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Absolute convergence

In mathematics, an infinite series of numbers is said to converge if the sum of the absolute values of the summands is finite. More a real or complex series ∑ n = 0 ∞ a n is said to converge if ∑ n = 0 ∞ | a n | = L for some real number L. Similarly, an improper integral of a function, ∫ 0 ∞ f d x, is said to converge if the integral of the absolute value of the integrand is finite—that is, if ∫ 0 ∞ | f | d x = L. Absolute convergence is important for the study of infinite series because its definition is strong enough to have properties of finite sums that not all convergent series possess, yet is broad enough to occur commonly. Convergent series behave "nicely". For instance, rearrangements do not change the value of the sum; this is not true for conditionally convergent series: The alternating harmonic series 1 − 1 2 + 1 3 − 1 4 + 1 5 − 1 6 + ⋯ converges to ln ⁡ 2, while its rearrangement 1 + 1 3 − 1 2 + 1 5 + 1 7 − 1 4 + ⋯ converges to 3 2 ln ⁡ 2. One may study the convergence of series ∑ n = 0 ∞ a n whose terms an are elements of an arbitrary abelian topological group.

The notion of absolute convergence requires more structure, namely a norm, a positive real-valued function ‖ ⋅ ‖: G → R + on an abelian group G such that: The norm of the identity element of G is zero: ‖ 0 ‖ = 0. For every x in G, ‖ x ‖ = 0 implies x = 0. For every x in G, ‖ − x ‖ = ‖ x ‖. For every x, y in G, ‖ x + y ‖ ≤ ‖ x ‖ + ‖ y ‖. In this case, the function d =. We can therefore consider G-valued series and define such a series to be convergent if ∑ n = 0 ∞ ‖ a n ‖ < ∞. In particular, these statements apply using the norm |x| in the space of real numbers or complex numbers. If G is complete with respect to the metric d every convergent series is convergent; the proof is the same as for complex-valued series: use the completeness to derive the Cauchy criterion for convergence—a series is convergent if and only if its tails can be made arbitrarily small in norm—and apply the triangle inequality. In particular, for series with values in any Banach space, absolute convergence implies convergence.

The converse is true: if absolute convergence implies convergence in a normed space the space is a Banach space. If a series is convergent but not convergent, it is called conditionally convergent. An example of a conditionally convergent series is the alternating harmonic series. Many standard tests for divergence and convergence, most notably including the ratio test and the root test, demonstrate absolute convergence; this is because a power series is convergent on the interior of its disk of convergence. Suppose that ∑ | a k |, a k ∈ C is convergent. Equivalently, ∑ [ R e (

Edward Little (philanthropist)

Edward Little was an attorney and philanthropist who founded Edward Little High School in Auburn, Maine. Little's father, was a descendant of one of the first settlers of what is now Auburn, Maine. Edward Little was born in 1773 in Newbury and attended Phillips Exeter before graduating from Dartmouth College in 1798. Little became a successful attorney and entrepreneur in the city of Newburyport, but after a devastating fire in 1811 he moved to Portland, several years and in 1826 he moved to what is now Auburn. After his father's death in 1830, Little inherited land in the Auburn area. Little was known as "a quiet, scholarly person, known for his devotion to the community." Little made many prominent donations, including the donation of a Congregational church building to Bowdoin College, in 1834 he founded the Lewiston Falls Academy, donating 9 acres and considerable funds to the academy, named the Little Institute and Edward Little High School. Edward Little lived in the Edward Little House and died in 1849.

Edward Little High School

Brent Barry

Brent Robert Barry known by the nickname Bones, is an American basketball executive and former player. He is the current vice president of basketball operations for the San Antonio Spurs; the 6 ft 7 in, 210 lb shooting guard played professionally in the National Basketball Association, winning two championships with the Spurs, won the 1996 NBA Slam Dunk Contest. He is the son of former NBA player Rick Barry. After retiring, Barry worked as a sports commentator for the NBA on TNT and was a studio host for the NBA TV show NBA Gametime. In 2018, he returned to the Spurs as an executive. Brent Barry was selected by the Denver Nuggets in the first round of the 1995 NBA draft, but was traded to the Los Angeles Clippers on draft night in a 4-player trade with Rodney Rogers for the No. 2 overall pick in the draft and Randy Woods. Barry was considered a good passer and had three seasons where he averaged more than 5 assists per game. Barry was a strong three-point shooter; these two strengths, combined with Barry's 6'7" frame, allowed him to play a variety of positions, including point guard, shooting guard, small forward.

He was on the San Antonio Spurs championship teams in 2005 and 2007. He won the Slam Dunk Contest in the NBA All-Star Weekend in 1996 with a Julius Erving-inspired slam dunk in which he took off from the free throw line to sail in and dunk one-handed, he was the first caucasian player to win the competition. After being drafted by the Denver Nuggets, Barry was traded to the Los Angeles Clippers. In his rookie season, Brent made 123 3-pointers. There Brent would average 10.4 ppg and 38% 3-pt field goal in 179 games. In his second season, he and the Clippers attempted a playoff run where Brent would average 11.7 ppg, his highest in the postseason. The Clippers only played in 3 games during the postseason. Barry was traded to the Miami Heat the day before the February 20 trade deadline from Los Angeles for Isaac Austin. In Miami, Barry would only play 17 games, not averaging only 4.1 ppg. Barry signed a 6-year $27 million contract. After sustaining an injury, he played only 37 of the 50 games played that season, starting 30 of those games, averaging 11.1 ppg.

Failing to fill the void of a Jordan-less Bulls, the team traded Brent for Hersey Hawkins and James Cotton from Seattle on August 12, 1999. Brent spent 4 seasons with the Seattle SuperSonics. Brent would begin his Seattle career as a back-up for fellow Oregon State alumnus Gary Payton, he would move to play the point position as a starter, filled in when needed as a small forward. There he would average 11.2 ppg, make 669 3-point shots, start the majority of his NBA career, total 4,107 points. In Seattle he would play 10 postseason games, starting 8 of the most in his career thus far. In the summer of 2004, Barry was signed as a free agent by the San Antonio Spurs, where he spent most of the season as a backup. After losing their first playoff game to the Denver Nuggets in the 2005 NBA Playoffs, San Antonio inserted Barry into the starting lineup; the Spurs' new lineup helped. In those same playoffs, Barry earned his first championship ring when the Spurs defeated the Detroit Pistons in the 2005 NBA Finals.

Brent and his father, Rick Barry, are the second father-son duo to each win an NBA Championship as a player. The only other father-son duos are Bill Walton and his son Luke Walton, Mychal Thompson and his son Klay Thompson. In June 2007, he won his second NBA championship ring when the Spurs swept the Cleveland Cavaliers 4–0. In January 2008, Barry tore his right calf muscle. On February 20, 2008, along with Francisco Elson and a 2009 first round draft pick, were traded by the San Antonio Spurs back to the Seattle SuperSonics in exchange for forward/center Kurt Thomas. Barry was waived the following day by the Sonics. After a mandatory 30-day waiting period, he re-signed with San Antonio on March 24, 2008 for 1 year with the possibility for the 2009–2010 season at Veteran Minimum. Coming off of injury Barry did not see much playing time in the first 2 rounds of the 2008 NBA Playoffs. Barry would shine against the Lakers in the Western Conference finals, getting 23 points in Game 4, with a controversial no-call foul with 2 seconds on the clock.

The Spurs would lose the series in 5 games, however. San Antonio provided Barry with the most playoff experience of his career, he totaled 1,888 points. Barry opted out of his contract and became a free agent on July 1, 2008. On July 10, Barry signed a 2-year contract with the Houston Rockets, becoming the third member of the family to join the franchise, his father, ended his career playing two seasons with the Rockets and his older brother, Jon finished his career with the Rockets, playing from 2004 to 06. Financial terms were not released. Brent's other brother Richard Francis "Scooter" Barry IV is a retired American professional basketball player. On October 23, 2009, Brent Barry's career ended when he was cut by the Rockets at the end of training camp, leading Barry to remark that "all the Barrys were buried in Houston


Aedini is a mosquito tribe in the subfamily Culicinae. It is the main tribe of mosquitoes with 1256 species classified in 81 genera and two groups incertae sedis. Genus Abraedes Genus Aedes Genus Alanstonea Genus Albuginosus Genus ArmigeresSubgenus Armigeres Subgenus LeicesteriaGenus Ayurakitia Genus Aztecaedes Genus Belkinius Genus Borichinda Genus Bothaella Genus Bruceharrisonius Genus Christophersiomyia Genus CollessiusSubgenus Alloeomyia Subgenus CollessiusGenus Dahliana Genus Danielsia Genus Diceromyia Genus Dobrotworskyius Genus Downsiomyia Genus Edwardsaedes Genus Eretmapodites Genus Finlaya Genus Fredwardsius Genus GeorgecraigiusSubgenus Georgecraigius Subgenus HorsfalliusGenus Gilesius Genus Gymnometopa Genus HaemagogusSubgenus Conopostegus Subgenus HaemagogusGenus Halaedes Genus HeizmanniaSubgenus Heizmannia Subgenus MattinglyiaGenus Himalaius Genus HopkinsiusSubgenus Hopkinsius Subgenus YamadaGenus Howardina Genus Huaedes Genus Hulecoeteomyia Genus Indusius Genus Isoaedes Genus JarnelliusSubgenus Jarnellius Subgenus LewnielseniusGenus Jihlienius Genus Kenknightia Genus Kompia Genus Leptosomatomyia Genus Lorrainea Genus Luius Genus MacleayaSubgenus Chaetocruiomyia Subgenus MacleayaGenus Molpemyia Genus MucidusSubgenus Mucidus Subgenus LewnielseniusGenus Neomelaniconion Genus OchlerotatusSubgenus Acartomyia Subgenus Buvirilia Subgenus Chrysoconops Subgenus Culicelsa Subgenus Empihals Subgenus Geoskusea Subgenus Gilesia Subgenus Levua Subgenus Ochlerotatus Subgenus Pholeomyia Subgenus Protoculex Subgenus Pseudoskusea Subgenus Rhinoskusea Subgenus Rusticoidus Subgenus SallumiaGenus OpifexSubgenus Nothoskusea Subgenus OpifexGenus Paraedes Genus Patmarksia Genus Phagomyia Genus Pseudarmigeres Genus PsorophoraSubgenus Grabhamia Subgenus Janthinosoma Subgenus PsorophoraGenus Rampamyia Genus Scutomyia Genus Skusea Genus Stegomyia Genus Tanakaius Genus Tewarius Genus Udaya Genus Vansomerenis Genus VerrallinaSubgenus Harbachius Subgenus Neomacleaya Subgenus VerrallinaGenus Zavortinkius Genus Zeugnomyia List of mosquito genera Huang, Y-M.

& Rueda, L. M. 2015. A pictorial key to the species of the Aedes in the Afrotropical Region. Zootaxa 4027: 593–599. Doi:10.11646/zootaxa.4027.4.9 Reinert, J. F.. E.. J. 2009: Phylogeny and classification of tribe Aedini. Zoological journal of the Linnean Society, 157: 700-794. Doi:10.1111/j.1096-3642.2009.00570.x Data related to Aedini at Wikispecies Aedini at the Mosquito Taxonomic Inventory

Sophia Jagiellon, Duchess of Brunswick-L√ľneburg

Sophia Jagiellon of Poland, a member of the Jagiellonian dynasty, was a Polish princess and Duchess of Brunswick-Wolfenbüttel from 1556 to 1568 by her marriage with Duke Henry V. Sophia was born in Kraków, a daughter of King Sigismund I of Poland and his second wife, the Italian princess Bona Sforza, she was the third of her parents' six children and raised at the royal court of Wawel Castle with her siblings including Isabella Jagiellon, Sigismund II Augustus, Anna Jagiellon, Catherine Jagiellon and Albert Jagiellon. When in 1548 her mother Bona Sforza entered into conflict with her son King Sigismund II Augustus over the marriage with his mistress Barbara Radziwiłł, Sophia and her sisters were removed from the Kraków court to live in Masovia. Between 22 and 25 February 1556 she married the 66-year-old Duke Henry V of Brunswick-Wolfenbüttel; the Catholic duke had been a loyal supporter of the Habsburg emperor Charles V in the Schmalkaldic War. He had been firstly married to a daughter of Count Henry of Württemberg.

The couple had eight children, though only one surviving son, Prince Julius, whose elder brothers were killed in the 1553 Battle of Sievershausen. His father wished for another heir to the throne, she was accompanied to Germany with a retinue of 500 courtiers, among whom Agnieszka was to be her influential confidante and favorite. On 11 June 1568 Sophia was widowed. After the death of her husband she retired to the families residence in Schöningen. Shortly after, she fell into dispute with her stepson Duke Julius of Brunswick-Wolfenbüttel. Julius, did not honor the terms and in 1573 Sophia had to ask for help from Emperor Maximilian II. In the spring of 1570 Sophia converted to Lutheranism and therefore was the first and only Protestant member of the Jagiellonian dynasty, she died on 28 May 1575 at Schöningen Castle. She is buried in the Church of the Blessed Virgin Mary in Wolfenbüttel

Fire Emblem: Genealogy of the Holy War

Fire Emblem: Genealogy of the Holy War is a tactical role-playing game developed by Intelligent Systems and published by Nintendo for the Super Famicom home video game console in 1996. It is the fourth installment of the Fire Emblem series, the second to be developed for the platform. Genealogy of the Holy War takes place on the continent of Jugdral, split between eight different countries founded by the Twelve Crusaders, an ancient group of soldiers who ended the rule of the ancient dragon Loptyr with divine aid. In the present, a cult working to revive Loptyr stir up war among the countries; the story is told over two generations — the first generation follows the Grannvalian prince Sigurd, while the second follows his son Seliph as he works to defeat the cult and avenge his father. Gameplay follows the traditional Fire Emblem system of tactical battles taking place on grid-based maps, while adding the Weapons Triangle and Support systems, which directly impacted both gameplay and story. Development began after the completion of Fire Emblem: Mystery of the Emblem.

Returning staff included director and scenario writer Shouzou Kaga, composer Yuka Tsujiyoko, character designer Katsuyoshi Koya, producer Gunpei Yokoi. A greater focus was placed on the story compared to previous entries, although the gameplay saw new additions. Production was turbulent due to staff moves and the unexpected addition of character romance and expanded storyline. First unveiled under the title Inheritors of Light, it was scheduled for a March release, before releasing in May, it met with commercial success. A follow-up title based within the game's storyline, Fire Emblem: Thracia 776, was released in 1999. Many elements introduced in Genealogy of the Holy War would reappear in titles. Fire Emblem: Genealogy of the Holy War is a tactical role-playing game in which the player takes the roles of Sigurd and his son Seliph across a variety of story-driven missions on the continent of Jugdral; the story is divided into chapters. Before and during missions, the player units may settle in a home base, where various actions can be taken such as repairing weapons and selling items, participating in arena battles.

Castle towns within mission maps can be visited for similar services. Battles play out using a turn-based system where each unit on both sides is given their chance to move and act. Characters move and attack within the same turn, in a few cases units can take two moves in a turn. A key part of combat is the Weapon Triangle, a new addition which governs the opposing strengths and weaknesses of weapon types based on a rock–paper–scissors system - lances are stronger than swords, swords are stronger than axes, axes are stronger than lances. A secondary system governs the magic system, where Fire and Wind spells have varying strengths and weaknesses against each other with Light and Dark magic existing outside of the magic triangle; each unit has a character class which determines their weapon, skill set and attack range, how much effect they have on other units, which latent skills they possess, whether they use passive or aggressive skills when in combat. Different weapon types affect battle performance: for instance, a powerful axe deals more damage, but weighs a character down more than a sword.

The actions taken in earlier parts of a map can affect parts of that mission, triggering scripted changes in objectives and enemy behavior: for instance, when a castle is raided, the neighboring castle will have troops ready to swarm attackers. After each battle, a player character gains experience points; when a unit gains 100 experience points, they receive random boosts to their statistics such as health and agility. All characters are subject to permanent death if they are defeated in battle, removing them from the rest of the game. If the army's leader is killed, the map must be restarted. Victory is achieved when the map's objective has been completed, which can vary from defeating an enemy force to capturing specific points on a map. Character relationships form a core part of gameplay, include both optional conversations and story-driven character romances. Conversations see selected characters in the mission map talking with each other, some romances are triggered by the story when certain characters have joined the party during the first generation storyline.

The second generation units have their stat values and personal skills influenced by the assigned attributes of their parents. Second generation units can form optional romantic attachments, but this only influences stats; when characters with family or romantic connection are next to each other, they grant stat boosts to each other, which can provide a higher chance to hit critically. In addition to normal stat growth, different high-ranking units on both sides have a separate "Leadership" rank, which grants stat boosts to all units within range, with the boost varying depending on that unit's current Leadership rank. Genealogy of the Holy War takes place on the continent of Jugdral, divided between eight countries: the Kingdom of Grannvale, the Kingdom of Verdane, the Dominion of Agustria, the Republic of Manster, the Kingdom of Thracia, the Republic of Miletos, the Kingdom of Silesse, the Kingdom of Isaach. According to staff, Jugdral is within the same world as Archanea, the continent featured in the original Fire Emblem and its sequels: the events of Genealogy of the Holy War are set hundreds of years prior to the time period of Archanea, with the latter being in a civilized state.

It was during this time. In ancient time