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Profinite group

In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups. They share many properties with their finite quotients: for example, both Lagrange's theorem and the Sylow theorems generalise well to profinite groups. A non-compact generalization of a profinite group is a locally profinite group. Profinite groups can be defined in either of two equivalent ways. A profinite group is a topological group, isomorphic to the inverse limit of an inverse system of discrete finite groups. In this context, an inverse system consists of a directed set, a collection of finite groups G =, each having the discrete topology, a collection of homomorphisms such that f i i is the identity on G i and the collection satisfies the composition property f i j ∘ f j k = f i k; the inverse limit is the set: lim ← G i = equipped with the relative product topology. In categorical terms, this is a special case of a filtered limit construction. One can define the inverse limit in terms of a universal property.

A profinite group is a Hausdorff and disconnected topological group: that is, a topological group, a Stone space. Given this definition, it is possible to recover the first definition using the inverse limit lim ← G / N where N ranges through the open normal subgroups of G ordered by inclusion. Finite groups are profinite; the group of p-adic integers Z p under addition is profinite. It is the inverse limit of the finite groups Z / p n Z where n ranges over all natural numbers and the natural maps Z / p n Z → Z / p m Z are used for the limit process; the topology on this profinite group is the same as the topology arising from the p-adic valuation on Z p. The Galois theory of field extensions of infinite degree gives rise to Galois groups that are profinite. If L/K is a Galois extension, we consider the group G = Gal consisting of all field automorphisms of L which keep all elements of K fixed; this group is the inverse limit of the finite groups Gal, where F ranges over all intermediate fields such that F/K is a finite Galois extension.

For the limit process, we use the restriction homomorphisms Gal → Gal, where F2 ⊆ F1. The topology we obtain on Gal is known as the Krull topology after Wolfgang Krull. Waterhouse showed that every profinite group is isomorphic to one arising from the Galois theory of some field K, but one cannot control which field K will be in this case. In fact, for many fields K one does not know in general which finite groups occur as Galois groups over K; this is the inverse Galois problem for a field K. Not every profinite group occurs as an absolute Galois group of a field; the fundamental groups considered in algebraic geometry are profinite groups speaking because the algebra can only'see' finite coverings of an algebraic variety. The fundamental groups of algebraic topology, are in general not profinite: for any prescribed group, there is a 2-dimensional CW complex whose fundamental group equals it The automorphism group of a local

Ribbon microphone

A ribbon microphone known as a ribbon velocity microphone, is a type of microphone that uses a thin aluminum, duraluminum or nanofilm of electrically conductive ribbon placed between the poles of a magnet to produce a voltage by electromagnetic induction. Ribbon microphones are bidirectional, meaning that they pick up sounds well from either side of the microphone. In a moving-coil microphone, the diaphragm is attached to a light movable coil that generates a voltage as it moves back and forth between the poles of a permanent magnet. In ribbon microphones, a light metal ribbon is suspended between the poles of a magnet; as the ribbon vibrates, a voltage is induced at right angles to both the ribbon velocity and magnetic field direction and is picked off by contacts at the ends of the ribbon. Ribbon microphones are called "velocity microphones" because the induced voltage is proportional to the velocity of the ribbon and thus of the air particles in the sound wave, unlike in some other microphones where the voltage is proportional to the displacement of the diaphragm and the air.

The advantage of the ribbon microphone when introduced was that the light ribbon had a much higher natural resonant frequency than diaphragms in existing microphones, above hearing range, so it had flatter response at high frequencies. The voltage output of older ribbon microphones is quite low compared to a dynamic moving coil microphone, a step-up transformer is used to increase the voltage output and increase the output impedance. Modern ribbon microphones do not suffer from this problem due to improved magnets and more efficient transformers and have output levels that can exceed typical stage dynamic microphones. Ribbon microphones were once delicate and expensive, but modern materials make certain present-day ribbon microphones durable, so they may be used for loud rock music and stage work, they are prized for their ability to capture high-frequency detail, comparing favorably with condenser microphones, which can sound subjectively "aggressive" or "brittle" in the high end of the frequency spectrum.

Due to their bidirectional pick-up pattern, ribbon microphones may be used in pairs to produce the Blumlein Pair recording array. In addition to the standard bidirectional pick-up pattern, ribbon microphones can be configured to have cardioid, hypercardioid and variable pattern; as many mixers are equipped with phantom power in order to enable the use of condenser microphones, care should be taken when using condenser and ribbon microphones at the same time. If the ribbon microphone is improperly wired, not unheard of with older microphones, this capability can damage some ribbon elements. In the early 1920s, Drs. Walter H. Schottky and Erwin Gerlach co-invented the first ribbon microphone. By turning the ribbon circuit in the opposite direction, they invented the first ribbon loudspeaker. A few years Dr. Harry F. Olson of RCA started developing ribbon microphones using field coils and permanent magnets; the RCA Photophone Type PB-31 was commercially manufactured in 1931 impacting the audio recording and broadcasting industries.

Condenser microphones at the time could not compare to its frequency response. Radio City Music Hall employed PB-31s in 1932; the following year, the 44A came on the scene. Its tone and pattern control helped reduce reverberation. Many RCA ribbon models valued by audio engineers; the BBC-Marconi Type A was an iconic ribbon microphone produced by the BBC and Marconi between 1934 and 1959. Of note is the ST&C Coles 4038, designed by the BBC in 1954 and still used for some applications to this day, its historical uses varied from talks to symphony concerts, it is regarded as a delicate, fine traditional microphone. Around 2002 inexpensive ribbon microphones manufactured in China and inspired by the RCA-44 and older Soviet Oktava ribbon microphones became available. In 2007, microphones employing ribbon elements made of strong nanomaterials became available, offering orders of magnitude improvement in signal purity and output level; the ribbon microphone is an electrically simple design with no active circuitry.

The acoustic complexity of ribbon microphones is comparable to other types of air coupled transducers. Audio recording

Shutonia variabilis

Shutonia variabilis is a species of sea snail, a marine gastropod mollusk in the family Pseudomelatomidae, the turrids and allies. The length of the shell attains its diameter 6 mm; the elongately fusiform shell has a long siphonal canal. It is yellowish-white; the shell contains eight whorls, of which about 2 form a smooth inflated, reddish-brown protoconch. The subsequent whorls are subangular, concave in their upper part and separated by a conspicuous waved suture; the sculpture consists of a row of tubercles at the periphery, sharper in upper whorls, more obtuse lower on, a row of granules, just below the suture, becoming scarcely visible in last whorl and or nearly wanting in some specimens. The lower part of the whorls show one or two rather faint, spiral lirae; the part of the last whorl below the keel shows more or less conspicuous spirals, which vary from regular flat lirae to more irregular riblike ones. In the latter case two spirals are stronger. Moreover there are fine spiral striae and rather conspicuous growth-striae.

The aperture is angular above. The peristome is thin, with a wide sinus above protracted; the columellar margin is nearly straight, only concave above, ending in a rather long, narrow siphonal canal, covered with a thin layer of enamel. The interior of the aperture is smooth; this marine species occurs in the Andaman Sea and off Thailand. Schepman, M. 1913. P. 425. Tucker, J. K.. "Catalog of recent and fossil turrids". Zootaxa. 682: 1–1295. Shutonia variabilis

Bob Hodge (athlete)

Robert J. "Bob" Hodge is an American distance runner who came third in the 1979 Boston Marathon with a time of 2:12:30. He has won the Mount Washington Road Race, the Bay to Breakers Road Race in San Francisco, the Beppu-Ōita Marathon in Japan, his personal best time was his second-place finish at the 1980 Nike OTC Marathon in Eugene, OR at 2:10:59. He comes from Lowell, MA and graduated in 1990 from the University of Massachusetts Lowell after having left the university in the mid-1970s in order to focus on his athletic career, he knows Shane "The Train" Donahoe. Official Site of Bob Hodge


Konstantinos-Napoleon Tzortziou, better known by his in-game name FORG1VEN and Karaflas, is a Greek professional League of Legends player who most played AD carry for Schalke 04. FORG1VEN was considered to be among the best Western players of the AD Carry/Marksman role in League history, one of the most mechanically skilled players in the game, he has played for the Copenhagen Wolves, SK Gaming, Gambit Gaming, H2k-Gaming. In 2014, FORG1VEN missed playing in the 2014 Summer European League of Legends Championship Series after he was benched by his team, the Copenhagen Wolves, for "attitude problems". In spring 2015, FORG1VEN played for SK Gaming, the top European team for most of that season, he established several statistical records and was the MVP of the 2015 Spring EU LCS Split while a member of SK. However, after claims of mismanagement and worsening relations with teammates, he was replaced on the active roster in favour of Adrian "CandyPanda" Wübbelmann. FORG1VEN requested a transfer and subsequently left SK Gaming before the start of the 2015 Summer European LCS split and joined Gambit Gaming, becoming their star player.

His play for Gambit led them into a three-way tie for the last playoff spot. However, he was suspended by Riot Games for four competitive games in July 2015 for "toxic behavior" in public competitive play, receiving a harsher penalty because of an April 2014 incident in which he was fined for similar behaviour; the ban hurt Gambit Gaming, unable to secure visas for its preferred replacement enough and used Moopz as a replacement for their last two games of the regular season, both of which were losses. On August 24, 2015, Gambit Gaming decided to replaced FORG1VEN at AD Carry for the 2015 EU LCS Spring Promotion with Kristoffer "P1noy" Albao Lund Pedersen. Gambit Gaming subsequently sold its spot in the LCS to Team Vitality, FORG1VEN was received numerous offers from other LCS teams before settling on H2k-Gaming. On 25 February 2016, Tzortziou announced that he would miss the remainder of the 2016 Spring EU LCS split, for which H2k was in a tie for first, as well as the 2016 Summer EU LCS and the 2016 World Championship in order to fulfill Greek military service requirements.

However, after talks with the Greek government, on March 3 H2k announced that FORG1VEN had been given a temporary deferment from service. According to former H2k teammate Jankos though FORG1VEN was a skilled player with good mechanics, he took losses against teams with players he considered inferior such as Rekkles and negatively impacted the squad's teamwork by blaming his teammates. In April 2016, FORG1VEN left H2k, although his in-game play no longer fit the team, he maintained good relations with his former teammates and team management, he said that he would not play the upcoming summer split, planned to return in the 2017 Spring EU split. FORG1VEN joined Origen in May 2016 for that year's Summer EU LCS, but his individualistic, communication-heavy playstyle clashed with fellow star player Glenn "Hybrid" Doornenbal's team-oriented style, which led to poor results for Origen in the first week of competition. On June 7, FORG1VEN announced on his Facebook profile that he was planning to stop playing League of Legends because of a lack of motivation and a preference for playing Overwatch.

He characterized his experience with Origen management as a "breach of trust". On June 8, 2016 FORG1VEN was removed from the Origen active roster, inability to find a replacement for FORG1VEN prompted team owner and former player XPeke to step into his role. In July 2016, FORG1VEN returned to H2k-Gaming as a substitute player on their roster, he will be on the starting roster for the final week of the season due to Aleš "Freeze" Kněžínek's wrist injury. FORG1VEN played for H2k-Gaming at the 2016 League of Legends World Championship, was one of the top players at the tournament, his team was eliminated by Samsung Galaxy 3-0 in the semifinals. 4th — 2015 EU LCS Spring Playoffs 7–10th — 2015 Summer EU LCS 2nd - 2016 Spring EU LCS season 4th - 2016 Spring EU LCS playoffs 3rd-4th - 2016 League of Legends World Championship? - 2016 Summer EU LCS 1st - 2018 European Masters Spring Matchhistory

India at the 1968 Summer Olympics

India competed at the 1968 Summer Olympics in Mexico City, Mexico. 25 competitors, all men, took part in 11 events in 5 sports. Field hockey, Men's Team Competition. Team members: Ajit Pal Singh Balbir Singh I Balbir Singh II Balbir Singh III Gurbux Singh Harbinder Singh Harmik Singh Inam-ur Rehaman Inder Singh Krishnamurthy Perumal Munir Sait John Victor Peter Prithipal Singh Rajendra Absolem Christy Tarsem Singh Men's Hammer Throw Praveen KumarQualification Round — 60.84 Two shooters represented India in 1968. TrapKarni SinghQualification Round — 194Randhir SinghQualification Round — 192SkeetKarni SinghQualification Round — 187 Key: VT - Victory by Fall. Pt - Decision by Points. Os - Obvious Superiority. Men's FreestyleMen's Greco-Roman Official Olympic Reports International Olympic Committee results database