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In mathematics, the discriminant of the quadratic polynomial a x 2 + b x + c, a ≠ 0 is b 2 − 4 a c. It is zero if and only if the polynomial has a double root, is positive if and only if the polynomial has two real roots. More the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them. For a cubic polynomial with real coefficients, the discriminant is zero when two roots coincide, positive if the roots are three distinct real numbers, negative if there is one real root and two distinct complex conjugate roots. For a real polynomial of degree 4 or greater, the discriminant is zero if and only if it has a multiple root, positive if and only if the number of non-real roots is a multiple of 4; the discriminant is used in number theory, either directly or through its generalization as the discriminant of a number field. For factoring a polynomial with integer coefficients, the standard method consists in first factoring its reduction modulo a prime number not dividing the discriminant.

In algebraic geometry, the discriminant with respect to one of the variables characterizes the points of a hypersurface where the implicit function theorem does not apply. The term "discriminant" was coined in 1851 by the British mathematician James Joseph Sylvester. Let A = a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 be a polynomial of degree n, such that the coefficients a 0, …, a n belong to a field, or, more to a commutative ring; the resultant of A and its derivative A ′ = n a n x n − 1 + a n − 1 x n − 2 + ⋯ + a 1 is a polynomial in a 0, …, a n with integer coefficients, the determinant of the Sylvester matrix of A and A′. The nonzero entries of the first column of the Sylvester matrix are a n and n a n, the resultant is thus a multiple of a n. So, the discriminant, up to its sign, is defined as the quotient of the resultant of A and A' by a n: Disc x ⁡ = n / 2 a n Res x ⁡ Historically, this sign has been chosen such that, over the reals, the discriminant will be positive when all the roots of the polynomial are real.

The division by a n may be not well defined. Such a problem may be avoided by replacing a n by 1 in the first column of the Sylvester matrix before computing the determinant. In any case, the discriminant is a polynomial in a 0, …, a n with integer coefficients; when the polynomial is defined over a field, the fundamental theorem of algebra implies that it has n roots, r1, r2... rn, not all distinct, in an algebraically closed extension of the field. In terms of the roots, the discriminant is equal to Disc x ⁡ = a n 2 n − 2 ∏ i < j 2 = n / 2 a n 2 n − 2 ∏ i ≠ j


The genus Gloeophyllum is characterized by the production of leathery to corky tough, shaggy-topped, revivable fruitbodies lacking a stipe and with a lamellate to daedaleoid or poroid fertile hymenial surfaces. The hyphal system is dimitic to trimitic; the genus is further characterized by the production of a brown rot of wood. Phylogenetically, it along with several other brown rot Basidiomycota, Neolentinus and Veluticeps form an order called the Gloeophyllales; the most encountered species in the Northern Hemisphere is Gloeophyllum sepiarium, found in a dried state on both bark-covered and decorticated conifer stumps and logs, timbers on wharfs, planks on unpainted wooden buildings, wood bridges, creosoted railroad ties. The name Gloeophyllum combines "gloeo-" a reference to anything sticky, "-phyllum", a reference to the lamellae, it is a combined reference to the fact the lamellae in the type species, G. sepiarium, other original species, appeared to be stuck together forming anastomosing bridges, to the point of forming a daedaleoid pattern.

There is nothing sticky about the actual fungal fruitbodies. The name was spelled Gleophyllum but was soon changed and the current spelling is sanctioned. An extract of Gleophyllum odoratum exhibits high inhibitory activity on thrombin and trypsin as well as cysteine protease

Thespianz Theatre

Thespianz Theatre is a social performing arts organization established in 2005 in Pakistan staged more than 56 social theater, string puppetry and mime plays including education, gender inequality, women's rights drugs prevention, anti book piracy theatre and flash mobs, HIV Aids and water scarcity around the country. All are directed by the artistic director Faisal Malik and his associate director Nouman Mehmood. Who took the Thespianz Theatre troupe to 18 countries around the worldThespianz Theatre revived old dying art of string puppetry in Pakistan and staged Pakistan's biggest string puppetry festival with more than 300 performances in 79 areas of Karachi, Pakistan. In October 2016, the theatre organised the Pakistan String Puppetry Festival in Karachi; the festival lasted from October 2016 to January 2017. The festival endeavors to charm audiences, raise awareness and urges the rejection of extremism and violence

List of maze video games

Maze game is a video game genre description first used by journalists during the 1980s to describe any game in which the entire playing field is a maze. Quick player action is required to escape monsters, outrace an opponent, or navigate the maze within a time limit. After the release of Namco's Pac-Man in 1980, many maze games followed its conventions of completing a level by traversing all paths and a way of temporarily turning the tables on pursuers. In a top down maze game, the player can see more of the maze. In rare cases, the maze is viewed from the side rather than the top. Maze chase games are a specific subset of the top down perspective. They’re listed in a separate section; this subgenre is exemplified by Namco's Pac-Man, where the goal is to collect dots while avoiding enemies that are chasing the player. Pac-Man spawned many clones. In Japan, they are called "dot eat games". In grid capture games called line coloring games, the maze consists of lines, the goal is to capture rectangular areas by traversing their perimeters.

The gameplay is not fundamentally different than Pac-Man but enough games have used the grid motif that it is a distinct style. One unique element is that it is possible to capture multiple rectangles usually for extra points. Amidar established the model for this subgenre

Beppu Onsen

Beppu Onsen is a group of hot springs in the city of Beppu, Ōita in Japan. Beppu Onsen is divided into eight major hot spring areas known as "Beppu Hatto"; the most significant characteristic of Beppu's hot springs is the richness of its resources. The volume of water discharged is second only to that of the Yellowstone National Park in the United States. There are 2,909 hot spring vents within the city, these account for more than 10% of the 27,644 hot spring vents in Japan, according to a survey conducted by the Ministry of the Environment in 2004. Statistics from the Beppu City Hall show that more than 130,000 tons of hot spring water gushes from the ground every day; this is the second largest amount of hot spring water discharge in the world, the largest amount in Japan. According to Iyo-no-Kuni Topography written in the beginning of the 8th century, once in the age of the gods, Sukunabikona and Ōkuninushi visited Iyo-no-Kuni, now known as Ehime Prefecture. Sukunabikona fainted from illness.

With a deep sorrow Ōkuninushi placed a long pipe at the bottom of the sea all the way through from Dōgo Onsen to Beppu to supply therapeutic thermal waters for him to bathe, by the grace of which he was saved. Bungo Topography tells about Akayusen, it is reported that in the Kamakura period Ōtomo Yoriyasu established some sanatoria in Beppu and Hamawaki to cure samurai wounded in the war against the Mongolian Army. From the Meiji period onward Beppu Onsen made great progress with the boring technique of Kazusa, in which more than 1000 wells were completed by the end of Meiji. In the 1960s and 1970s, after World War Two, Beppu Onsen made rapid development with social stability and economical revival. From about 1919 to 1955, the amount of hot water taken rose to use the heat in agriculture and salt production, many problems happened; because of this, a new source of hot springs was searched and in 1957, a new layer of hot springs was found in 200m~300m below ground and was started for use. Since 1964 using hot springs for salt production has been banned, using them for agriculture and aqua farming of fish has continued for the moment.

Close to Beppu Station in the centre of town, Beppu Onsen is the most popular area. Ekimae-Kotō Onsen is a two-minute walk from the station and provides tired visitors and locals with invigoration and relaxation. Having the finest endowments of nature among the eight hot springs, this onsen site is located on a hill in the south-west urban area of Beppu. Bathers can enjoy medicinal hot spring waters along with spectacular scenery; this onsen area neighboring. Beppu Kaihin Sunayu is known for its open-air sand bathing found near Beppu City's seashore. Located along a mountain stream, Shibaseki Onsen is a picturesque, quiet onsen area much noted for its hot steam bath. With a nice woodland trail, it is designated as a national health onsen resort. With numerous jets of white steam emitting from gushing hot springs, this area is a must see destination for Beppu sightseers. Charming shops and Ryokan are tucked along the winding streets, it is known for steam baths. Myoban Onsen, on the hill facing Beppu Bay, is a quiet mountain resort.

Visitors enjoy several types of thermals such as mud bath or milky water bath accompanied by a distinctive sulphuric odor. Mineral deposits are worked at the thatched Yunohana-goya. Located west of Kankaiji Onsen area, Horita Onsen is a rustic hot-spring resort. Appreciated since the Edo Period, its soothing waters relieve the fatigue of a long journey; the waters of two public baths work on symptoms such as nerve pains. With quaint streets lined with old-fashioned inns and houses, Hamawaki Onsen is the birthplace of Beppu Onsen. Built in 1991, Yutopia Hamawaki, a multi-purpose health facility, is transforming the town's ancient flavour to a new, modern ambiance. Built in 1879, "Takegawara Onsen" is located a short 7 minutes walk from Beppu Station. A fine bamboo thatched roof and elaborate facade is a proud symbol of Beppu Onsen. Relaxing and fun are the sand baths, where attendants envelop appreciative guest's bodies in heaps of warm, soothing sand. A popular site in Kannawa Onsen mushi-yu steam bath has long served as a welcome facility for local citizens.

"Ashimushi", a rarity in the country, is effective in relieving fatigued lower limbs. "Sekisho" room is popular for its soothing aroma. Beppu travel guide from Wikivoyage Information about the hot spring "onsen" baths Site about the various baths in the town of Beppu List of onsen in Beppu Travel Itinerary for best experiencing Beppu Jigoku


Dahabshiil is an international funds transfer company headquartered in Dubai, United Arab Emirates. Formed in the early 1970s, the firm operates from over 24,000 outlets and employs more than 2,000 people across 126 countries, it provides financial services to international organisations, as well as to both large and small businesses and private individuals. The company is involved in numerous community building projects in Somaliland, it is the largest money-transfer business in Africa. Dahabshiil was founded in 1970 by Abdirashid Duale, a Somali entrepreneur based in Burao, the capital city of Togdheer province in the modern-day Somaliland. A general trading enterprise, the firm began specialising in remittance broking during the 1970s, when many Somali males from Somaliland migrated to the Gulf States for work; this resulted in a growing demand for services to transfer money from those migrant workers back to their families. Because of foreign exchange controls imposed by the Somali government at the time, most of the funds were transferred via a trade-based system known as Franco Valuta.

These transactions formed the bulk of Dahabshiil's business throughout the 1980s. With the Somali Civil War fast approaching, the Duale family were among the hundreds of thousands who retreated to the Somali-inhabited Ogaden region in neighbouring Ethiopia; the business in Somaliland collapsed, but Duale was able to draw on an extensive network of contacts in the Gulf to re-establish the venture, setting up a small office in Ethiopia to serve displaced Somali communities there and in Djibouti. In 1989, Dahabshiil opened its first office in London, where a number of Somalis had arrived during the war; the UK arm was managed by Mohammed Duale's son, Abdirashid Duale, who began to expand the business as the Somali population in the UK grew. Funds transfer services have become a large industry in Somaliland. Estimates of the aggregate value of remittances from the Somali diaspora back to the home country vary. However, a recent study by the United Nations Development Programme suggested a figure of around $1.6 billion, sent by emigrants in the US, Europe and the Gulf region.

Industry experts estimate that Dahabshiil handles around two-thirds of all remittances to Somali-speaking regions. Most of the Somali money transfer operators are credentialed members of either the Somali Money Transfer Association, an umbrella organisation that regulates the community's money transfer sector, or its predecessor, the Somali Financial Services Association. Besides Dahabshiil, Somali MTOs include Qaran Express, Amal Express, Kaah Express, Hodan Global, Amana Express, Iftin Express and Tawakal Express. A unique feature of these Somali funds transfer companies is that they all charge lower commission fees than their Western counterparts. For amounts greater than $1,000, Somali MTOs charge commissions of 3% to 4% lower than Western Union's 7.1% fee and MoneyGram's 7.2% fee for sending similar amounts to Ethiopia. Charges for the remittance of charity funding vary between 0% and 2%. Accounting for a quarter of household income in Somaliland, funds remitted by the Somali diaspora have helped to sustain communities in some of the most remote locations in the Horn of Africa.

With around 40% of households receiving such assistance from relatives working abroad, remittances have proved significant in promoting private sector activity in telecoms and housing, as well as in basic infrastructure and education. It has been argued that the inflow of such foreign-based capital has helped keep the Somali shilling afloat and offset depreciatory and inflationary pressures. Dahabshiil is the largest of the Somali money transfer operators, having captured most of the market vacated by Al-Barakaat; the firm has its headquarters in Dubai and employs more than 2,000 people across 144 countries, with 130 branches in Somalia, a further 130 branches in the United Kingdom, 400 branches globally. Its worldwide network comprises more than 24,000 agent and branch locations, the company offers both SMS notification and 24-hour online transfers. Remittance transfer remains Dahabshiil's core business, but the company has diversified to offer financial services to international organisations and private individuals.

Most of the major international development organisations operating in Somaliland use Dahabshiil to transfer funds, including the UN, WHO, World Bank, Save the Children and Care International. In 2008, Dahabshiil acquired a majority stake in Somtel, a Somaliland-based telecommunications firm specializing in high speed broadband, mobile internet, mobile phone services; the acquisition provided Dahabshiil with the necessary platform for a subsequent expansion into mobile banking, a growth industry in the regional banking sector. In early 2009, Dahabshiil opened Dahabshil Bank International, in Djibouti. An international bank, DBI provides services to business and private clients demanding Shariah-compliant financing. Operations centre on partnership finance and lease finance; that same year, Dahabshiil teamed up with leading Somali retailers, hotels and petrol stations to launch ‘Dahabshiil eCash’, Somaliland's first debit card service. Dahabshiil invests 5% of its annual profits in community projects aimed at improving schools, hospitals and sanitation services.

It sponsors a number of social events, including the Somali Week Festival and the So