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Floquet theory

Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form x ˙ = A x, with A a piecewise continuous periodic function with period T and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet, gives a canonical form for each fundamental matrix solution of this common linear system, it gives a coordinate change y = Q − 1 x with Q = Q that transforms the periodic system to a traditional linear system with constant, real coefficients. In solid-state physics, the analogous result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a vector space. A matrix ϕ is called a fundamental matrix solution if all columns are linearly independent solutions. A matrix Φ is called a principal fundamental matrix solution if all columns are linearly independent solutions and there exists t 0 such that Φ is the identity.

A principal fundamental matrix can be constructed from a fundamental matrix using Φ = ϕ ϕ − 1. The solution of the linear differential equation with the initial condition x = x 0 is x = ϕ ϕ − 1 x 0 where ϕ is any fundamental matrix solution. Let x ˙ = A x be a linear first order differential equation, where x is a column vector of length n and A an n × n periodic matrix with period T. Let ϕ be a fundamental matrix solution of this differential equation. For all t ∈ R, ϕ = ϕ ϕ − 1 ϕ. Here ϕ −. In addition, for each matrix B such that e T B = ϕ − 1 ϕ, there is a periodic matrix function t ↦ P such that ϕ = P e t B for all t ∈ R. Also, there is a real matrix R and a real periodic matrix function t ↦ Q such that ϕ = Q e t R for all t ∈ R. In the above B, P, Q and R are n × n matrices; this mapping ϕ = Q e t R {\displaystyle \phi \,=Q(t

Pennsylvania House of Representatives, District 169

The 169th Pennsylvania House of Representatives District is located in South Eastern Pennsylvania and has been represented by Kate Klunk since 2014. The 169th Pennsylvania House of Representatives District is located in York County and includes the following areas: Codorus Township Glen Rock Hanover Heidelberg Township Jefferson Manheim Township New Freedom Penn Township Railroad Shrewsbury Township West Manheim Township Cox, Harold. "Legislatures - 1776-2004". Wilkes University Election Statistics Project. Wilkes University. District map from the United States Census Bureau Pennsylvania House Legislative District Maps from the Pennsylvania Redistricting Commission. Population Data for District 44 from the Pennsylvania Redistricting Commission

Ale González

Alejandro "Ale" González Hernández is a Spanish footballer who plays for CD Mensajero as a right winger. Born in Las Palmas, Canary Islands, González finished his formation with Acodetti CF, made his debut as a senior with the club in the regional leagues, in 2013; the following year he moved to Real Sporting San José, being an important unit during his first and only campaign at San José in Tercera División, as his club only missed out another promotion in the play-offs. On 2 July 2015 González and his brother joined CD Tenerife, being assigned to the reserves in the fourth tier. On 19 March 2016, he scored a hat-trick with the B-side in a 3–0 home win against San Fernando CD, taking his tally up to 12 goals. Seven days he made his first team debut, coming on as a late substitute for Suso Santana in a 0–0 Segunda División away draw against CA Osasuna. On 30 August 2016, González was loaned for one year. Upon returning he moved to another reserve team, UD Las Palmas Atlético in the third division.

On 18 June 2018, González returned to Mensajero, now in a permanent deal and wit the side in the fourth division. González's twin brother Óscar is a footballer. A defender, he too was groomed at Acodetti, his father named Óscar, represented UD Las Palmas in the early 1990s. Tenerife official profile Ale González at Futbolme Ale González at Soccerway

A Night to Remember World Tour

A Night to Remember Tour was a concert tour in 1989 by American singer-songwriter Cyndi Lauper to support her 1989 multi-platinum album, A Night to Remember. Starting on April 21 in North America, it was her second major world tour, with dates scheduled throughout Asia, South America and Australia; the trek ended in late November in Mexico City. Three of the shows were filmed and aired on television in the respective countries in which they were filmed: Rio de Janeiro, Brazil. Sue Hadjopoulos - Percussion & Vocals Kevin Jenkins - Bass & Back Vocals Pat Buchanan - Guitar & Vocals Jim Yaeger - Keyboards & Vocals Tony James - Drums John Turi - Saxophone, Keyboards & Vocals Cyndi Lauper's Official Website

Religion in Sussex

Religion in Sussex has been dominated over the last 1,400 years by Christianity. Like the rest of England, the established church in Sussex is the Church of England, although other Christian traditions exist. After Christianity, the religion with the most adherents is Islam, followed by Hinduism, Buddhism and Sikhism. Sussex is sometimes referred to as'Silly Sussex', for silly is a corruption of Old Saxon saelig meaning'holy'; the historic county has been a single diocese after St Wilfrid converted the kingdom of Sussex in the seventh century. The west of the county has had a tendency towards Catholicism while the east of the county has had a tendency towards non-conformism; the county has been home to several pilgrimage sites, including the shrine to St Richard of Chichester, destroyed during the Reformation, the more recent Catholic shrine at West Grinstead. During the Marian persecutions, several Sussex men were martyred for their Protestant faith, including 17 men at Lewes; the Society of Dependants were a non-conformist sect formed in Loxwood.

The Quaker and founding father of Pennsylvania, William Penn worshipped near Thakeham. Sussex is connected with several saints, including St Wilfrid, sometimes known as the'Apostle of Sussex'. In folklore and Devil's Dyke are linked with St Dunstan, while West Tarring has links with St Thomas a Becket; the statistics for current religion from the 2011 census are set out in the tables below. After the Roman conquest of AD 43, the Celtic society of Sussex became Romanized; the first written account of Christianity in Britain comes from the early Christian Berber author, writing in the third century, who said that "Christianity could be found in Britain." Emperor Constantine, granted official tolerance to Christianity with the Edict of Milan in AD 313. In the reign of Emperor Theodosius "the Great", Christianity was made the official religion of the Roman Empire; when Roman rule ceased, Christianity was confined to urban communities. After the departure of the Roman army, the Saxons arrived in Sussex in the fifth century and brought with them their polytheistic religion.

The Saxon pagan culture caused a reversal of the spread of Christianity. In AD 691 Saint Wilfrid, the exiled Bishop of York, landed at Selsey and is credited with evangilising the locals and founding the church in Sussex. According to Bede, it was the last area of the country to be converted. Following the Norman Conquest of 1066, there was a purge of the English episcopate in 1070; the Anglo-Saxon Bishop of Selsey was deposed and replaced with William the Conquerors personal chaplain Stigand. During Stigand's episcopate the see, established at Selsey was transferred to Chichester after the Council of London of 1075 decreed that sees should be centred in cities rather than vills. Bishop Ralph Luffa is credited with the foundation of the current Chichester Cathedral; the original structure, built by Stigand was destroyed by fire in 1114. The archdeaconries of Chichester and Lewes were created in the 12th century under Ralph Luffa. Like the rest of the country the Church of Englands split with Rome during the reign of Henry VIII, was felt in Sussex.

In 1535, the king appointed Sir Thomas Cromwell as vicar-general. Cromwell visited Sussex in 1535, as part of his national census of churches and monasteries; the census was carried out with the intention of taxing church property more effectively. During the following year of 1536, an act was passed that decreed the dissolution of monasteries with an income of less than £200 per annum; the first phase was followed by the voluntary surrenders of the larger houses. Lewes Priory with Battle, was the first house in England, during the Dissolution, to surrender on a voluntary basis; the monks surrendered the house in November 1537 in return for either being given a small pension or a living as a priest. Sussex did not do too badly compared to the rest of the country, as it only had one person in 500, a member of a religious order, compared to the national average of one in 256. In 1538 there was a royal order for the demolition of the shrine of Saint Richard, in Chichester Cathedral. Thomas Cromwell saying that there was a certain kind of idolatry about the shrine.

Richard Sampson, the Bishop of Chichester incurred the displeasure of Cromwell and ended up imprisoned in the Tower of London at the end of 1539. Sampson was released, after the fall from favour and execution of Cromwell in 1540. Sampson continued at the see of Chichester for a further two years. Sampson was succeeded as Bishop of Chichester by George Day. Day opposed the changes, incurred the displeasure of the royal commissioners who promptly suspended him as Bishop and allowed him only preach in his cathedral church. Henry VIII died in 1547, his son Edward VI continued on the path; however his reign was only short-lived. The bishops of Chichester had not been for the Reformation until the appointment of John Scory, to the episcopate, who replaced Day in 1552. During Henry VIII's reign two of the canons of Chichester cathedral had been executed for their opposition to the Reformation and during his sons Edward VI reign George Day had been imprisoned for his opposition to the reforms. There had been twenty years of religious reform, when the catholic, Mary Tudor succeeded to the throne of England

Odette Jasse

Odette Jasse was a French astronomer who spent most of her career as administrator at the Marseille Observatory. Jasse was born in Saint-Victoret, her parents were a customs inspector. Jasse attended a school for girls in Marseille before going on to graduate in mathematics and physics. In August 1920 she took a position as an intern at the Marseille Observatory. From 1923 she began working as an assistant astronomer, a position she was appointed to in 1927, she had achieved a graduate degree in physics, completing out spectroscopy research at Henri Buisson's laboratory. Jasse observed the travel paths of Aldebaran and the Moon. However, Jasse never completed her doctoral thesis, she assumed administrative duties at the observatory from 1934. She was the editorial secretary of the Journal des Observateurs, she died in 1949 in Marseille, where a street is named in her honour