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# Bluetongue disease **Bluetongue (BT) disease** is a noncontagious, arthropod-borne viral disease affecting ruminants, primarily sheep and other domestic or wild ruminants, including cattle, yaks, goats, buffalo, deer, dromedaries, and antelope. It is caused by Bluetongue virus (**BTV**), a non-enveloped, double-stra...
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# Bluetongue disease ## Microbiology Bluetongue is caused by the pathogenic vector-borne RNA virus, Bluetongue virus (BTV), of the genus *Orbivirus* within the *Sedoreoviridae* family. The virus particle consists of 10 strands of double-stranded RNA surrounded by two protein shells. Unlike other arboviruses, BTV lack...
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# Bluetongue disease ## Evolution The viral genome is replicated via structural protein VP1, an RNA-dependent RNA polymerase. The lack of proof-reading abilities results in high levels of transcription errors, resulting in single nucleotide mutations. Despite this, the BTV genome is quite stable, exhibiting a low rat...
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# Bluetongue disease ## Epidemiology The presence of the insect vectors determines the bluetongue disease\'s global distribution, with regions in Africa, Asia, Australia, Europe, North America, and other tropical/subtropical area being most affected. The virus persists in areas where climatic conditions support the ...
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# Bluetongue disease ## Treatment and prevention {#treatment_and_prevention} There are currently no antiviral medications that have been approved for the treatment of bluetongue disease. The standard of care involves the administration of anti-inflammatory drugs and supportive nursing care to alleviate the clinical s...
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# Bluetongue disease ## History In the early stages of its identification, BT was referred to by a number of different names, including \"epizootic catarrh,\" \"fever,\" \"malarial catarrhal fever of sheep,\" and \"epizootic malignant catarrhal fever of sheep.\" This was due to the prevailing belief at the time that ...
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# Bruce Perens **Bruce Perens** (born around 1958) is an American computer programmer and advocate in the free software movement. He created *The Open Source Definition* and published the first formal announcement and manifesto of open source. He co-founded the Open Source Initiative (OSI) with Eric S. Raymond. In 20...
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# Bruce Perens ## Career ### Computer graphics {#computer_graphics} Perens worked for seven years at the New York Institute of Technology Computer Graphics Lab. After that, he worked at Pixar for 12 years, from 1987 to 1999. He is credited as a studio tools engineer on the Pixar films *A Bug\'s Life* (1998) and *Toy...
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# Bruce Perens ## Career ### UserLinux In 2003 Perens created UserLinux, a Debian-based distribution whose stated goal was, \"Provide businesses with freely available, high quality Linux operating systems accompanied by certifications, service, and support options designed to encourage productivity and security while...
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# Bruce Perens ## Views Perens poses \"Open Source\" as a means of marketing the free and open-source software idea to business people and mainstream who might be more interested in the practical benefits of an open source development model and ecosystem than abstract ethics. He states that open source and free softw...
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# Bruce Perens ## Amateur radio and other activities {#amateur_radio_and_other_activities} Perens is an avid amateur radio enthusiast (call sign K6BP) and maintained technocrat.net, which he closed in late 2008, because its revenues did not cover its costs. ## Media appearances {#media_appearances} Perens is featur...
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# Bundle theory **Bundle theory**, originated by the 18th century Scottish philosopher David Hume, is the ontological theory about objecthood in which an object consists only of a collection (*bundle*) of properties, relations or tropes. According to bundle theory, an object consists of its properties and nothing mor...
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# Bundle theory ## Objections Bundle theory maintains that properties are *bundled* together in a collection without describing how they are tied together. For example, bundle theory regards an apple as red, 4 in wide, and juicy but lacking an underlying *substance*. The apple is said to be a *bundle of properties* i...
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# List of major biblical figures The Bible is a collection of canonical sacred texts of Judaism and Christianity. Different religious groups include different books within their canons, in different orders, and sometimes divide or combine books, or incorporate additional material into canonical books. Christian Bibles...
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# Basketball **Basketball** is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular court, compete with the primary objective of shooting a basketball (approximately 9.4 in in diameter) through the defender\'s hoop (a basket 18 in in diameter mounted 10 ft high to ...
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# Basketball ## History ### Early history {#early_history} A game similar to basketball is mentioned in a 1591 book published in Frankfurt am Main that reports on the lifestyles and customs of coastal North American residents, *Wahrhafftige Abconterfaytung der Wilden* (German; translates as *Truthful Depictions of t...
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# Basketball ## History ### College basketball {#college_basketball} Basketball\'s early adherents were dispatched to YMCAs throughout the United States, and it quickly spread through the United States and Canada. By 1895, it was well established at several women\'s high schools. While YMCA was responsible for initia...
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# Basketball ## History ### High school basketball {#high_school_basketball} Before widespread school district consolidation, most American high schools were far smaller than their present-day counterparts. During the first decades of the 20th century, basketball quickly became the ideal interscholastic sport due to ...
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# Basketball ## History ### Professional basketball {#professional_basketball} Teams abounded throughout the 1920s. There were hundreds of men\'s professional basketball teams in towns and cities all over the United States, and little organization of the professional game. Players jumped from team to team and teams p...
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# Basketball ## History ### International basketball {#international_basketball} FIBA (International Basketball Federation) was formed in 1932 by eight founding nations: Argentina, Czechoslovakia, Greece, Italy, Latvia, Portugal, Romania and Switzerland. At this time, the organization only oversaw amateur players. It...
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# Basketball ## History ### Women\'s basketball {#womens_basketball} upright=1.8\|thumb\|The Australian women\'s basketball team on winning the 2006 FIBA World Championship for Women Women began to play basketball in the fall of 1892 at Smith College through Senda Berenson, substitute director of the newly opened gy...
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# Basketball ## Rules and regulations {#rules_and_regulations} *Main article: Rules of basketball* Measurements and time limits discussed in this section often vary among tournaments and organizations; international and NBA rules are used in this section. The object of the game is to outscore one\'s opponents by th...
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# Basketball ## Rules and regulations {#rules_and_regulations} ### Equipment The only essential equipment in a basketball game is the ball and the court: a flat, rectangular surface with baskets at opposite ends. Competitive levels require the use of more equipment such as clocks, score sheets, scoreboards, alternati...
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# Basketball ## Rules and regulations {#rules_and_regulations} ### Violations The ball may be advanced toward the basket by being shot, passed between players, thrown, tapped, rolled or dribbled (bouncing the ball while running). The ball must stay within the court; the last team to touch the ball before it travels ...
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# Basketball ## Rules and regulations {#rules_and_regulations} ### Fouls *Main article: Personal foul (basketball), Technical foul* An attempt to unfairly disadvantage an opponent through certain types of physical contact is illegal and is called a personal foul. These are most commonly committed by defensive players...
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# Basketball ## Common techniques and practices {#common_techniques_and_practices} ### Positions thumb\|upright=1.15\|Basketball positions in the offensive zone Although the rules do not specify any positions whatsoever, they have evolved as part of basketball. During the early years of basketball\'s evolution, two ...
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# Basketball ## Common techniques and practices {#common_techniques_and_practices} ### Shooting Shooting is the act of attempting to score points by throwing the ball through the basket, methods varying with players and situations. Typically, a player faces the basket with both feet facing the basket. A player will ...
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# Basketball ## Common techniques and practices {#common_techniques_and_practices} ### Blocking A block is performed when, after a shot is attempted, a defender succeeds in altering the shot by touching the ball. In almost all variants of play, it is illegal to touch the ball after it is in the downward path of its a...
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# Basketball ## Height At the professional level, most male players are above 6 ft and most women above 5 ft. Guards, for whom physical coordination and ball-handling skills are crucial, tend to be the smallest players. Almost all forwards in the top men\'s pro leagues are 6 ft or taller. Most centers are over 6 ft t...
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# Basketball ## Variations and similar games {#variations_and_similar_games} Variations of basketball are activities based on the game of basketball, using common basketball skills and equipment (primarily the ball and basket). Some variations only have superficial rule changes, while others are distinct games with v...
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# Basketball ## Variations and similar games {#variations_and_similar_games} ### Other variations {#other_variations} Variations of basketball with their own page or subsection include: - **21** (also known as **American**, **cutthroat** and **roughhouse**) ```{=html} <!-- --> ``` - **42** - **Around the Worl...
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# Basketball ## Social forms of basketball {#social_forms_of_basketball} Basketball as a social and communal sport features environments, rules and demographics different from those seen in professional and televised basketball. ### Recreational basketball {#recreational_basketball} Basketball is played widely as a...
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# Basketball ## Fantasy basketball {#fantasy_basketball} **Fantasy basketball** was popularized during the 1990s by ESPN Fantasy Sports, NBA.com, and Yahoo! Fantasy Sports. On the model of fantasy baseball and football, players create fictional teams, select professional basketball players to \"play\" on these teams ...
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# Blowfish (cipher) **Blowfish** is a symmetric-key block cipher, designed in 1993 by Bruce Schneier and included in many cipher suites and encryption products. Blowfish provides a good encryption rate in software, and no effective cryptanalysis of it has been found to date for smaller files. It is recommended Blowfis...
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# Blowfish (cipher) ## Blowfish in pseudocode {#blowfish_in_pseudocode} `P[18]            // `*`P-array of 18 elements`*\ `S[4][256]        // `*`S-boxes: 4 arrays of 256 elements`*\ \ **`function`**` f(x):`\ `    // `*`Calculates a function f on a 32-bit input x, using S-boxes and bit manipulation`*\ `    high_byte ...
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# Blowfish (cipher) ## Blowfish in practice {#blowfish_in_practice} Blowfish is a fast block cipher, except when changing keys. Each new key requires the pre-processing equivalent of encrypting about 4 kilobytes of text, which is very slow compared to other block ciphers. This prevents its use in certain applications...
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# Bijection `{{Functions}}`{=mediawiki} In mathematics, a **bijection**, **bijective function**, or **one-to-one correspondence** is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a rel...
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# Bijection ## Examples ### Batting line-up of a baseball or cricket team {#batting_line_up_of_a_baseball_or_cricket_team} Consider the batting line-up of a baseball or cricket team (or any list of all the players of any sports team where every player holds a specific spot in a line-up). The set *X* will be the play...
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# Bijection ## More mathematical examples {#more_mathematical_examples} - For any set *X*, the identity function **1**~*X*~: *X* → *X*, **1**~*X*~(*x*) = *x* is bijective. - The function *f*: **R** → **R**, *f*(*x*) = 2*x* + 1 is bijective, since for each *y* there is a unique *x* = (*y* − 1)/2 such that *f*(*x*)...
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# Bijection ## Cardinality If *X* and *Y* are finite sets, then there exists a bijection between the two sets *X* and *Y* if and only if *X* and *Y* have the same number of elements. Indeed, in axiomatic set theory, this is taken as the definition of \"same number of elements\" (equinumerosity), and generalising this...
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# Binary function In mathematics, a **binary function** (also called **bivariate function**, or **function of two variables**) is a function that takes two inputs. Precisely stated, a function $f$ is binary if there exists sets $X, Y, Z$ such that $$\,f \colon X \times Y \rightarrow Z$$ where $X \times Y$ is the Car...
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# Binary function ## Category theory {#category_theory} In category theory, *n*-ary functions generalise to *n*-ary morphisms in a multicategory. The interpretation of an *n*-ary morphism as an ordinary morphisms whose domain is some sort of product of the domains of the original *n*-ary morphism will work in a monoi...
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# Binary operation In mathematics, a **binary operation** or **dyadic operation** is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a **binary operation** on a set is a binary function that maps every p...
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# Binary operation ## Properties and examples {#properties_and_examples} Typical examples of binary operations are the addition ($+$) and multiplication ($\times$) of numbers and matrices as well as composition of functions on a single set. For instance, - On the set of real numbers $\mathbb R$, $f(a,b)=a+b$ is a ...
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# Binary operation ## Other binary operations {#other_binary_operations} For example, scalar multiplication in linear algebra. Here $K$ is a field and $S$ is a vector space over that field. Also the dot product of two vectors maps $S \times S$ to $K$, where $K$ is a field and $S$ is a vector space over $K$. It depen...
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# Bedrock Records **Bedrock Records** is an English record label for trance, progressive house and techno started by John Digweed. Its name comes from a long running and successful club night held in Hastings and also at Heaven nightclub, London -- both also called Bedrock. Bedrock Records has released many singles fr...
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# Boolean algebra (structure) In abstract algebra, a **Boolean algebra** or **Boolean lattice** is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or...
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# Boolean algebra (structure) ## Definition A **Boolean algebra** is a set `{{math|1=''A''}}`{=mediawiki}, equipped with two binary operations `{{math|1=∧}}`{=mediawiki} (called \"meet\" or \"and\"), `{{math|1=∨}}`{=mediawiki} (called \"join\" or \"or\"), a unary operation `{{math|1=¬}}`{=mediawiki} (called \"complem...
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# Boolean algebra (structure) ## Examples - The simplest non-trivial Boolean algebra, the two-element Boolean algebra, has only two elements, `{{math|0}}`{=mediawiki} and `{{math|1}}`{=mediawiki}, and is defined by the rules: +---+------------+---+---+------------+---+---+------------+ | | -- -- -- | | | ...
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# Boolean algebra (structure) ## Boolean rings {#boolean_rings} Every Boolean algebra `{{math|1=(''A'', ∧, ∨)}}`{=mediawiki} gives rise to a ring `{{math|(''A'', +, ·)}}`{=mediawiki} by defining `{{math|1=''a'' + ''b'' := (''a'' ∧ ¬''b'') ∨ (''b'' ∧ ¬''a'') = (''a'' ∨ ''b'') ∧ ¬(''a'' ∧ ''b'')}}`{=mediawiki} (this op...
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# Boolean algebra (structure) ## Ideals and filters {#ideals_and_filters} An *ideal* of the Boolean algebra `{{mvar|A}}`{=mediawiki} is a nonempty subset `{{mvar|I}}`{=mediawiki} such that for all `{{mvar|x}}`{=mediawiki}, `{{mvar|y}}`{=mediawiki} in `{{mvar|I}}`{=mediawiki} we have `{{math|{{var|x}} ∨ {{var|y}}}}`{=...
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# Boolean algebra (structure) ## Axiomatics +-----------------------------------------------------------------------------------------------------+ | **Proven properties** | +=================================================================...
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# Boolean algebra (structure) ## Axiomatics The first axiomatization of Boolean lattices/algebras in general was given by the English philosopher and mathematician Alfred North Whitehead in 1898. It included the above axioms and additionally `{{math|1=''x'' ∨ 1 = 1}}`{=mediawiki} and `{{math|1=''x'' ∧ 0 = 0}}`{=media...
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# Bill Joy vi{{•}}csh{{•}}chroot{{•}}TCP/IP driver{{•}}co-founder of Sun Microsystems{{•}}Java{{•}}SPARC{{•}}Solaris{{•}}NFS{{•}}*Why The Future Doesn\'t Need Us* \| author_abbrev_bot = \| author_abbrev_zoo = \| influences = \| influenced = \| spouse = \| children = 2 \| awards = \*ACM Grace Murray Hopper Award (1986)...
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# Bill Joy ## Technology concerns {#technology_concerns} In 2000, Joy gained notoriety with the publication of his article in *Wired* magazine, \"Why The Future Doesn\'t Need Us\", in which he declared, in what some have described as a \"neo-Luddite\" position, that he was convinced that growing advances in genetic e...
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# Bandwidth (signal processing) **Bandwidth** is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in unit of hertz (symbol Hz). It may refer more specifically to two subcategories: *Passband bandwidth* is the difference between the upper and lower cu...
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# Bandwidth (signal processing) ## *x* dB bandwidth {#x_db_bandwidth} In some contexts, the signal bandwidth in hertz refers to the frequency range in which the signal\'s spectral density (in W/Hz or V^2^/Hz) is nonzero or above a small threshold value. The threshold value is often defined relative to the maximum val...
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# Bandwidth (signal processing) ## Relative bandwidth {#relative_bandwidth} The absolute bandwidth is not always the most appropriate or useful measure of bandwidth. For instance, in the field of antennas the difficulty of constructing an antenna to meet a specified absolute bandwidth is easier at a higher frequency ...
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# Bandwidth (signal processing) ## Noise equivalent bandwidth {#noise_equivalent_bandwidth} Further information: Spectral leakage#Noise bandwidth The **noise equivalent bandwidth** (or **equivalent noise bandwidth (enbw)**) of a system of frequency response $H(f)$ is the bandwidth of an ideal filter with rectangular...
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# Bernie Federko **Bernard Allan Federko** (born May 12, 1956) is a Canadian former professional ice hockey centre who played fourteen seasons in the National Hockey League from 1976 through 1990. ## Playing career {#playing_career} Federko began playing hockey at a young age in his home town of Foam Lake, Saskatche...
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# Bernie Federko ## Awards - Bob Brownridge Memorial Trophy (WCHL leading scorer) - 1976 - Named to the WCHL First All-Star Team (1976) - Named WCHL MVP (1976) - Named to the CHL Second All-Star Team (1977) - Won Ken McKenzie Trophy as CHL Rookie of the Year (1977) - Played in the NHL All-Star Game (1980,...
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# Contract bridge *Pandoc failed*: ``` Error at (line 83, column 2): unexpected '+' |+ {{center|'''Example auction'''}} ^ ``
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# Basel Convention The **Basel Convention on the Control of Transboundary Movements of Hazardous Wastes and Their Disposal**, usually known as the **Basel Convention**, is an international treaty that was designed to reduce the movements of hazardous waste between nations, and specifically to restrict the transfer of ...
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# Basel Convention ## History With the tightening of environmental laws (for example, RCRA) in developed nations in the 1970s, disposal costs for hazardous waste rose dramatically. At the same time, the globalization of shipping made cross-border movement of waste easier, and many less developed countries were desper...
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# Basel Convention ## Obligations In addition to conditions on the import and export of the above wastes, there are stringent requirements for notice, consent and tracking for movement of wastes across national boundaries. The convention places a general prohibition on the exportation or importation of wastes between...
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# Basel Convention ## Basel Ban Amendment {#basel_ban_amendment} After the initial adoption of the convention, some least developed countries and environmental organizations argued that it did not go far enough. Many nations and NGOs argued for a total ban on shipment of all hazardous waste to developing countries. I...
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# Basel Convention ## Regulation of plastic waste {#regulation_of_plastic_waste} In the wake of popular outcry, in May 2019 most of the world\'s countries, but not the United States, agreed to amend the Basel Convention to include plastic waste as a regulated material. The world\'s oceans are estimated to contain 100...
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# Basel Convention ## Basel watchdog {#basel_watchdog} The Basel Action Network (BAN) is a charitable civil society non-governmental organization that works as a consumer watchdog for implementation of the Basel Convention. BAN\'s principal aims is fighting exportation of toxic waste, including plastic waste, from in...
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# Bar Kokhba (album) ***Bar Kokhba*** is a double album by John Zorn, recorded between 1994 and 1996. It features music from Zorn\'s *Masada* project, rearranged for small ensembles. It also features the original soundtrack from *[The Art of Remembrance -- Simon Wiesenthal](http://riverlightspictures.com/taor/index.ht...
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# Brian Kernighan \| birth_place = Toronto, Ontario, Canada \| residence = \| citizenship = Canada \| nationality = Canadian \| field = Computer science \| work_institution = Princeton University \| alma_mater = University of Toronto (BASc)\ Princeton University (PhD) \| thesis_title = Some Graph Partitioning Problems...
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# Brian Kernighan ## Career and research {#career_and_research} Kernighan has held a professorship in the department of computer science at Princeton since 2000. Each fall he teaches a course called \"Computers in Our World\", which introduces the fundamentals of computing to non-majors. Kernighan was the software e...
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# Battlecruiser upright=1.5\|thumb\|right\|`{{HMS|Hood}}`{=mediawiki}, the largest battlecruiser ever built, in Australia on 17 March 1924 The **battlecruiser** (also written as **battle cruiser** or **battle-cruiser**) was a type of capital ship of the first half of the 20th century. These were similar in displaceme...
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# Battlecruiser ## Background The battlecruiser was developed by the Royal Navy in the first years of the 20th century as an evolution of the armoured cruiser. The first armoured cruisers had been built in the 1870s, as an attempt to give armour protection to ships fulfilling the typical cruiser roles of patrol, trad...
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# Battlecruiser ## First battlecruisers {#first_battlecruisers} Under the Selborne plan of 1903,`{{Ambiguous|date=April 2025}}`{=mediawiki} the Royal Navy intended to start three new battleships and four armoured cruisers each year. However, in late 1904 it became clear that the 1905--1906 programme would have to be ...
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# Battlecruiser ## Battlecruisers in the dreadnought arms race {#battlecruisers_in_the_dreadnought_arms_race} Between the launching of the *Invincible*s to just after the outbreak of the First World War, the battlecruiser played a junior role in the developing dreadnought arms race, as it was never wholeheartedly ado...
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# Battlecruiser ## World War I {#world_war_i} ### Construction For most of the combatants, capital ship construction was very limited during the war. Germany finished the *Derfflinger* class and began work on the `{{sclass|Mackensen|battlecruiser|4}}`{=mediawiki}. The *Mackensen*s were a development of the *Derfflin...
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# Battlecruiser ## World War I {#world_war_i} ### Battlecruisers in action {#battlecruisers_in_action} The first combat involving battlecruisers during World War I was the Battle of Heligoland Bight in August 1914. A force of British light cruisers and destroyers entered the Heligoland Bight (the part of the North Se...
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# Battlecruiser ## Interwar period {#interwar_period} In the years immediately after World War I, Britain, Japan and the US all began design work on a new generation of ever more powerful battleships and battlecruisers. The new burst of shipbuilding that each nation\'s navy desired was politically controversial and p...
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# Battlecruiser ## Interwar period {#interwar_period} ### Rebuilding programmes {#rebuilding_programmes} In total, nine battlecruisers survived the Washington Naval Treaty, although HMS *Tiger* later became a victim of the London Naval Conference 1930 and was scrapped. Because their high speed made them valuable surf...
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# Battlecruiser ## World War II {#world_war_ii} The Royal Navy deployed some of its battlecruisers during the Norwegian Campaign in April 1940. The `{{ship|German battleship|Gneisenau||2}}`{=mediawiki} and the `{{ship|German battleship|Scharnhorst||2}}`{=mediawiki} were engaged during the action off Lofoten by *Renow...
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# Battlecruiser ## World War II {#world_war_ii} ### Large cruisers or \"cruiser killers\" {#large_cruisers_or_cruiser_killers} A late renaissance in popularity of ships between battleships and cruisers in size occurred on the eve of World War II. Described by some as battlecruisers, but never classified as capital sh...
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# Battlecruiser ## Cold War--era designs {#cold_warera_designs} In spite of the fact that most navies abandoned the battleship and battlecruiser concepts after World War II, Joseph Stalin\'s fondness for big-gun-armed warships caused the Soviet Union to plan a large cruiser class in the late 1940s. In the Soviet Navy...
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# Battlecruiser ## Operators - operates one `{{sclass|Kirov|battlecruiser|2}}`{=mediawiki} with one more being overhauled. ### Former operators {#former_operators} - five surviving battlecruisers were all scuttled at Scapa Flow in 1919. - decommissioned its only battlecruiser HMAS *Australia* in 1921. - w...
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# Baldr **Baldr** (Old Norse also **Balder**, **Baldur**) is a god in Germanic mythology. In Norse mythology, he is a son of the god Odin and the goddess Frigg, and has numerous brothers, such as Thor and Váli. In wider Germanic mythology, the god was known in Old English as ***Bældæġ***, and in Old High German as ***...
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# Baldr ## Attestations ### Merseburg Incantation {#merseburg_incantation} One of the two Merseburg Incantations names *Balder* (in the genitive singular *Balderes*), but also mentions a figure named *Phol*, considered to be a byname for Baldr (as in Scandinavian *Falr*, *Fjalarr*; (in Saxo) *Balderus* : *Fjallerus*...
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# Baldr ## Attestations ### *Prose Edda* {#prose_edda} In *Gylfaginning*, Baldr is described as follows: Apart from this description, Baldr is known primarily for the story of his death, which is seen as the first in a chain of events that will ultimately lead to the destruction of the gods at Ragnarök. Baldr had a...
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# Baldr ## Attestations ### *Gesta Danorum* {#gesta_danorum} Writing during the end of the 12th century, the Danish historian Saxo Grammaticus tells the story of Baldr (recorded as *Balderus*) in a form that professes to be historical. According to him, Balderus and Høtherus were rival suitors for the hand of Nanna, ...
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# Breidablik `{{About|the location in Nordic mythology|other uses|Breiðablik (disambiguation){{!}}`{=mediawiki}Breiðablik}} **Breiðablik** (sometimes anglicised as **Breithablik** or **Breidablik**) is the home of Baldr in Nordic mythology. ## Meaning The word *Breiðablik* has been variously translated as \'broad sh...
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# Bilskirnir **Bilskirnir** (Old Norse \"lightning-crack\") is the hall of the god Thor in Norse mythology. Here he lives with his wife Sif and their children. According to *Grímnismál*, the hall is the greatest of buildings and contains 540 rooms, located in Asgard, as are all the dwellings of the gods, in the kingdo...
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# Brísingamen In Norse mythology, ***Brísingamen**\'\' (or***Brísinga men**\'\') is the torc or necklace of the goddess Freyja, of which little else is known for certain. ## Etymology The name is an Old Norse compound *brísinga-men* whose second element is *men* \"(ornamental) neck-ring (of precious metal), torc\".`...
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# Brísingamen ## Modern influence {#modern_influence} Alan Garner wrote a children\'s fantasy novel called *The Weirdstone of Brisingamen*, published in 1960, about an enchanted teardrop bracelet. Diana Paxson\'s novel *Brisingamen* features Freyja and her necklace. Black Phoenix Alchemy Lab has a perfumed oil scen...
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# Borsuk–Ulam theorem In mathematics, the **Borsuk--Ulam theorem** states that every continuous function from an *n*-sphere into Euclidean *n*-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere\'s cent...
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# Borsuk–Ulam theorem ## Proofs ### 1-dimensional case {#dimensional_case} The 1-dimensional case can easily be proved using the intermediate value theorem (IVT). Let $g$ be the odd real-valued continuous function on a circle defined by $g(x)=f(x)-f(-x)$. Pick an arbitrary $x$. If $g(x)=0$ then we are done. Otherwi...
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# Borsuk–Ulam theorem ## Equivalent results {#equivalent_results} Above we showed how to prove the Borsuk--Ulam theorem from Tucker\'s lemma. The converse is also true: it is possible to prove Tucker\'s lemma from the Borsuk--Ulam theorem. Therefore, these two theorems are equivalent. `{{Analogous fixed-point theorem...
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# Bragi **Bragi** (Old Norse) is the skaldic god of poetry in Norse mythology. ## Etymology The theonym Bragi probably stems from the masculine noun *bragr*, which can be translated in Old Norse as \'poetry\' (cf. Icelandic *bragur* \'poem, melody, wise\') or as \'the first, noblest\' (cf. poetic Old Norse *bragnar*...
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# Bragi ## Skalds named Bragi {#skalds_named_bragi} ### Bragi Boddason {#bragi_boddason} In the *Prose Edda* Snorri Sturluson quotes many stanzas attributed to **Bragi Boddason** the old (*Bragi Boddason inn gamli*), a Norwegian court poet who served several Swedish kings, Ragnar Lodbrok, Östen Beli and Björn at Hau...
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# Bragi ## In popular culture {#in_popular_culture} In the 2002 Ensemble Studios game *Age of Mythology*, Bragi is one of nine minor gods Norse players can worship
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# Bronski Beat *Pandoc failed*: ``` Error at (line 216, column 1): unexpected end of input ``
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# BPP (complexity) In computational complexity theory, a branch of computer science, **bounded-error probabilistic polynomial time** (**BPP**) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded by 1/3 for all instances. **BPP** is one of th...
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# BPP (complexity) ## Related classes {#related_classes} If the access to randomness is removed from the definition of **BPP**, we get the complexity class **P**. In the definition of the class, if we replace the ordinary Turing machine with a quantum computer, we get the class **BQP**. Adding postselection to **BPP...
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