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In Greek mythology, Polynices was the son of Oedipus and either Jocasta or Euryganeia and the younger brother of Eteocles. When his father, was discovered to have killed his father and married his mother, he was expelled from Thebes, leaving his sons Eteocles and Polynices to rule; because of a curse put on them by their father Oedipus, the two sons did not share the rule peacefully and died as a result, killing each other in battle for control over Thebes. In the Thebaid, the brothers were cursed by their father for their disrespect towards him on two occasions; the first of these occurred when they served him using the silver table of Cadmus and a golden cup, which he had forbidden. The brothers sent him the haunch of a sacrificed animal, rather than the shoulder, which he deserved. Enraged, Oedipus prayed to Zeus. However, in Sophocles' Oedipus at Colonus, Oedipus desired to stay in Thebes but was expelled by Creon, his sons argued over the throne, but Eteocles gained the support of the Thebans and expelled Polynices, who went to Oedipus to ask for his blessing to retake the city, but instead was cursed to die by his brother's hand.

His son was Thersander. There are several accounts of how Eteocles and Polynices shared the rule after Oedipus' departure from the city. In Hellanicus' account, Eteocles offers his brother his choice of either the rule of the city or a share of the property. In Pherekydes, Eteocles expels Polynices by force, keeps the rule of Thebes and the inheritance; the Bibliotheca and Diodorus state that the brothers agree to divide the kingship between them, switching each year. Eteocles, was allotted the first year, refused to surrender the crown. Eteocles has his brother exiled, though Polynices soon finds refuge in the city of Argos. There he is welcomed by the king, Adrastus who gives him his daughter, for his wife. Polynices pleads his case to King Adrastus, requesting his help to restore him to the throne of Thebes. Adrastos promises to do so and to that end sets out to gather an expeditionary force to march against Thebes, he appoints seven individual champions to lead this assault, one for each of the seven gates in the walls of the city.

Together, these champions, including Adrastus and Polynices, are known as the “Seven Against Thebes”. The expedition soon proved to be complete disaster, as all of the Argive champions were slain in the ensuing battle. Ten years after Polynices' death, the sons of the seven fallen champions gathered to launch a second assault against the city of Thebes to avenge the deaths of their fathers. Unlike their fathers before them, these Epigoni are successful in their attempt to take Thebes, after which they install Thersander, Polynices' son by Argea, as the city's new ruler. In Sophocles' tragedy Antigone, Polynices' story continues after his death. King Creon, who ascended to the throne of Thebes, decreed that Polynices was not to be buried or mourned, on pain of death by stoning. Antigone, his sister, was caught. Creon decreed this in spite of her betrothal to his son Haemon. Antigone's sister, Ismene declared she had aided Antigone and wanted the same fate. Creon imprisoned Antigone in a sepulchre.

He went to bury Polynices himself, release Antigone. However, she had hanged herself rather than be buried alive; when Creon arrived at the tomb where she was to be interred, his son Haemon made as if to attack him and killed himself. When Creon's wife, was informed of their deaths, she too took her own life. Epigoni The Thebans

David Ridler

David Ridler is an English footballer and manager. He began his career with Wrexham, turning professional in August 1995. In May 2001, after over 100 football league appearances, he was released and joined Macclesfield Town. In March 2003 he left in July that year to join Shrewsbury Town. In May 2004 he was part of the Conference play-off winning side that took Shrewsbury back into the Football League, he lost his place in the Shrewsbury side and was made available for loan in September 2004. In March 2005 he left Shrewsbury to join Conference National side Leigh RMI, he left in October 2007 to join Winsford United. He left Winsford to join Caernarfon Town in September 2008. On 21 May 2009 Dave was appointed assistant manager of Prescot Cables, he became Caretaker Manager when boss Joe Gibliru left in November 2010 and was chosen as full-time boss a month later. He left the club to coach overseas in late 2011. David is working with Liverpool F. C. at their academy in Egypt. David Ridler at Soccerbase Welsh Premier League profile

A Comprehensive Retrospective: or How I Learned to Stop Worrying and Release Bad and Useless Recordings

A Comprehensive Retrospective Or: How We Learned to Stop Worrying and Release Bad and Useless Recordings is a compilation album by hardcore punk band Shai Hulud. It is a collection of early demos; the title is a play on the film Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb. Tracks 1-6 are the original Shai Hulud demo, with Damien Moyal on vocals. Tracks 7-9 are live recordings from the Crucial Chaos radio show at WNYU in 1997. Track 10 is a brief recording of Damien Moyal saying, "the end. Stop now. All you're gonna get after this is bullshit." Track 11 is message left on Matt Fox's answering machine by his friends mocking the fact that the band's name was misspelled on the first 5,000 copies of their EP "A Profound Hatred of Man". Tracks 12-15 are taken from a practice session. Track 16 is a guitar only demo version of "This Wake I Myself Have Stirred". Tracks 17-19 are demo recordings with Chad Gilbert on vocals. Tracks 20-24 are scratch tracks recorded by Matt Fox in 1995.

"Hardly" – 3:11 "Orwell" – 2:13 "Unlearned" – 2:08 "Sauve Qui Peut" – 2:38 "This Wake I Myself Have Stirred" – 2:45 "Favor" – 3:04 "Solely Concentrating On The Negative Aspects Of Life" – 4:07 "Gyroscope" – 1:53 "Hardly" – 4:14 "Stop Now"! – 0:07 "Keep Your Day Jobs" – 0:52 "New Song" – 3:07 "Tree" – 3:16 "This Wake I Myself Have Stirred" – 2:44 "Unlearned" – 2:11 "This Wake I Myself Have Stirred" – 3:02 "For The World" – 3:02 "This Wake I Myself Have Stirred" – 2:54 "Hardly" – 3:28 "Unlearned" –2.

Semigroup with involution

In mathematics in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application "cancelling itself out", the same interaction law with the binary operation as in the case of the group inverse. It is thus not a surprise. However, there are significant natural examples of semigroups with involution. An example from linear algebra is the multiplicative monoid of real square matrices of order n; the map which sends a matrix to its transpose is an involution because the transpose is well defined for any matrix and obeys the law T = BTAT, which has the same form of interaction with multiplication as taking inverses has in the general linear group. However, for an arbitrary matrix, AAT does not equal the identity element.

Another example, coming from formal language theory, is the free semigroup generated by a nonempty set, with string concatenation as the binary operation, the involution being the map which reverses the linear order of the letters in a string. A third example, from basic set theory, is the set of all binary relations between a set and itself, with the involution being the converse relation, the multiplication given by the usual composition of relations. Semigroups with involution appeared explicitly named in a 1953 paper of Viktor Wagner as result of his attempt to bridge the theory of semigroups with that of semiheaps. Let S be a semigroup with its binary operation written multiplicatively. An involution in S is a unary operation * on S satisfying the following conditions: For all x in S, * = x. For all x, y in S we have * = y*x*; the semigroup S with the involution * is called a semigroup with involution. Semigroups that satisfy only the first of these axioms belong to the larger class of U-semigroups.

In some applications, the second of these axioms has been called antidistributive. Regarding the natural philosophy of this axiom, H. S. M. Coxeter remarked that it "becomes clear when we think of and as the operations of putting on our socks and shoes, respectively." If S is a commutative semigroup the identity map of S is an involution. If S is a group the inversion map *: S → S defined by x* = x−1 is an involution. Furthermore, on an abelian group both this map and the one from the previous example are involutions satisfying the axioms of semigroup with involution. If S is an inverse semigroup the inversion map is an involution which leaves the idempotents invariant; as noted in the previous example, the inversion map is not the only map with this property in an inverse semigroup. There may well be other involutions. A regular semigroup is an inverse semigroup if and only if it admits an involution under which each idempotent is an invariant. Underlying every C*-algebra is a *-semigroup. An important instance is the algebra Mn of n-by-n matrices over C, with the conjugate transpose as involution.

If X is a set, the set of all binary relations on X is a *-semigroup with the * given by the converse relation, the multiplication given by the usual composition of relations. This is an example of a *-semigroup, not a regular semigroup. If X is a set the set of all finite sequences of members of X forms a free monoid under the operation of concatenation of sequences, with sequence reversal as an involution. A rectangular band on a Cartesian product of a set A with itself, i.e. with elements from A × A, with the semigroup product defined as =, with the involution being the order reversal of the elements of a pair * =. This semigroup is a regular semigroup, as all bands are. An element x of a semigroup with involution is sometimes called hermitian when it is left invariant by the involution, meaning x* = x. Elements of the form xx* or x*x are always hermitian, so are all powers of a hermitian element; as noted in the examples section, a semigroup S is an inverse semigroup if and only if S is a regular semigroup and admits an involution such that every idempotent is hermitian.

Certain basic concepts may be defined on *-semigroups in a way that parallels the notions stemming from a regular element in a semigroup. A partial isometry is an element s such that ss*s = s. A projection is an idempotent element e, hermitian, meaning that ee = e and e* = e; every projection is a partial isometry, for every partial isometry s, s*s and ss* are projections. If e and f are projections e = ef if and only if e = fe. Partial isometries can be ordered by s ≤ t defined as holding whenever s = ss*t and ss* = ss*tt*. Equivalently, s ≤ t if and only if s = et and e = ett* for some projection e. In a *-semigroup, PI is an ordered groupoid with the partial product given by s⋅t = st if s*s = tt*. In terms of examples for these notions, in the *-semigroup of binary relations on a set, the partial isometries are the relations that are difunctional; the projections in this *-semigroup are the partial equivalence relations. The partial isometries in a C*-algebra are those defined in this section.

In the case of Mn more can be said. If

Frank McGill

Air Vice-Marshal Francis Scholes ‘Frank’ McGill, CB was a prominent member of Canada's military, having been an air vice marshal in the RCAF, a considerable sports figure, amongst other things a star football player in the Canadian Football League for the Montreal AAA Winged Wheelers. McGill was born on June 20, 1894 in Montreal, Quebec to Eliza Jane Bryson, he played college football at McGill University, where he starred at hockey, water polo and swimming. He was inducted into the Canadian Football Hall of Fame in 1965 and into the Canada's Sports Hall of Fame in 1959. Frank McGill served in First World War as a pilot for the Royal Naval Air Service, after graduating from McGill in 1913. At the outbreak of War in 1914, a brief period in the Army training corps found McGill bored, following which he promptly joined the Royal Naval Air Service. During the First World War he served in combat and as a test pilot, was decorated for his Royal Flying Corps work. In 1915 while flying with an instructor over the Thames estuary, McGill's plane crashed, resulting in a fractured arm and stay in the Royal Naval Hospital.

In 1917 he was appointed second-in-command to a small flying boat force in the Scilly Isles, England. In February 1919 Capt. McGill was the 1st Pilot in a flying boat that crashed in poor weather off Newlyn in Cornwall. Capt. McGill saved the life of 2nd Lt. HD Morley; the two remained in correspondence until the death of HD Morley in 1978. During the inter-war period, Air Vice Marshal McGill organized and led an RCAF squadron which became the country's primary fighter unit and participated in the Battle of Britain, he played a founding role in the development of the Commonwealth Air Training Plan, as well as serving as the first commanding officer of Uplands and Trenton airforce bases. In September 1939 Wing Commander McGill was called up to active service, he was the commanding officer of no. 1 Service Flying Training School at Camp Borden, during 1940-1941, he was organizer and first commanding officer of no. 2 Service Flying Training School at Uplands. Further postings followed as Director of Postings and Records in 1941 to Air Force Headquarters, as commanding officer to No. 2 Group Headquarters at Halifax in 1941-1942 and to RCAF Station Trenton in 1942-1942.

In 1943, he was promoted given command of No. 2 Training command in Toronto. Following another promotion to Air Vice Marshal, he returned to Air Force Headquarters in December 1943, where he remained for the rest of the war as Air Member for Organization Air Member for Supply and Organization. McGill retired from the RCAF in 1946. From 1951 to 1961 he was Director of the Aircraft Production branch of the Department of Defence Production, he died in Montreal on June 28, 1980. Canada's Sports Hall of Fame profile

Polish Legions (Napoleonic period)

The Polish Legions in the Napoleonic period, were several Polish military units that served with the French Army from 1797 to 1803, although some units continued to serve until 1815. After the Third Partition of Poland in 1795, many Poles believed that Revolutionary France and her allies would come to Poland's aid. France's enemies included Poland's partitioners, Prussia and Imperial Russia. Many Polish soldiers and volunteers therefore emigrated to the parts of Italy under French rule or serving as client states or sister republics to France and to France itself, where they joined forces with the local military; the number of Polish recruits soon reached many thousands. With support from Napoleon Bonaparte, Polish military units were formed, bearing Polish military ranks and commanded by Polish officers, they became known as a Polish army in exile, under French command. Their best known Polish commanders included Jan Henryk Dąbrowski, Karol Kniaziewicz and Józef Wybicki; the Polish Legions serving alongside the French Army during the Napoleonic Wars saw combat in most of Napoleon's campaigns, from the West Indies, through Italy and Egypt.

When the Duchy of Warsaw was created in 1807, many of the veterans of the Legions formed a core around which the Duchy's army was raised under Józef Poniatowski. This force fought a victorious war against Austria in 1809 and would go on to fight alongside the French army in numerous campaigns, culminating in the disastrous invasion of Russia in 1812, which marked the end of the Napoleonic empire, including the Legions, allied states like the Duchy of Warsaw. Among historians there is a degree of uncertainty about the period. Magocsi et al. notes that "the heyday of their activity" falls in the years 1797–1801, while Lerski defines the Legions as units that operated between 1797 and 1803. Davies defines the time of their existence as five to six years; the Polish PWN Encyklopedia defines them as units operating in the period of 1797–1801. The Polish WIEM Encyklopedia notes that the Legions ended with the death of most of their personnel in the Haitian campaign, which concluded in 1803; when recounting the history of the Polish Legions, some works describe the operations of Polish units under the French in the period after 1803.

Estimates of the strength of the Polish Legions vary and it is believed that between 20,000 and 30,000 men served in the Legions' ranks at any one time over the course of their existence. The WIEM Encyklopedia estimate is 21,000 for the period up to 1803. Davies suggests 25,000 for the period of up to 1802 -- 1803. Bideleux and Jeffries offer an estimate of up to 30,000 for the period up to 1801. Most of the soldiers came from the ranks of the peasantry, with only about 10 percent being drawn from the nobility. After the Third Partition of Poland, many Poles believed that revolutionary France, whose public opinion was sympathetic to the ideals of the Polish Constitution of 3 May 1791, would come to Poland's aid. France's enemies included Poland's partitioners, Prussia and Imperial Russia. Paris was the seat of two Polish organizations laying the claim to be the Polish government-in-exile, the Deputation of Franciszek Ksawery Dmochowski and the Agency of Józef Wybicki. Many Polish soldiers and volunteers therefore emigrated to Italy and to France.

The Agency was successful in convincing the French government to organize a Polish military unit. As the French Constitution did not allow for the employment of foreign troops on French soil, the French decided to use the Poles to bolster their allies in Italy, the Cisalpine Republic. Jan Henryk Dąbrowski, a former high-ranking officer in the army of the Polish-Lithuanian Commonwealth, began his work in 1796 – a year after the total destruction of the Commonwealth. At that time he went to Paris, Milan, where his idea received support from Napoleon Bonaparte, who saw the Poles as a promising source of new recruits, who superficially appeared receptive to the idea of liberating Poland. Dąbrowski was soon authorized by the French-allied Cisalpine Republic to create the Polish Legions, which would be part of the army of the newly created Republic of Lombardy; this agreement, drafted by Napoleon, was signed on 9 January 1797, marked the formal creation of the Legions. The Polish soldiers serving in the Dąbrowski Legion were granted Lombardian citizenship and were paid the same wage as other troops.

They were allowed to use their own unique Polish-style uniforms, with some French and Lombardian symbols, were commanded by other Polish speakers. By early February 1797 the Legion was 1,200 strong, having been bolstered by the arrival of many new recruits who had deserted from the Austrian army; the Dąbrowski Legion was first used against their allies in Italy. In March 1797 it garrisoned Mantua, by the end of the month it took part in its first combat during the Ten Days of Brescia. By the end of April the ranks of the Legion had swelled to 5,000. At that time Dąbrowski lobbied for a plan to push through to the Polish territories in Galicia, but, rejected by Napoleon who instead decided to use those troops on the Italian front. In April, the Legion took part in quelling the uprising in Verona, known as Veronese Easters; the Treaty of Leoben signed that month, which promised peace between Austri