ordered his forces to set up camp. The false intelligence caused Ramesses to march hastily towards Kadesh, where the Egyptians were caught off-guard.


title: Battle of Kadesh

text: Ramesses II describes his arrival on the battlefield in the two principal inscriptions that he wrote concerning the battle, which were the so-called "Poem" and the "Bulletin":


title: Battle of Kadesh

text: As Ramesses and the Egyptian advance guard were about 11 kilometers from Kadesh, south of Shabtuna, he met two Shasu nomads who told him that the Hittite king was "in the land of Aleppo, on the north of Tunip" 200 kilometers away, where, the Shasu said, he was "(too much) afraid of Pharaoh, L.P.H., to come south". This was, state the Egyptian texts, a false report ordered by the Hittites "with the aim of preventing the army of His Majesty from drawing up to combat with the foe of Hatti". An Egyptian scout then arrived at the camp bringing two Hittite prisoners. The prisoners revealed that the entire Hittite army and the Hittite king were actually close at hand:


title: Battle of Kadesh

text: After this, Ramesses II called his princes to meet with him and discuss the fault of his governors and officials in not informing the position of Muwatalli II and his army. As Ramesses was alone with his bodyguard and the Amun division, the vizier was ordered to hasten the arrival of the Ptah and Seth divisions, with the Re division having almost arrived at the camp. While Ramesses was talking with the princes, the Hittite chariots crossed the river and charged the middle of the Re division as they were making their way toward Ramesses' position. The Re division was caught in the open and scattered in all directions. Some fled northward to the Amun camp, all the while being pursued by Hittite chariots.


title: Battle of Kadesh

text: The Hittite chariotry then rounded north and attacked the Egyptian camp, crashing through the Amun shield wall and creating panic among the Amun division. However, the momentum of the Hittite attack was already starting to wane, as the impending obstacles of such a large camp forced many Hittite charioteers to slow their attack; some were killed in chariot crashes. In the Egyptian account of the battle, Ramesses describes himself as being deserted and surrounded by enemies: "No officer was with me, no charioteer, no soldier of the army, no shield-bearer[.]"


title: Battle of Kadesh

text: Ramesses was able to defeat his attackers and to return to the Egyptian lines: "I was before them like Set in his moment. I found the mass of chariots in whose midst I was, scattering them before my horses[.]" The pharaoh, now facing a desperate fight for his life, summoned up his courage, called upon his god Amun, and fought to save himself. Ramesses personally led several charges into the Hittite ranks together with his personal guard, some of the chariots from his Amun division and survivors from the routed division of Re.


title: Battle of Kadesh

text: The Hittites, who believed their enemies to be totally routed, had stopped to plunder the Egyptian camp and so became easy targets for Ramesses's counterattack. His action was successful in driving the looters back towards the Orontes River and away from the Egyptian camp, and in the ensuing pursuit, the heavier Hittite chariots were easily overtaken and dispatched by the lighter, faster Egyptian chariots.


title: Battle of Kadesh

text: Although he had suffered a significant reversal, Muwatalli II still commanded a large force of reserve chariotry and infantry, as well as the walls of the town. As the retreat reached the river, he ordered another thousand chariots to attack the Egyptians, the stiffening element being the high nobles who surrounded the king. As the Hittite forces approached the Egyptian camp again, the Ne'arin troop contingent from Amurru suddenly arrived, surprising the Hittites. Finally, the Ptah division arrived from the south, threatening the Hittite rear.


title: Battle of Kadesh

text: After six charges, the Hittite forces were almost surrounded, and the survivors were pinned against the Orontes. The remaining Hittite elements, which had not been overtaken in the withdrawal, were forced to abandon their chariots and attempt to swim across the river, according to Egyptian accounts hurriedly ("as fast as crocodiles swimming"), where many of them drowned.


title: Battle of Kadesh

text: There is no consensus about the outcome or what took place, with views ranging from an Egyptian victory to a draw, or, in the view of Iranian Egyptologist Mehdi Yarahmadi, an Egyptian defeat, with the Egyptian accounts being simply propaganda. The Hittite army was ultimately forced to retreat, but the Egyptians were unsuccessful in capturing Kadesh.


title: Battle of Kadesh

text: Logistically unable to support a long siege of the walled city of Kadesh, Ramesses gathered his troops and retreated south towards Damascus and ultimately back to Egypt. Once back in Egypt, Ramesses then proclaimed victory since he had routed his enemies, but he did not even attempt to capture Kadesh. In a personal sense, however, the Battle of Kadesh was a triumph for Ramesses since after blundering into a devastating Hittite chariot ambush, the young king had courageously rallied his scattered troops to fight on the battlefield and escaped death or capture. The new lighter faster two-man Egyptian chariots were able to pursue and take down the slower three-man Hittite chariots from behind as they overtook them.


title: Battle of Kadesh

text: Hittite records from Hattusa, however, tell of a very different conclusion to the greater campaign in which a chastened Ramesses was forced to depart from Kadesh in defeat. Modern historians conclude that the battle ended in a draw from a practical point of view but was a turning point for the Egyptians, who had developed new technologies and rearmed before pushing back against the years-long steady incursions by the Hittites.


title: Battle of Kadesh

text: The Hittite king, Muwatalli II, continued to campaign as far south as the Egyptian province of Upi (Apa), which he captured and placed under the control of his brother Hattusili, the future Hattusili III. Egypt's sphere of influence in Asia was now restricted to Canaan. Even that was threatened for a time by revolts among Egypt's vassal states in the Levant, and Ramesses was compelled to embark on a series of campaigns in Canaan to uphold his authority there before he could initiate further assaults against the Hittite Empire.


title: Battle of Kadesh

text: In the eighth and ninth years of his reign, Ramesses extended his military successes. This time, he proved more successful against his Hittite foes by successfully capturing the cities of Dapur and Tunip, where no Egyptian soldier had been seen since under Thutmose III, almost 120 years earlier.


title: Battle of Kadesh

text: Ramesses's victory proved to be ephemeral, however. The thin strip of territory pinched between Amurru and Kadesh did not make for a stable possession. Within a year, it had returned to the Hittite fold, which meant that Ramesses had to march against Dapur once more in his tenth year. His second success was just as meaningless as his first since neither Egypt nor Hatti could decisively defeat the other in battle.


title: Battle of Kadesh

text: An official peace treaty with Hattusili III, the new king of the Hittites some 15 years after the Battle of Kadesh, and in the 21st year of Ramesses II's reign (1258 BC in conventional chronology), finally concluded running borderlands conflicts. The treaty was inscribed on a silver tablet, of which a clay copy survived in the Hittite capital of Hattusa, now in Turkey, and is on display at the Istanbul Archaeology Museum. An enlarged replica of the agreement hangs on a wall at the headquarters of the United Nations, as the earliest international peace treaty known to historians. Its text, in the Hittite version, appears in the links below. An Egyptian version survives on a papyrus.


title: Battle of Kadesh

text: There is more evidence in the form of texts and wall reliefs for this battle than for any other in the Ancient Near East, but almost all of it is from an Egyptian perspective. Indeed, the first scholarly report on the battle, by James Henry Breasted in 1903, praised the sources that allowed the reconstruction of the battle with certainty. However, some historians argue that the battle was a draw at best and that Egyptian influence over Amurru and Qadesh seems to have been lost forever.


title: Battle of Kadesh

text: The main source of information is in the Egyptian record of the battle for which a general level of accuracy is assumed, despite factual errors and propaganda. The bombastic nature of Ramesses's version has long been recognized. The Egyptian version of the battle is recorded in two primary forms, known as the "Poem" and the "Bulletin". The "Poem" has been questioned as actual verse, as opposed to a prose account similar to that recorded by other pharaohs. Likewise, the "Bulletin" is itself simply a lengthy caption accompanying the reliefs. The inscriptions are repeated multiple times (seven for the "Bulletin" and eight for the "Poem", in temples in Abydos, Temple of Luxor, Karnak, Abu Simbel and the Ramesseum).


title: Battle of Kadesh

text: In addition to these lengthy presentations, there are also numerous small captions used to point out various elements of the battle. Besides the inscriptions, there are textual occurrences preserved in "Papyrus Raifet" and "Papyrus Sallier III", and a rendering of these same events in a letter from Ramesses to Hattusili III written in response to a scoffing complaint by Hattusili about the pharaoh's victorious depiction of the battle.


title: Battle of Kadesh

text: Hittite references to the battle, including the above letter, have been found at Hattusa, but no annals have been discovered that might describe it as part of a campaign. Instead, there are various references made to it in the context of other events. That is especially true of Hattusili III for whom the battle marked an important milestone in his career.


title: Battle of Kadesh

text: Sources: Goetze, A., "The Hittites and Syria (1300–1200 B.C.)", in "Cambridge Ancient History" (1975) p. 253; Gardiner, Alan, "The Kadesh Inscriptions of Ramesses II" (1975) pp. 57ff.; Breasted, James Henry, "Ancient Records of Egypt; Historical Records" (1906) pp. 125ff.; Lichtheim, Miriam, "Ancient Egyptian Literature, Vol. 2: The New Kingdom" (1978), pp. 57ff.


title: Battle of Kadesh

text: In addition to these allies, the Hittite king also hired the services of some of the local Shasu tribes.


title: Bare Knuckle Fighting Championship

text: Bare Knuckle Fighting Championship (BKFC) is an American bare-knuckle boxing promotion based in Philadelphia. BKFC is the first promotion to hold an official state-sanctioned and commissioned bare-knuckle boxing event in the United States since 1889. Its first event was held in 2018, with 24 "numbered" events held as of April 2022. It is the largest bare knuckle boxing promotion company in the world and has featured notable talents such as Luis Palomino, Elvin Leon Brito, Jim Alers, Artem Lobov, Ricco Rodriguez, Charles Bennett, Kendall Grove, Chris Lytle, Joe Riggs, Chase Sherman, Leonard Garcia, Eric Prindle, Joey Beltran, Bec Rawlings, Shannon Ritch, Bobby Gunn, Jason Knight, Johnny Bedford, Paulie Malignaggi, Steve Banks, Sirimongkol Singmanasak, Buakaw Banchamek, Saenchai, Robert Morrow, and Chris Leben .


title: Bare Knuckle Fighting Championship

text: BKFC was founded in April 2018 and is presided over by former American professional boxer David Feldman. After first receiving approval to hold a sanctioned event in Cheyenne, Wyoming, BKFC held the first state sanctioned bare-knuckle boxing event in the United States since 1889. Each fight takes place in a specialized circular four-rope ring, referred to as the "Squared Circle.” BKFC 1, which took place on June 2, 2018, featured the first American sanctioned women's bare-knuckle fight in modern history. The Bare-Knuckle Boxing Hall of Fame recognized this milestone and awarded the victor of this contest, Bec Rawlings, with the National Police Gazette World Diamond Belt several days after her victory. BKFC recognizes the Police Gazette champions, and they may defend their titles within this promotion. At BKFC 3, Arnold Adams defeated Sam Shewmaker in the finals of an eight man tournament to be crowned as the inaugural BKFC Heavyweight Champion. This event also hosted the quarterfinals of a tournament to crown a Lightweight champion. In February, 2019, former UFC light heavyweight title contender Anthony Johnson announced that he will be joining the company in an administrative role.


title: Bare Knuckle Fighting Championship

text: On February 24, 2022, David Feldman announced on Ariel Helwani's show that TrillerNet had acquired a majority stake of BKFC, while not disclosing the value of the deal or percentages of the stake.


title: Bare Knuckle Fighting Championship

text: On June 24, 2022, Luis Palomino, Lightweight Champion, won the Welterweight Championship and becomes the first double champion in BKFC History.


title: Bare Knuckle Fighting Championship

text: In September 2022 it was announced by David Feldman that BKFC had acquired the U.K. based Bare Fist Boxing Association (BFBA) forming Bare Knuckle Fighting Championship UK (BKFC UK).


title: Bare Knuckle Fighting Championship

text: On August 20, 2021, BKFC was involved in controversy after the death of boxer Justin Thornton at BKFC 20.


title: Bare Knuckle Fighting Championship

text: Justin Thornton died as a result of spinal injury suffered during his BKFC debut. Thornton had been on a five-fight losing streak ahead of the fight. The matchmaking and regulations were criticised following the news on social media and by UFC president Dana White.


title: Bare Knuckle Fighting Championship

text: Initially, BKFC pay-per-view bouts were carried worldwide via FITE TV. On July 24, 2020 it was announced that starting on August, DAZN will be streaming BKFC events.


title: Bare Knuckle Fighting Championship

text: BKFC holds all bouts in a circular four-rope ring, referred to as the "Squared Circle". This ring incorporates elements of historical bare knuckle fighting by containing two scratch lines, three feet apart and in the middle of the ring. These scratch lines are based on the Broughton Rules, which governed bare knuckle fighting in the 19th century. It is a requirement that each fighter must start each round with their front foot on their scratch line. This is referred to as “Toe the Line”, and it is an instruction given to the fighters at the beginning of each round, followed by "Knuckle Up" which signals the beginning of the round.


title: Allen Stanford

text: Robert Allen Stanford (born March 24, 1950) is an American financial fraudster, former financier, and sponsor of professional sports. He is serving a 110-year federal prison sentence, having been convicted in 2012 of fraud, on charges that his investment company was the vehicle for a massive Ponzi scheme.


title: Allen Stanford

text: Stanford was the chairman of the now-defunct Stanford Financial Group of Companies. A fifth-generation Texan who once resided in Saint Croix, U.S. Virgin Islands, he holds dual citizenship, as a citizen of Antigua and Barbuda and of the United States. He contributed millions of dollars to politicians in Antigua and the United States, amongst other countries.


title: Allen Stanford

text: In early 2009, Stanford became the subject of several fraud investigations, and on February 17, 2009, was charged by the U.S. Securities and Exchange Commission with fraud and multiple violations of U.S. securities laws for alleged "massive ongoing fraud" involving $7 billion in certificates of deposits. The Federal Bureau of Investigation raided Stanford's offices in Houston, Texas; Memphis, Tennessee; and Tupelo, Mississippi. On February 27, 2009, the SEC amended its complaint to describe the alleged fraud as a "massive Ponzi scheme". He voluntarily surrendered to authorities on June 18, 2009. On March 6, 2012, Stanford was convicted on all charges except a single count of wire fraud. He is serving a 110-year sentence at United States Penitentiary, Coleman II in Coleman, Florida. In September 2014, Stanford filed an appeal; it was rejected in October 2015.


title: Allen Stanford

text: Stanford grew up in Mexia, Texas. His father, James Stanford (1927–2021), was mayor of Mexia and a member of the Board of Directors of Stanford Financial Group. His mother, Sammie (née Conn), is a nurse. After his parents divorced in 1959, Stanford and his brother went to live with their mother.


title: Allen Stanford

text: Stanford graduated from Eastern Hills High School in Fort Worth, Texas. In 1974, Stanford graduated from Baylor University in Waco, Texas, earning a BA degree in finance.


title: Allen Stanford

text: Stanford started in business in Waco, Texas, opening a bodybuilding gym that failed. His first success in business came from speculating in real estate in Houston after the Texas oil bubble burst in the early 1980s; his father was his partner in this venture. The men made a fortune in the 1980s, buying up depressed real estate and selling it years later as the market recovered. After his father retired in 1993, Stanford took control of the company, which by then had 500 employees.


title: Allen Stanford

text: Stanford moved to the Caribbean in the 1980s, first to Montserrat, then to Antigua. With Stanford Finance, he started Guardian International Bank on the island of Montserrat in 1985; he moved it to Antigua during a British crackdown on Montserrat's offshore-banking industry in the 1980s, renaming it Stanford International Bank, an affiliate of Stanford Financial.


title: Allen Stanford

text: Early in 2007, Stanford and Baldwin Spencer, prime minister of Antigua and Barbuda and formerly an ally, began verbally feuding in public.


title: Allen Stanford

text: In 2009, Antigua's Financial Services Regulatory Commission named a British firm, Vantis Business Recovery Services, the receiver for Stanford International Bank and Stanford Trust Company, the Associated Press reported.


title: Allen Stanford

text: Reports surfaced in early February 2009 that the SEC, the FBI, the Florida Office of Financial Regulation, and the Financial Industry Regulatory Authority, a major U.S. private-sector oversight body, were investigating Stanford Financial Group, questioning the consistently higher-than-market returns which Stanford International Bank claimed to make for its depositors. A former executive told SEC officials that Stanford presented hypothetical investment results as actual historical data in sales pitches to clients. Stanford claimed his certificates of deposit were as safe as, or safer than, U.S. government-insured accounts. A leaked cable message from the U.S. Embassy in the Bahamas reported as early as 2006 that companies under Stanford's control were "rumored to engage in bribery, money laundering, and political manipulation". The U.S. Ambassador to the Bahamas at the time was reported to have "managed to stay out of any one-on-one photos with Stanford" during a charity breakfast event.


title: Allen Stanford

text: Federal agents raided the offices of Stanford Financial on February 17, 2009, and treated it as "a kind of crime scene—cautioning people not to leave fingerprints". The SEC charged Stanford with "massive ongoing fraud" centered on an eight-billion-dollar investment scheme. Stanford's assets, along with those of his companies, were frozen and placed into receivership by a U.S. federal judge, who ordered Stanford to surrender his passport.


title: Allen Stanford

text: CNBC reported that Stanford tried to flee the country on the same day as the raids on his headquarters. He contacted a private jet owner and attempted to pay for a flight to Antigua with a credit card, but was refused because the company would accept only a wire transfer.


title: Allen Stanford

text: On February 19, acting at the request of the SEC, FBI agents located Stanford at his girlfriend's house near Fredericksburg, Virginia, and served him with civil legal papers filed by the SEC. The SEC often files civil charges before criminal charges are filed. Stanford was arrested on June 18, 2009. He surrendered his passport to federal prosecutors, and hired criminal defense lawyer Brendan Sullivan, who had represented Oliver North.


title: Allen Stanford

text: Various governments took over Stanford's business operations. The Eastern Caribbean Central Bank announced that it had taken over the local operations of the Bank of Antigua, which was renamed the Eastern Caribbean Amalgamated Bank. The Venezuelan government took over Stanford Bank Venezuela, the branch of Stanford's bank in that nation.


title: Allen Stanford

text: On February 27, 2009, the SEC said that Stanford and his accomplices operated a "massive Ponzi scheme", misappropriating billions of dollars of investors' money and falsifying the Stanford International Bank's records to hide their fraud. "Stanford International Bank's financial statements, including its investment income, are fictional," the SEC said. In an interview on April 20 at the law offices of Houston criminal attorney Dick DeGuerin, Stanford denied any wrongdoing. His companies had been well-run, he claimed, until the SEC "disembowelled" them.


title: Allen Stanford

text: On June 18, 2009, Stanford was taken into custody by FBI agents. On June 25, 2009, he appeared in a Houston court and pleaded not guilty to charges of fraud, conspiracy, and obstruction. On August 27, 2009, Stanford was admitted into the Conroe, Texas, Regional Medical Center. He had complained of a racing heart while being transported from the private prison in Huntsville, Texas, to the Federal Courthouse in Houston to attend a hearing concerning his attorney, Dick DeGuerin, who had asked the court for permission to withdraw from Stanford's case. Robert Luskin of Patton-Boggs, which had been representing Stanford in a simultaneous civil case, was to be lead counsel.


title: Allen Stanford

text: On September 26, 2009, Stanford was hospitalized due to injuries sustained while being severely beaten by another inmate at the Cornell Companies-operated, Joe Corley Detention Facility in Conroe. His injuries were described as non-life-threatening.


title: Allen Stanford

text: In March 2010, SEC Inspector General H. David Kotz issued a report finding the SEC had failed to uncover the Ponzi scheme perpetrated by Stanford. Because of concerns raised by former SEC Chief Investigator David P. Weber of improper conduct by Kotz, Inspector General David C. Williams of the U.S. Postal Service was brought in to conduct an independent review. The Williams report found that Kotz "appeared to have a conflict of interest" because he had a personal relationship with an attorney representing Stanford's victims.


title: Allen Stanford

text: Stanford's trial date was set for January 2011. The district judge deemed that Stanford's anti-anxiety drug addiction impaired his judgment and therefore made him unfit to stand trial. Stanford was incarcerated at the Federal Detention Center, Houston. In February 2011 Stanford issued a counter-claim of $7.2 billion of damages against the FBI and the SEC. In May, prosecutors dropped seven charges against Stanford, leaving 14 charges ongoing.


title: Allen Stanford

text: By November 5, 2011, Stanford was being held at the Federal Medical Center at the Federal Correctional Complex, Butner in Butner, North Carolina. His attorneys claimed that Stanford was unfit to stand trial due to amnesia resulting from his sustained injuries. On December 22, 2011, he was found competent to stand trial by U.S. District Judge David Hittner.


title: Allen Stanford

text: The trial began on January 24, 2012, at the Houston Federal Courthouse, Judge Hittner presiding. On March 6, after three hours of deliberation, the jury convicted him of masterminding a Ponzi scheme. Prosecutors sought a sentence of 230 years in prison—the maximum permitted by law, and 80 years more than the 150-year sentence handed to Bernard Madoff—calling him "a ruthless predator" who "lived a life steeped in deceit." Stanford's lawyers pressed for a sentence of 31 to 44 months and a maximum of 10 years; the former sentence, with credit for time served, could have allowed him to walk out of prison without further jail time. According to Peter Henning of "The New York Times", judges have been more willing to impose sentences for financial fraudsters that effectively amount to life sentences in recent years. The extent to which such frauds wreck people's lives, Henning wrote, amounts to "economic homicide," and such outsized sentences are a way to express society's anger at such conduct.


title: Allen Stanford

text: On June 14, 2012, Stanford was sentenced to 110 years in prison. Although it is less than half of the maximum sentence sought by prosecutors, it ensures he will obviously die in prison. Hittner ordered Stanford to forfeit $5.9 billion, saying that Stanford had orchestrated "one of the most egregious frauds ever presented to a trial jury in federal court." At sentencing, Stanford spoke for the first time in the proceedings, denying that he had ever swindled anyone. He blamed his company's failure on "Gestapo tactics" by government regulators. He is incarcerated at Coleman II USP in Sumterville, Florida; his earliest possible release is March 13, 2103 – at which time he would be 152 years old.


title: Allen Stanford

text: On April 26, 2013, federal district judge David Godbey sided with the SEC in its civil suit against Stanford and ordered him to disgorge $6.7 billion ($5.9 billion in illegal profits and $861 million in interest) and pay a $5.9 billion fine. He was permanently banned from the securities industry. Godbey wrote that Stanford had carried out the fraud for over a decade "with a high degree of scienter," or knowledge that what he was doing was illegal.


title: Allen Stanford

text: Stanford filed a 299-page brief in September 2014 with the 5th U.S. Circuit Court of Appeals in New Orleans on his conviction. The appeal was rejected in October 2015.


title: Allen Stanford

text: The United States Court of Appeals for the Fifth Circuit, affirming much of a United States Tax Court’s ruling, found that Stanford and his wife, Susan, under-reported their 1990 federal taxes by $423,531.36. Public records suggest that Stanford may owe hundreds of millions of dollars in federal taxes. There are four federal tax liens from 2007 and 2008 against Stanford, totaling more than $212 million.


title: Allen Stanford

text: The FBI and other agencies have been conducting an ongoing investigation of Stanford since 2008 for possible involvement in money laundering for Mexico's Gulf Cartel. According to "The New York Times", Stanford once held a Cook Islands trust called "Baby Mama", with his mistress and two children as beneficiaries. The trust protected proceeds deposited into Swiss and Isle of Man bank accounts from the sale of a $2.5 million Florida home.


title: Allen Stanford

text: In 2001, Stanford said that his great-great-great grandfather was a relative of Leland Stanford, the founder of Stanford University. He funded the restoration of Leland Stanford's mansion in Sacramento, California, in an effort "to help preserve an important piece of Stanford family history," and hired genealogists to prove he was a member of the Leland Stanford family. A university spokesperson said "We are not aware of any genealogical relationship between Allen Stanford and Leland Stanford". In 2008 the university filed a trademark infringement suit against Stanford, claiming the school's name was being used "in a way that creates public confusion" and is "injurious".


title: Allen Stanford

text: A February 2009 "Houston Chronicle" article described Stanford as "the leading benefactor, promoter, employer and public persona" of Antigua and Barbuda. On November 1, 2006, Stanford was appointed Knight Commander of the Order of the Nation (KCN) of Antigua and Barbuda by the Antiguan government. Prince Edward, Earl of Wessex, joined the then Governor-General of Antigua and Barbuda, Sir James Carlisle, to make this announcement during the Silver Jubilee Independence Day Celebration. After being knighted, Stanford used the awarded title "Sir Allen" often; he was generally referred to as such both by Antiguans and internationally.


title: Allen Stanford

text: In October 2009, the National Honours Committee of Antigua and Barbuda voted unanimously to strip Stanford of his knighthood. On November 2, 2009, the recommendation was forwarded to the Governor-General, Dame Louise Lake-Tack. The order to revoke Stanford's knighthood and insignia was approved and was served upon Stanford on April 1, 2010.


title: Allen Stanford

text: Stanford created and funded the Stanford 20/20 cricket tournament in the West Indies, for which he built his own ground in Antigua. The first Stanford 20/20 Cricket Tournament was held in July and August 2006 where Guyana took 1st place defeating Trinidad and Tobago in the final. The second tournament took place in January and February 2008 with a global television audience of 300 million. Trinidad and Tobago took first place and with it the US $280,000 Stanford Super Series prize after defeating Middlesex on October 27, 2008.


title: Allen Stanford

text: In June 2008, Stanford and the England and Wales Cricket Board (ECB) signed a deal for five Twenty20 internationals between England and a West Indies all-star XI, with a total prize fund of £12.27 million (US$20 million) to be awarded to the team that won the Championship. It was the largest prize ever offered to a team for a single tournament. This was in jeopardy after a row with Digicel, the sponsors of the West Indies cricket team, who were unhappy about sponsorship of the event. Eventually, the dispute was sorted out and the championship was won by Stanford Superstars, who defeated the England team by 10 wickets.


title: Allen Stanford

text: On February 17, 2009, when news of the fraud investigation became public, the ECB and WICB withdrew from talks with Stanford on sponsorship. On February 20, 2009, the ECB announced it had severed its ties with Stanford and cancelled all contracts with him.


title: Allen Stanford

text: Stanford owned two newspaper businesses in Antigua and Barbuda and Saint Kitts and Nevis, both called "The Sun". Following the scandal, both newspapers put workers on notice that their full operations would cease in April 2010.


title: Birefringence

text: Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.


title: Birefringence

text: Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. This effect was first described by Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. In the 19th century Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarization (perpendicular to the direction of the wave vector).


title: Birefringence

text: A mathematical description of wave propagation in a birefringent medium is presented below. Following is a qualitative explanation of the phenomenon.


title: Birefringence

text: The simplest type of birefringence is described as "uniaxial", meaning that there is a single direction governing the optical anisotropy whereas all directions perpendicular to it (or at a given angle to it) are optically equivalent. Thus rotating the material around this axis does not change its optical behaviour. This special direction is known as the optic axis of the material. Light propagating parallel to the optic axis (whose polarization is always "perpendicular" to the optic axis) is governed by a refractive index (for "ordinary") regardless of its specific polarization. For rays with any other propagation direction, there is one linear polarization that would be perpendicular to the optic axis, and a ray with that polarization is called an "ordinary ray" and is governed by the same refractive index value . For a ray propagating in the same direction but with a polarization perpendicular to that of the ordinary ray, the polarization direction will be partly in the direction of the optic axis, and this "extraordinary ray" will be governed by a different, "direction-dependent" refractive index. Because the index of refraction depends on the polarization when unpolarized light enters a uniaxial birefringent material, it is split into two beams travelling in different directions, one having the polarization of the ordinary ray and the other the polarization of the extraordinary ray.


title: Birefringence

text: The ordinary ray will always experience a refractive index of , whereas the refractive index of the extraordinary ray will be in between and , depending on the ray direction as described by the index ellipsoid. The magnitude of the difference is quantified by the birefringence:


title: Birefringence

text: The propagation (as well as reflection coefficient) of the ordinary ray is simply described by as if there were no birefringence involved. The extraordinary ray, as its name suggests, propagates unlike any wave in an isotropic optical material. Its refraction (and reflection) at a surface can be understood using the effective refractive index (a value in between and ). Its power flow (given by the Poynting vector) is not exactly in the direction of the wave vector. This causes an additional shift in that beam, even when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate slightly around that of the ordinary ray, which remains fixed.


title: Birefringence

text: When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. In the first case, both polarizations are perpendicular to the optic axis and see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity (corresponding to ) but still has the power flow in the direction of the wave vector. A crystal with its optic axis in this orientation, parallel to the optical surface, may be used to create a waveplate, in which there is no distortion of the image but an intentional modification of the state of polarization of the incident wave. For instance, a quarter-wave plate is commonly used to create circular polarization from a linearly polarized source.


title: Birefringence

text: The case of so-called biaxial crystals is substantially more complex. These are characterized by "three" refractive indices corresponding to three principal axes of the crystal. For most ray directions, "both" polarizations would be classified as extraordinary rays but with different effective refractive indices. Being extraordinary waves, the direction of power flow is not identical to the direction of the wave vector in either case.


title: Birefringence

text: The two refractive indices can be determined using the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will "not" be an ellipsoid of revolution ("spheroid") but is described by three unequal principle refractive indices , and . Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid "is" a spheroid).


title: Birefringence

text: Although there is no axis of symmetry, there are "two" optical axes or "binormals" which are defined as directions along which light may propagate without birefringence, i.e., directions along which the wavelength is independent of polarization. For this reason, birefringent materials with three distinct refractive indices are called "biaxial". Additionally, there are two distinct axes known as "optical ray axes" or "biradials" along which the group velocity of the light is independent of polarization.


title: Birefringence

text: When an arbitrary beam of light strikes the surface of a birefringent material at non-normal incidence, the polarization component normal to the optic axis (ordinary ray) and the other linear polarization (extraordinary ray) will be refracted toward somewhat different paths. Natural light, so-called unpolarized light, consists of equal amounts of energy in any two orthogonal polarizations. Even linearly polarized light has some energy in both polarizations, unless aligned along one of the two axes of birefringence. According to Snell's law of refraction, the two angles of refraction are governed by the effective refractive index of each of these two polarizations. This is clearly seen, for instance, in the Wollaston prism which separates incoming light into two linear polarizations using prisms composed of a birefringent material such as calcite.


title: Birefringence

text: The different angles of refraction for the two polarization components are shown in the figure at the top of this page, with the optic axis along the surface (and perpendicular to the plane of incidence), so that the angle of refraction is different for the polarization (the "ordinary ray" in this case, having its electric vector perpendicular to the optic axis) and the polarization (the "extraordinary ray" in this case, whose electric field polarization includes a component in the direction of the optic axis). In addition, a distinct form of double refraction occurs, even with normal incidence, in cases where the optic axis is not along the refracting surface (nor exactly normal to it); in this case, the dielectric polarization of the birefringent material is not exactly in the direction of the wave's electric field for the extraordinary ray. The direction of power flow (given by the Poynting vector) for this inhomogenous wave is at a finite angle from the direction of the wave vector resulting in an additional separation between these beams. So even in the case of normal incidence, where one would compute the angle of refraction as zero (according to Snell's law, regardless of the effective index of refraction), the energy of the extraordinary ray is propagated at an angle. If exiting the crystal through a face parallel to the incoming face, the direction of both rays will be restored, but leaving a "shift" between the two beams. This is commonly observed using a piece of calcite cut along its natural cleavage, placed above a paper with writing, as in the above photographs. On the contrary, waveplates specifically have their optic axis "along" the surface of the plate, so that with (approximately) normal incidence there will be no shift in the image from light of either polarization, simply a relative phase shift between the two light waves.


title: Birefringence

text: Much of the work involving polarization preceded the understanding of light as a transverse electromagnetic wave, and this has affected some terminology in use. Isotropic materials have symmetry in all directions and the refractive index is the same for any polarization direction. An anisotropic material is called "birefringent" because it will generally refract a single incoming ray in two directions, which we now understand correspond to the two different polarizations. This is true of either a uniaxial or biaxial material.


title: Birefringence

text: In a uniaxial material, one ray behaves according to the normal law of refraction (corresponding to the ordinary refractive index), so an incoming ray at normal incidence remains normal to the refracting surface. As explained above, the other polarization can deviate from normal incidence, which cannot be described using the law of refraction. This thus became known as the "extraordinary ray". The terms "ordinary" and "extraordinary" are still applied to the polarization components perpendicular to and not perpendicular to the optic axis respectively, even in cases where no double refraction is involved.


title: Birefringence

text: A material is termed "uniaxial" when it has a single direction of symmetry in its optical behavior, which we term the optic axis. It also happens to be the axis of symmetry of the index ellipsoid (a spheroid in this case). The index ellipsoid could still be described according to the refractive indices, , and , along three coordinate axes; in this case two are equal. So if corresponding to the and axes, then the extraordinary index is corresponding to the axis, which is also called the "optic axis" in this case.


title: Birefringence

text: Materials in which all three refractive indices are different are termed "biaxial" and the origin of this term is more complicated and frequently misunderstood. In a uniaxial crystal, different polarization components of a beam will travel at different phase velocities, "except" for rays in the direction of what we call the optic axis. Thus the optic axis has the particular property that rays in that direction do "not" exhibit birefringence, with all polarizations in such a beam experiencing the same index of refraction. It is very different when the three principal refractive indices are all different; then an incoming ray in any of those principal directions will still encounter two different refractive indices. But it turns out that there are two special directions (at an angle to all of the 3 axes) where the refractive indices for different polarizations are again equal. For this reason, these crystals were designated as "biaxial", with the two "axes" in this case referring to ray directions in which propagation does not experience birefringence.


title: Birefringence

text: In a birefringent material, a wave consists of two polarization components which generally are governed by different effective refractive indices. The so-called "slow ray" is the component for which the material has the higher effective refractive index (slower phase velocity), while the "fast ray" is the one with a lower effective refractive index. When a beam is incident on such a material from air (or any material with a lower refractive index), the slow ray is thus refracted more towards the normal than the fast ray. In the example figure at top of this page, it can be seen that refracted ray with "s" polarization (with its electric vibration along the direction of the optic axis, thus called the extraordinary ray) is the slow ray in given scenario.


title: Birefringence

text: Using a thin slab of that material at normal incidence, one would implement a waveplate. In this case, there is essentially no spatial separation between the polarizations, the phase of the wave in the parallel polarization (the slow ray) will be retarded with respect to the perpendicular polarization. These directions are thus known as the slow axis and fast axis of the waveplate.


title: Birefringence

text: Uniaxial birefringence is classified as positive when the extraordinary index of refraction is greater than the ordinary index . Negative birefringence means that is less than zero. In other words, the polarization of the fast (or slow) wave is perpendicular to the optic axis when the birefringence of the crystal is positive (or negative, respectively). In the case of biaxial crystals, all three of the principal axes have different refractive indices, so this designation does not apply. But for any defined ray direction one can just as well designate the fast and slow ray polarizations.


title: Birefringence

text: While the best known source of birefringence is the entrance of light into an anisotropic crystal, it can result in otherwise optically isotropic materials in a few ways:


title: Birefringence

text: The best characterized birefringent materials are crystals. Due to their specific crystal structures their refractive indices are well defined. Depending on the symmetry of a crystal structure (as determined by one of the 32 possible crystallographic point groups), crystals in that group may be forced to be isotropic (not birefringent), to have uniaxial symmetry, or neither in which case it is a biaxial crystal. The crystal structures permitting uniaxial and biaxial birefringence are noted in the two tables, below, listing the two or three principal refractive indices (at wavelength 590 nm) of some better-known crystals.


title: Birefringence

text: In addition to induced birefringence while under stress, many plastics obtain permanent birefringence during manufacture due to stresses which are "frozen in" due to mechanical forces present when the plastic is molded or extruded. For example, ordinary cellophane is birefringent. Polarizers are routinely used to detect stress, either applied or frozen-in, in plastics such as polystyrene and polycarbonate.


title: Birefringence

text: Cotton fiber is birefringent because of high levels of cellulosic material in the fibre's secondary cell wall which is directionally aligned with the cotton fibers.


title: Birefringence

text: Polarized light microscopy is commonly used in biological tissue, as many biological materials are linearly or circularly birefringent. Collagen, found in cartilage, tendon, bone, corneas, and several other areas in the body, is birefringent and commonly studied with polarized light microscopy. Some proteins are also birefringent, exhibiting form birefringence.


title: Birefringence

text: Inevitable manufacturing imperfections in optical fiber leads to birefringence, which is one cause of pulse broadening in fiber-optic communications. Such imperfections can be geometrical (lack of circular symmetry), or due to unequal lateral stress applied to the optical fibre. Birefringence is "intentionally" introduced (for instance, by making the cross-section elliptical) in order to produce polarization-maintaining optical fibers. Birefringence can be induced (or corrected!) in optical fibers through bending them which causes anisotropy in form and stress given the axis around which it is bent and radius of curvature.


title: Birefringence

text: In addition to anisotropy in the electric polarizability that we have been discussing, anisotropy in the magnetic permeability could be a source of birefringence. At optical frequencies, there is no measurable magnetic polarizability ("μ"="μ") of natural materials, so this is not an actual source of birefringence at optical wavelengths.


title: Birefringence

text: Birefringence and other polarization-based optical effects (such as optical rotation and linear or circular dichroism) can be observed by measuring any change in the polarization of light passing through the material. These measurements are known as polarimetry. Polarized light microscopes, which contain two polarizers that are at 90° to each other on either side of the sample, are used to visualize birefringence, since light that has "not" been affected by birefringence remains in a polarization that is totally rejected by the second polarizer ("analyzer"). The addition of quarter-wave plates permits examination using circularly polarized light. Determination of the change in polarization state using such an apparatus is the basis of ellipsometry, by which the optical properties of specular surfaces can be gauged through reflection.


title: Birefringence

text: Birefringence measurements have been made with phase-modulated systems for examining the transient flow behaviour of fluids. Birefringence of lipid bilayers can be measured using dual-polarization interferometry. This provides a measure of the degree of order within these fluid layers and how this order is disrupted when the layer interacts with other biomolecules.


title: Birefringence

text: Birefringence is used in many optical devices. Liquid-crystal displays, the most common sort of flat-panel display, cause their pixels to become lighter or darker through rotation of the polarization (circular birefringence) of linearly polarized light as viewed through a sheet polarizer at the screen's surface. Similarly, light modulators modulate the intensity of light through electrically induced birefringence of polarized light followed by a polarizer. The Lyot filter is a specialized narrowband spectral filter employing the wavelength dependence of birefringence. Waveplates are thin birefringent sheets widely used in certain optical equipment for modifying the polarization state of light passing through it.


title: Birefringence

text: Birefringence also plays an important role in second-harmonic generation and other nonlinear optical components, as the crystals used for this purpose are almost always birefringent. By adjusting the angle of incidence, the effective refractive index of the extraordinary ray can be tuned in order to achieve phase matching, which is required for the efficient operation of these devices.


title: Birefringence

text: Birefringence is utilized in medical diagnostics. One powerful accessory used with optical microscopes is a pair of crossed polarizing filters. Light from the source is polarized in the direction after passing through the first polarizer, but above the specimen is a polarizer (a so-called "analyzer") oriented in the direction. Therefore, no light from the source will be accepted by the analyzer, and the field will appear dark. Areas of the sample possessing birefringence will generally couple some of the -polarized light into the polarization; these areas will then appear bright against the dark background. Modifications to this basic principle can differentiate between positive and negative birefringence.


title: Birefringence

text: For instance, needle aspiration of fluid from a gouty joint will reveal negatively birefringent monosodium urate crystals. Calcium pyrophosphate crystals, in contrast, show weak positive birefringence. Urate crystals appear yellow, and calcium pyrophosphate crystals appear blue when their long axes are aligned parallel to that of a red compensator filter, or a crystal of known birefringence is added to the sample for comparison.


title: Birefringence

text: The birefringence of tissue inside a living human thigh was measured using polarization-sensitive optical coherence tomography at 1310 nm and a single mode fiber in a needle. Skeletal muscle birefringence was Δn = 1.79 × 10± 0.18×10, adipose Δn = 0.07 × 10 ± 0.50 × 10, superficial aponeurosis Δn = 5.08 × 10 ± 0.73 × 10 and interstitial tissue Δn = 0.65 ×10 ±0.39 ×10. These measurements may be important for the development of a less invasive method to diagnose Duchenne muscular dystrophy.


title: Birefringence

text: Birefringence can be observed in amyloid plaques such as are found in the brains of Alzheimer's patients when stained with a dye such as Congo Red. Modified proteins such as immunoglobulin light chains abnormally accumulate between cells, forming fibrils. Multiple folds of these fibers line up and take on a beta-pleated sheet conformation. Congo red dye intercalates between the folds and, when observed under polarized light, causes birefringence.


title: Birefringence

text: In ophthalmology, binocular retinal birefringence screening of the "Henle fibers" (photoreceptor axons that go radially outward from the fovea) provides a reliable detection of strabismus and possibly also of anisometropic amblyopia. In healthy subjects, the maximum retardation induced by the Henle fiber layer is approximately 22 degrees at 840 nm. Furthermore, scanning laser polarimetry uses the birefringence of the optic nerve fibre layer to indirectly quantify its thickness, which is of use in the assessment and monitoring of glaucoma. Polarization-sensitive optical coherence tomography measurements obtained from healthy human subjects have demonstrated a change in birefringence of the retinal nerve fiber layer as a function of location around the optic nerve head. The same technology was recently applied in the living human retina to quantify the polarization properties of vessel walls near the optic nerve.


title: Birefringence

text: Birefringence characteristics in sperm heads allow the selection of spermatozoa for intracytoplasmic sperm injection. Likewise, "zona imaging" uses birefringence on oocytes to select the ones with highest chances of successful pregnancy. Birefringence of particles biopsied from pulmonary nodules indicates silicosis.


title: Birefringence

text: Dermatologists use dermatoscopes to view skin lesions. Dermoscopes use polarized light, allowing the user to view crystalline structures corresponding to dermal collagen in the skin. These structures may appear as shiny white lines or rosette shapes and are only visible under polarized dermoscopy.


title: Birefringence

text: Isotropic solids do not exhibit birefringence. When they are under mechanical stress, birefringence results. The stress can be applied externally or is "frozen in" after a birefringent plastic ware is cooled after it is manufactured using injection molding. When such a sample is placed between two crossed polarizers, colour patterns can be observed, because polarization of a light ray is rotated after passing through a birefringent material and the amount of rotation is dependent on wavelength. The experimental method called photoelasticity used for analyzing stress distribution in solids is based on the same principle. There has been recent research on using stress induced birefringence in a glass plate to generate an Optical vortex and full Poincare beams (optical beams that have every possible polarization state across a cross-section).


title: Birefringence

text: Birefringence is observed in anisotropic elastic materials. In these materials, the two polarizations split according to their effective refractive indices, which are also sensitive to stress.


title: Birefringence

text: The study of birefringence in shear waves traveling through the solid Earth (the Earth's liquid core does not support shear waves) is widely used in seismology.


title: Birefringence

text: In an isotropic medium (including free space) the so-called electric displacement () is just proportional to the electric field () according to where the material's permittivity is just a scalar (and equal to where is the index of refraction). In an anisotropic material exhibiting birefringence, the relationship between and must now be described using a tensor equation:


title: Birefringence

text: where is now a 3 × 3 permittivity tensor. We assume linearity and no magnetic permeability in the medium: . The electric field of a plane wave of angular frequency can be written in the general form:


title: Birefringence

text: where is the position vector, is time, and is a vector describing the electric field at , . Then we shall find the possible wave vectors . By combining Maxwell's equations for and , we can eliminate to obtain:


title: Birefringence

text: We can apply the vector identity to the left hand side of , and use the spatial dependence in which each differentiation in (for instance) results in multiplication by to find:


title: Birefringence

text: The right hand side of can be expressed in terms of through application of the permittivity tensor and noting that differentiation in time results in multiplication by , then becomes:


title: Birefringence

text: Finding the allowed values of for a given is easiest done by using Cartesian coordinates with the , and axes chosen in the directions of the symmetry axes of the crystal (or simply choosing in the direction of the optic axis of a uniaxial crystal), resulting in a diagonal matrix for the permittivity tensor :


title: Birefringence

text: where the diagonal values are squares of the refractive indices for polarizations along the three principal axes , and . With in this form, and substituting in the speed of light using , the component of the vector equation becomes


title: Birefringence

text: where , , are the components of (at any given position in space and time) and , , are the components of . Rearranging, we can write (and similarly for the and components of )


title: Birefringence

text: This is a set of linear equations in , , , so it can have a nontrivial solution (that is, one other than ) as long as the following determinant is zero:


title: Birefringence

text: Evaluating the determinant of , and rearranging the terms according to the powers of formula_2, the constant terms cancel. After eliminating the common factor formula_2 from the remaining terms, we obtain


title: Birefringence

text: In the case of a uniaxial material, choosing the optic axis to be in the direction so that and , this expression can be factored into


title: Birefringence

text: Setting either of the factors in to zero will define an ellipsoidal surface in the space of wavevectors that are allowed for a given . The first factor being zero defines a sphere; this is the solution for so-called ordinary rays, in which the effective refractive index is exactly regardless of the direction of . The second defines a spheroid symmetric about the axis. This solution corresponds to the so-called extraordinary rays in which the effective refractive index is in between and , depending on the direction of . Therefore, for any arbitrary direction of propagation (other than in the direction of the optic axis), two distinct wavevectors are allowed corresponding to the polarizations of the ordinary and extraordinary rays.


title: Birefringence

text: For a biaxial material a similar but more complicated condition on the two waves can be described; the locus of allowed vectors (the "wavevector surface") is a 4th-degree two-sheeted surface, so that in a given direction there are generally two permitted vectors (and their opposites). By inspection one can see that is generally satisfied for two positive values of . Or, for a specified optical frequency and direction normal to the wavefronts , it is satisfied for two wavenumbers (or propagation constants) (and thus effective refractive indices) corresponding to the propagation of two linear polarizations in that direction.


title: Birefringence

text: When those two propagation constants are equal then the effective refractive index is independent of polarization, and there is consequently no birefringence encountered by a wave traveling in that particular direction. For a uniaxial crystal, this is the optic axis, the ±"z" direction according to the above construction. But when all three refractive indices (or permittivities), , and are distinct, it can be shown that there are exactly two such directions, where the two sheets of the wave-vector surface touch; these directions are not at all obvious and do not lie along any of the three principal axes (, , according to the above convention). Historically that accounts for the use of the term "biaxial" for such crystals, as the existence of exactly two such special directions (considered "axes") was discovered well before polarization and birefringence were understood physically. These two special directions are generally not of particular interest; biaxial crystals are rather specified by their three refractive indices corresponding to the three axes of symmetry.


title: Birefringence

text: A general state of polarization launched into the medium can always be decomposed into two waves, one in each of those two polarizations, which will then propagate with different wavenumbers . Applying the different phase of propagation to those two waves over a specified propagation distance will result in a generally "different" net polarization state at that point; this is the principle of the waveplate for instance. With a waveplate, there is no spatial displacement between the two rays as their vectors are still in the same direction. That is true when each of the two polarizations is either normal to the optic axis (the ordinary ray) or parallel to it (the extraordinary ray).


title: Birefringence

text: In the more general case, there "is" a difference not only in the magnitude but the direction of the two rays. For instance, the photograph through a calcite crystal (top of page) shows a shifted image in the two polarizations; this is due to the optic axis being neither parallel nor normal to the crystal surface. And even when the optic axis "is" parallel to the surface, this will occur for waves launched at non-normal incidence (as depicted in the explanatory figure). In these cases the two vectors can be found by solving constrained by the boundary condition which requires that the components of the two transmitted waves' vectors, and the vector of the incident wave, as projected onto the surface of the interface, must all be identical. For a uniaxial crystal it will be found that there is "not" a spatial shift for the ordinary ray (hence its name) which will refract as if the material were non-birefringent with an index the same as the two axes which are not the optic axis. For a biaxial crystal neither ray is deemed "ordinary" nor would generally be refracted according to a refractive index equal to one of the principal axes.


title: The Sugarcubes

text: The Sugarcubes (Icelandic: Sykurmolarnir) were an Icelandic alternative rock band from Reykjavík formed in 1986 and disbanded in 1992. For most of their career, the band consisted of Björk Guðmundsdóttir (vocals, keyboards), Einar Örn Benediktsson (vocals, trumpet), Þór Eldon (guitar), Bragi Ólafsson (bass), Margrét "Magga" Örnólfsdóttir (keyboards) and Sigtryggur Baldursson (drums).


title: The Sugarcubes

text: The Sugarcubes' debut album, "Life's Too Good" (1988), was an unexpected international success, and produced their signature song "Birthday". It is credited as the first Icelandic album to have a worldwide impact and influenced Icelandic popular music. Their follow-up album, "Here Today, Tomorrow Next Week!", was released 1989 to mixed reviews. Their third and final album, "Stick Around for Joy", released in February 1992, was better received and produced the successful singles "Hit" and "Leash Called Love". "Rolling Stone" referred to them as "the biggest rock band to emerge from Iceland." Björk would later become an internationally successful solo musician and the bestselling Icelandic musician of all time.


title: The Sugarcubes

text: The members of the Sugarcubes had formerly been in a variety of Icelandic bands. Björk Guðmundsdóttir had the longest career out of any of the members; she had recorded an album when she was 11. In her late teens, she joined the Icelandic post-punk band Tappi Tíkarrass, who released two albums before splitting in 1983. Drummer Sigtryggur "Siggi" Baldursson was a member of Þeyr, while Einar Örn Benediktsson and Bragi Ólafsson formed a punk band called Purrkur Pillnikk. By 1984, Björk, Einar Örn and Siggi had formed the group Kukl with keyboardist Einar Melax, and released two albums on the independent British record label Crass Records.


title: The Sugarcubes

text: The Sugarcubes formed on 8 June 1986 with Björk on vocals, Björk's then-husband Þór Eldon on guitar and Bragi Ólafsson on bass. On the same day, Björk gave birth to her and Þór Eldon's son, Sindri Eldon. The band's name was assumed by its fans to be an LSD usage reference.


title: The Sugarcubes

text: In late 1987, the band signed to One Little Indian in the UK and to Elektra Records in the US. They released their debut album, "Life's Too Good", in 1988 to critical acclaim in both the UK and the US. They first came to notice in the UK when BBC radio DJ John Peel played "Birthday", which was later voted by his listeners as #1 in the 1987 Festive Fifty, and #23 in the All Time Chart. Their music has been described as avant-pop, and was characterized by a psychedelic post-punk sound sometimes reminiscent of the B-52's and Talking Heads, whimsical yet heartfelt lyrics, and the imploring, girlish voice of Björk, accompanied by Einar Örn's erratic vocal performances. In the last quarter of 1988, The Sugarcubes toured North America to positive reception. In September, the band played at The Ritz in New York, a concert attended by David Bowie and Iggy Pop. On 15 October the band appeared on "Saturday Night Live" with a performance of their songs "Birthday" and "Motorcrash".


title: The Sugarcubes

text: "Here Today, Tomorrow Next Week!", the band's second album, was released in September 1989. The greater vocal contribution by Einar Örn on the record was criticized in many of the record's reviews, which were noticeably weaker than those for "Life's Too Good". Not all critics agreed that it was worse than their debut album, though. Robert Christgau rated it a B+, higher than the B− he gave "Life's Too Good". The singles "Regina" and "Planet" topped the UK indie charts but fared poorly in the mainstream charts outside of Iceland. After the release of "Here Today, Tomorrow Next Week!", the band embarked on a lengthy international tour. At the end of the tour, they started to ponder splitting up and went on a hiatus.


title: The Sugarcubes

text: At the conclusion of the tour in late 1990, the band members pursued their own interests. "Stick Around for Joy", their third and final album, was released in February 1992. It featured guest guitarist John McGeoch (formerly of Magazine and Siouxsie and the Banshees) on the opening track, "Gold". The album received noticeably better reviews than "Here Today, Tomorrow Next Week!", and spawned the band's first big hit single, the aptly titled "Hit". Further singles "Walkabout" and "Vitamin" failed to make any chart impact. The Sugarcubes opened for U2 during the US leg of their Zoo TV Tour in October and November 1992, playing to a total of 700,000 people.


title: The Sugarcubes

text: A remix album, "It's-It", was released in October 1992 along with a re-release of "Birthday" which was backed by numerous remixes of the song. One single that was released from the compilation, the Tony Humphries remix of "Leash Called Love", reached number one on "Billboard"'s Hot Dance Club Songs Chart in 1992.


title: The Sugarcubes

text: The Sugarcubes disbanded in late December 1992. The members remain involved in the management of record label Smekkleysa (Bad Taste Ltd). Björk embarked on a solo career, coming to prominence with albums such as "Debut" (1993), "Post" (1995), and "Homogenic" (1997).


title: The Sugarcubes

text: On 17 November 2006 the band had a one-off reunion concert at Laugardalshöll sport arena in Reykjavík, Iceland, to celebrate the 20th anniversary of their debut single, "Birthday", with all profits going to the non-profit Smekkleysa SM to promote Icelandic music. They were supported by fellow Icelandic groups múm and Rass. Despite this reunion, the group has expressed that it has no intention to play future shows or record new material.


title: The Sugarcubes

text: "Trouser Press" wrote that the drumming and guitar work were influenced by Joy Division, Siouxsie and the Banshees and also Cocteau Twins on the slow numbers. The group also incorporated "electronically mutated trumpet and sound effects". The other instrument is Björk's voice, containing a "range of emotions", being one moment "a little girl soprano" and then next "a crazed animal". Einar also sings on certain tracks with Björk on background vocals. "Pitchfork" characterized the band as avant-rock.


title: Voiceless velar fricative

text: The voiceless velar fricative is a type of consonantal sound used in some spoken languages. It was part of the consonant inventory of Old English and can still be found in some dialects of English, most notably in Scottish English, e.g. in "loch", "broch" or "saugh" (willow).