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Year 1518 was a common year starting on Friday of the Julian calendar. In France, year 1518 lasted from 4 April 1518 to 23 April 1519. Since Constantine and until the year 1565, the year was reckoned as beginning at Easter. For instance, the will of Leonardo da Vinci, drafted in Amboise on 23 April 1519, shows the legend "Given on the 23rd of April of 1518, before Easter". See Wikisource "1911 Encyclopædia Britannica/Easter" April 18 – The widowed Sigismund I the Old, King of Poland and Grand Duke of Lithuania, marries Milanese noblewoman Bona Sforza in Wawel Cathedral and she is crowned as Queen consort of Poland. May 26 – A transit of Venus occurs. July – Dancing plague of 1518: A case of dancing mania breaks out in Strasbourg, in which many people die from constant dancing. August – Construction of the Manchester Grammar School is completed in England. October 3 – The Treaty of London temporarily ensures peace in Western Europe; the Rajput Mewar Kingdom under Rana Sanga achieves a major victory over Sultan Ibrahim Lodi of Delhi.

A swarm of tropical fire ants devastates crops on Hispaniola. Erasmus publishes his Colloquies. Henricus Grammateus publishes Ayn neu Kunstlich Buech in Vienna, containing the earliest printed use of plus and minus signs for arithmetic; the African slave trade begins. February 2 Johann Hommel, German astronomer and mathematician Godfried van Mierlo, Dutch Dominican friar and bishop February 7 – Johann Funck, German theologian February 13 – Antonín Brus z Mohelnice, Moravian Catholic archbishop February 20 – Georg, Count Palatine of Simmern-Sponheim, February 21 – John of Denmark, Danish prince February 28 – Francis III, Duke of Brittany, Duke of Brittany March 8 – Sidonie of Saxony, Duchess of Brunswick-Calenberg April 22 – Antoine de Bourbon, father of Henry IV of France July 3 – Li Shizhen, Chinese physician and mineralogist August 8 – Conrad Lycosthenes, Alsatian humanist and encyclopedist October 26 – John Basset, Devonshire gentleman November 26 – Guido Ascanio Sforza di Santa Fiora, Italian Catholic cardinal December 13 – Clara of Saxe-Lauenburg, Princess of Saxe-Lauenburg and Duchess of Brunswick-Gifhorn by marriage December 17 – Ernest III, Duke of Brunswick-Grubenhagen December 19 – Enrique de Borja y Aragón, Spanish noble of the House of Borgia date unknown James Halyburton, Scottish reformer Hubert Languet, French diplomat and reformer Connor MacLeod, Scottish Highlander & Immortal Edmund Plowden, English legal scholar Tintoretto, Italian painter possible – Catherine Howard, fifth queen consort of Henry VIII of England February 9 – Jean IV de Rieux, Breton noble and Marshal May 31 – Elisabeth of Brandenburg-Ansbach-Kulmbach, German margravine July 10 – Sibylle of Baden, Countess consort of Hanau-Lichtenberg August 16 – Loyset Compère, French composer August 27 – Joan of Naples, queen consort of Naples November 20 Marmaduke Constable, English soldier Pierre de La Rue, Flemish composer November 24 – Vannozza dei Cattanei, mistress of Pope Alexander VI December 5 – Gian Giacomo Trivulzio, Italian military commander December 27 – Mahmood Shah Bahmani II, sultan of the Bahmani Sultanate date unknown Moxammat Amin of Kazan, khan of Kazan Kabir, Indian mystic Aruj, Ottoman corsair, brother of Hayreddin Barbarossa Muhammad ibn Azhar ad-Din, sultan of Adal


In mathematics, the permutohedron of order n is an -dimensional polytope embedded in an n-dimensional space. Its vertex coordinates are the permutations of the first n natural numbers; the edges are the shortest possible connections between these points. Two permutations connected by an edge differ in two places, the numbers on these places are neighbors; the image on the right shows the permutohedron of order 4, the truncated octahedron. Its vertices are the 24 permutations of. Parallel edges have the same edge color; the 6 edge colors correspond to the 6 possible transpositions of 4 elements, i.e. they indicate in which two places the connected permutations differ. According to Günter M. Ziegler, permutohedra were first studied by Pieter Hendrik Schoute; the name permutoèdre was coined by Georges Th. Guilbaud and Pierre Rosenstiehl, they describe the word as barbaric, but easy to remember, submit it to the criticism of their readers. The alternative spelling permutahedron is sometimes used. Permutohedra are sometimes called permutation polytopes, but this terminology is used for the related Birkhoff polytope, defined as the convex hull of permutation matrices.

More V. Joseph Bowman uses that term for any polytope whose vertices have a bijection with the permutations of some set; the permutohedron of order n has n! vertices, each of, adjacent to n − 1 others, so the total number of edges is n!/2. Each edge has length √2, connects two vertices that differ by swapping two coordinates the values of which differ by one; the permutohedron has one facet for each nonempty proper subset S of, consisting of the vertices in which all coordinates in positions in S are smaller than all coordinates in positions not in S. Thus, the total number of facets is 2n − 2. More the faces of the permutohedron are in 1-1 correspondence with the strict weak orderings on a set of n items: a face of dimension d corresponds to a strict weak ordering in which there are n − d equivalence classes; because of this correspondence, the number of faces is given by the ordered Bell numbers. The number of -dimensional faces in a permutohedron of order n is found in the triangle T = k!

⋅ S,where S are the Stirling numbers of the second kind — shown on the right, together with its row sums, the ordered Bell numbers. The permutohedron is vertex-transitive: the symmetric group Sn acts on the permutohedron by permutation of coordinates; the permutohedron is a zonotope. The vertices and edges of the permutohedron are isomorphic to one of the Cayley graphs of the symmetric group, namely the one generated by the transpositions that swap consecutive elements; the vertices of the Cayley graph are the inverse permutations of those in the permutohedron. The image on the right shows the Cayley graph of S4, its edge colors represent the 3 generating transpositions:, This Cayley graph is Hamiltonian. The permutohedron of order n lies in the -dimensional hyperplane consisting of all points whose coordinates sum to the number 1 + 2 + … + n = n/2. Moreover, this hyperplane can be tiled by infinitely many translated copies of the permutohedron; each of them differs from the basic permutohedron by an element of a certain -dimensional lattice, which consists of the n-tuples of integers that sum to zero and whose residues are all equal: x1 + x2 + … + xn = 0, x1 ≡ x2 ≡ … ≡ xn.

Thus, the permutohedron of order 4 shown above tiles the 3-dimensional space by translation. Here the 3-dimensional space is the affine subspace of the 4-dimensional space R4 with coordinates x, y, z, w that consists of the 4-tuples of real numbers whose sum is 10, x + y + z + w = 10. One checks that for each of the following four vectors, and,the sum of the coordinates is zero and all coordinates are congruent to 1. Any three of these vectors generate the translation lattice; the tessellations formed in this way from the order-2, order-3, order-4 permutohedra are the apeirogon, the regular hexagonal tiling, the bitruncated cubic honeycomb. The dual tessellations contain all simplex facets, although they are not regular polytopes beyond order-3. Associahedron Cyclohedron Bowman, V. Joseph, "Permutation polyhedra", SIAM Journal on Applied Mathematics, 22: 580–589, doi:10.1137/0122054, JSTOR 2099695, MR 0305800. Gaiha, Prabha. "Adjacent vertices on a permutohedron", SIAM Journal on Applied Mathematics, 32: 323–327, doi:10.1137/0132025, JSTOR 2100417, MR 0427102.

Guilbaud, Georges Th.. Schoute, Pieter Hendrik, "Analytic treatment of the polytopes derived from the regular polytopes", Verhandelingen der Koninklijke Akademie van Wetenschappen Te Amsterdam, 11: 87 pp Googlebook, 370–381 Also online on the KNAW Digital Library at http://www

Get in the Ring

"Get in the Ring" is the fifth song on the Guns N' Roses album Use Your Illusion II. Written by Axl Rose, Duff McKagan and Slash, it is directed at music critics. Mentioned by name are critics from Hit Parader, Kerrang! and Spin. The song was written by McKagan as "Why Do You Look at Me When You Hate Me?", its first line. In the interview that precipitated Mick Wall's mention in the song, Rose said: "I've brought in an album. Duff brought in one song. It's called'Why Do You Look At Me When You Hate Me?' and it's just bad-assed. And I wrote a bunch of words to that." The song was going to be titled "Get in the Ring Motherfucker" but, changed too. At the time of the song's release, Mick Wall of Kerrang! was thought to have been mentioned because of his book Guns N' Roses: The Most Dangerous Band in the World, a no holds barred collection of interviews and stories about the band. Wall denies this, claims the real reason was an interview he conducted in early 1990 for Kerrang! that included Rose's threat to harm Vince Neil of Mötley Crüe after an incident involving Neil's wife and Izzy Stradlin.

The song suggests that Jr.'s father "gets more pussy" than Guccione Jr.. The younger Guccione responded in a letter to Rose, saying he accepted the challenge to a fight and could use the promotion to help sell magazines. Rose backed down from the fight after learning that Guccione Jr. had nine years of fight training."Get in the Ring" is notorious for its amount of swearing. The chants of "Guns. And. Roses" and "Get in the ring" were recorded with the audience at a Saratoga Springs concert on June 10, 1991. W. Axl Rose – lead vocals, production Slash – lead guitar, production Izzy Stradlin – rhythm guitar, production Duff McKagan – bass, backing vocals, production Matt Sorumdrums, production Dizzy Reedpiano, production Lyrics of this song at MetroLyrics

St Cynhaearn's Church, Ynyscynhaearn

St Cynhaearn's Church is a redundant church standing in an isolated position on Ynyscynhaearna, a former island in Llyn Ystumllyn, 900 metres south of the village of Pentrefelin, Wales. It is designated by Cadw as a Grade II* listed building; the church is approached from the village by an ancient causeway, is in the care of the Friends of Friendless Churches. The church was the parish church for Porthmadog, its nave dates from the 12th century, the north transept was added in the 16th century. The south transept was built in 1622. Most of the interior fittings are Georgian in style and date from 1832, it came into the care of the Friends of Friendless Churches in 2003, since when repair work has been undertaken. It is constructed in stone rubble, with the walls of the nave and the east side of the chancel being stucco; the roofs are of modern slates. Its plan consists of a short nave and south transepts, a short chancel. At the west end is a bellcote; the entrance is through a west door. The windows in the nave and transepts have two lights, at the east end are three lancet windows.

The interior is plastered above a timber dado. The floor of the body of the church is stone-flagged, there is a painted floor in the sanctuary. At the west end is a gallery. Dating from 1832, the pulpit is a three-decker, approached by nine steps, below, a lectern with a reading shelf, under this is the reader's desk. On each side of the altar are box pews; the gallery is supported on slender columns. The chamber organ by Flight and Robson was given by a Mrs Walker, it has a Gothic style case. On each side of it are six steeply raked pews and many carry the names of the families who used them. One of the pews is curtained off for mothers to feed their babies; the font stands on an octagonal pillar of limestone and was erected in 1900. There are a number of memorials; the stained glass includes windows by James Powell and Sons dated 1899 and 1906. An earlier grave records the early passing of David Owen, a local blind composer and harpist, known as "Dafydd y Garreg Wen" or David of the White Rock, as he came from Garreg Wen Farm.

Owen wrote a tune called Dafydd y Garreg Wen on his deathbed after calling for his harp. Amongst the memorials is one to John Ystumllyn known as Jack Black, he was a black man brought back from Africa by a member of the Wynne family who lived at Ystumllyn, which can be seen from the church. It was fashionable at the time to have a black servant, he was given his own house, he died at the end of the 18th century. Local people claim him as their ancestor. There is a memorial to James Spooner, the surveyor who built the Ffestiniog Railway and members of his family in the form of a stone urn surrounded by iron railings, it is located to the right when facing the church from the gate. There are many children's graves. Daniel Morris, the first harbourmaster of Porthmadog, is buried there, together with three of his young daughters. There are the graves of ropemakers, ships' captains and many young sailors drowned at sea, as well as that of Captain Thomas Jones, an ancestor of Lord Snowdon

Fred Tilson

Samuel Frederick Tilson was an English professional footballer who played for Manchester City and England. He was born in South Yorkshire, he was part of the City team that won both the League Championship in the 1930s. He has been described as'a quick thinker with an elusive body-swerve'. Tilson was born in Swinton, South Yorkshire on 19 April 1904, he began his football career at Barnsley Congregationals and was able to play in both inside forward and centre forward positions. He subsequently moved to Barnsley; the form of both players attracted bigger teams and in 1928 they were both transferred to Manchester City for a combined fee of £6,000, the pair making their debuts on 17 March against Grimsby Town. Brook and Tilson joined a strong forward line at the club that included two England internationals in Tommy Johnson and Frank Roberts. In his first season Tilson helped City earn promotion to the first division. Tilson score 110 goals. In his second season with the team he played 22 times and scored 12 goals making him City's third highest goalscorer behind Tommy Johnson who scored a club record of 38 goals and Eric Brook who scored 14 goals.

Injuries restricted his appearances in the football season of 1929–1930 and 1930–1931. He scored 13 league goals in the 1931 -- 3 FA Cup goals. City managed to reach the semi final of the FA Cup that year but were defeated by Arsenal by 1–0. In the 1932–1933 football season Tilson was the club's leading goalscorer with 23 goals in all competitions; this included 6 FA Cup goals. In the 1933 FA Cup final Manchester City were defeated three goals to nil by Everton who were captained by England international Dixie Dean. Tilson did not play in the final of that year's competition but did play in the 1934 FA Cup final in which he scored twice in a 2–1 victory over Portsmouth. City had been trailing by a goal to nil at half time and City goalkeeper Frank Swift blamed himself for that had given Portsmouth the lead. Tilson in an attempt to console the young keeper told him not to worry because he would score two in the second half, he was true to his words. Tilson has been inducted into the Manchester City Hall of Fame.

In 1977 the Manchester City Council named eleven streets in a new estate in Moss Side after famous City players including Tilson. He is listed as the twenty-eighth greatest City player on the Time website and eighteenth in Ian Penney's book The Essential History of Manchester City

1998 Newham London Borough Council election

The 1998 Newham London Borough election for the Newham London Borough Council was held on 7 May 1998. The whole council was up for election. Turnout was 28.4%. Labour won every seat for the second time since the councils formation. A total of 138 candidates stood in the election for the 60 seats being contested across 24 wards. Candidates included a full slate from the Labour party, whilst the Conservative party ran 31 candidates and the Liberal Democrats ran 11 candidates. In both cases this was a lot less than 4 years before. Other candidates running were 8 Socialist Labour, 2 National Democrats, 11 BNP, 1 Monster Raving Looney and 14 Independents; the by-election was called following the death of Cllr. Thomas A. Jenkinson; the by-election was called following the resignation of Cllr. Glynis A. Carpenter; the by-election was called following the resignation of Cllr. Christopher B. Allen; the by-election was called following the resignation of Cllr. Dennis R. Horwood; the by-election was called following the resignation of Cllr.

Stephen C. Timms; the by-election was called following the death of Cllr. Theodore L. Etherden; the by-election was called following the resignation of Cllr. Judith A. Jorsling