Z (named zed /zɛd/ or zee /ziː/^{[1]}) is the 26th and final letter of the modern English alphabet and the ISO basic Latin alphabet.
Z | |
---|---|
Z z | |
(See below, Typography) | |
Usage | |
Writing system | Latin script |
Type | Alphabetic and Logographic |
Language of origin | Latin language |
Phonetic usage | [z] [ʒ] [t͡s] [d͡z] [ð] [θ] [s] [ʃ] /zɛd/ /ziː/ |
Unicode value | U+005A, U+007A |
Alphabetical position | 26 |
History | |
Development | |
Time period | ~-700 to present |
Descendants | • ʒ • Ƹ • Ƶ • Ž • Ż • 𐌶 • ℤ • Ꮓ |
Variations | (See below, Typography) |
Other | |
Other letters commonly used with | z(x), cz, dž, dz, sz, dzs, tzsch |
In most English-speaking countries, including the United Kingdom, Canada, India, Ireland, New Zealand, Zambia, and Australia, the letter's name is zed /zɛd/, reflecting its derivation from the Greek zeta (this dates to Latin, which borrowed X, Y, and Z from Greek, along with their names), but in American English its name is zee /ziː/, analogous to the names for B, C, D, etc., and deriving from a late 17th-century English dialectal form.^{[2]}
Another English dialectal form is izzard /ˈɪzərd/. This dates from the mid-18th century and probably derives from Occitan izèda or the French ézed, whose reconstructed Latin form would be *idzēta,^{[1]} perhaps a Vulgar Latin form with a prosthetic vowel. Its variants are still used in Hong Kong English although they are usually seen as mispronunciations.^{[3]}
Other languages spell the letter's name in a similar way: zeta in Italian, Basque, Spanish, and Icelandic (no longer part of its alphabet but found in personal names), zê in Portuguese, zäta in Swedish, zæt in Danish, zet in Dutch, Indonesian, Polish, Romanian, and Czech, Zett in German (capitalised as a noun), zett in Norwegian, zède in French, and zét in Vietnamese. Several languages render it as /ts/ or /dz/, e.g. zeta /tsetɑ/ or /tset/ in Finnish. In Standard Chinese pinyin, the name of the letter Z is pronounced [tsɨ], as in "zi", although the English zed and zee have become very common. In Esperanto, the name of the letter Z is pronounced /zo/.
Phoenician Zayin |
Etruscan Z |
Greek Zeta |
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The Semitic symbol was the seventh letter, named zayin, which meant "weapon" or "sword". It represented either the sound /z/ as in English and French, or possibly more like /dz/ (as in Italian zeta, zero).
The Greek form of Z was a close copy of the Phoenician Zayin (), and the Greek inscriptional form remained in this shape throughout ancient times. The Greeks called it zeta, a new name made in imitation of eta (η) and theta (θ).
In earlier Greek of Athens and Northwest Greece, the letter seems to have represented /dz/; in Attic, from the 4th century BC onwards, it seems to have stood for /zd/ and /dz/ – there is no consensus concerning this issue.^{[4]} In other dialects, such as Elean and Cretan, the symbol seems to have been used for sounds resembling the English voiced and voiceless th (IPA /ð/ and /θ/, respectively). In the common dialect (koine) that succeeded the older dialects, ζ became /z/, as it remains in modern Greek.
The Etruscan letter Z was derived from the Phoenician alphabet, most probably through the Greek alphabet used on the island of Ischia. In Etruscan, this letter may have represented /ts/.
The letter z was part of the earliest form of the Latin alphabet, adopted from Etruscan. Because the sound /z/ in Latin changed to /r/ by rhotacism in the fifth century BC, z was dropped and its place given to the new letter g. In the 1st century BC, z was reintroduced at the end of the Latin alphabet to represent the sound of the Greek zeta /dz/, as the letter y was introduced to represent the sound of the Greek upsilon /y/.^{[5]}
Before the reintroduction of z, the sound of zeta was written s at the beginning of words and ss in the middle of words, as in sōna for ζώνη "belt" and trapessita for τραπεζίτης "banker".
In some inscriptions, z represented a Vulgar Latin sound, likely an affricate, formed by the merging of the reflexes of Classical Latin /j/, /dj/ and /gj/: for example, zanuariu for ianuariu "January", ziaconus for diaconus "deacon", and oze for hodie "today".^{[6]} Likewise, /di/ sometimes replaced /z/ in words like baptidiare for baptizare "to baptize". In modern Italian, z represents /ts/ or /dz/, whereas the reflexes of ianuarius and hodie are written with the letter g (representing /dʒ/ when before i and e): gennaio, oggi. In other languages, such as Spanish, further evolution of the sound occurred.
Early English used S alone for both the unvoiced and the voiced sibilant. The Latin sound imported through French was new and was not written with Z but with G or I. The successive changes can be well seen in the double forms from the same original, jealous and zealous. Both of these come from a late Latin zelosus, derived from the imported Greek ζῆλος zêlos. The earlier form is jealous; its initial sound is the [dʒ], which developed to Modern French [ʒ]. John Wycliffe wrote the word as gelows or ielous.
Z at the end of a word was pronounced ts, as in English assets, from Old French asez "enough" (Modern French assez), from Vulgar Latin ad satis ("to sufficiency").^{[7]}
In earlier times, the English alphabets used by children terminated not with Z but with & or related typographic symbols.^{[8]} In her 1859 novel Adam Bede, George Eliot refers to Z being followed by & when her character Jacob Storey says, "He thought it [Z] had only been put to finish off th' alphabet like; though ampusand would ha' done as well, for what he could see."^{[9]}
Some Latin based alphabets have extra letters on the end of the alphabet. The last letter for the Icelandic, Finnish and Swedish alphabets is Ö, while it is Å for Danish and Norwegian. In the German alphabet, the umlauts (Ä/ä, Ö/ö, and Ü/ü) and the letter ß (Eszett or scharfes S) are regarded respectively as modifications of the vowels a/o/u and as a (standardized) variant spelling of ss, not as independent letters, so they come after the unmodified letters in the alphabetical order. The German alphabet ends with z.
A glyph variant of Z originating in the medieval Gothic minuscules and the Early Modern Blackletter typefaces is the "tailed z" (German geschwänztes Z, also Z mit Unterschlinge). In some Antiqua typefaces, this letter is present as a standalone letter or in ligatures. Ligated with long s (ſ), it is part of the origin of the Eszett (ß) in the German alphabet. The character ezh (Ʒ) resembles a tailed z, as does the yogh (ȝ), with which it came to be indistinguishable in Middle English writing.
Unicode assigns codepoints U+2128 ℨ BLACK-LETTER CAPITAL Z (HTML ℨ
) and U+1D537 𝔷 MATHEMATICAL FRAKTUR SMALL Z (HTML 𝔷
) in the Letterlike Symbols and Mathematical alphanumeric symbols ranges respectively.
There is also a variant with a stroke.
In modern English orthography, the letter ⟨z⟩ usually represents the sound /z/.
It represents /ʒ/ in words like seizure. More often, this sound appears as ⟨su⟩ or ⟨si⟩ in words such as measure, decision, etc. In all these words, /ʒ/ developed from earlier /zj/ by yod-coalescence.
Few words in the Basic English vocabulary begin with ⟨z⟩, though it occurs in words beginning with other letters. It is the least frequently used letter in written English.^{[10]} It is more common in American English than in British English, due to the endings -ize vs -ise and -ization vs -isation, where the American spelling is derived from Greek and the British from French. ⟨z⟩ is more common in the Oxford spelling of British English, as this variant prefers the more etymologically 'correct' -ize endings to -ise endings; however, -yse is preferred over -yze in Oxford spelling, as it is closer to the original Greek roots of words like analyse. One native Germanic English word that contains 'z', freeze (past froze, participle frozen) came to be spelled that way by convention, even though it could have been spelled with 's' (as with choose, chose and chosen).
⟨z⟩ is used in writing to represent the act of sleeping (sometimes using multiple z's like zzzz). It is used because closed-mouth human snoring often sounds like the pronunciation of this letter.
⟨z⟩ stands for a voiced alveolar or voiced dental sibilant /z/, in Albanian, Breton, Czech, Dutch, French, Hungarian, Latvian, Lithuanian, Romanian, Serbo-Croatian, Slovak, and the International Phonetic Alphabet. It stands for /t͡s/ in Chinese pinyin, Finnish (occurs in loanwords only), and German, and it likewise expressed /ts/ in Old Norse. In Italian, it represents two phonemes, /t͡s/ and /d͡z/. Castilian Spanish uses the letter to represent /θ/ (as English ⟨th⟩ in thing), though in other dialects (Latin American, Andalusian) this sound has merged with /s/. In Portuguese, it stands for /z/ in most cases, but also for /s/ or /ʃ/ (depending on the regional variant) at the end of syllables. In Basque, it represents the sound /s/.
In Danish, Norwegian, and Swedish, ⟨z⟩ usually stands for the sound /s/ and thus shares the value of ⟨s⟩; it normally occurs only in loanwords that are spelt with ⟨z⟩ in the source languages.
The letter ⟨z⟩ on its own represents /z/ in Polish. It is also used in four of the seven officially recognized digraphs: ⟨cz⟩ (/t͡ʂ/), ⟨dz⟩ (/d͡z/ or /t͡s/), ⟨rz⟩ (/ʐ/ or /ʂ/, sometimes it represents a sequence /rz/) and ⟨sz⟩ (/ʂ/), and is the most frequently used of the consonants in that language. (Other Slavic languages avoid digraphs and mark the corresponding phonemes with the háček (caron) accent: ⟨č⟩, ⟨ď⟩, ⟨ř⟩, ⟨š⟩; this system has its origin in Czech orthography of the Hussite period.) Two more Polish digraphs include ⟨z⟩ with diacritical marks, as accent and dot: ⟨dź⟩ (/d͡ʑ/ or /t͡ɕ/) and ⟨dż⟩ (/d͡ʐ/ or /t͡ʂ/). ⟨z⟩ can also appear alone with diacritical marks, namely ⟨ź⟩ or ⟨ż⟩. Similarly, Hungarian uses ⟨z⟩ in the digraphs ⟨sz⟩ (expressing /s/, as opposed to the value of ⟨s⟩, which is ʃ), and ⟨zs⟩ (expressing ʒ).
Among non-European languages that have adopted the Latin alphabet, ⟨z⟩ usually stands for [z], such as in Azerbaijani, Igbo, Indonesian, Shona, Swahili, Tatar, Turkish, and Zulu. ⟨z⟩ represents [d͡z] in Northern Sami and Inari Sami. In Turkmen, ⟨z⟩ represents [ð].
In the Kunrei-shiki and Hepburn romanisations of Japanese, ⟨z⟩ stands for a phoneme whose allophones include [z] and [dz].
A graphical variant of ⟨z⟩ is ⟨ʒ⟩, which has been adopted into the International Phonetic Alphabet as the sign for the voiced postalveolar fricative.
In mathematics, U+2124 ℤ (DOUBLE-STRUCK CAPITAL Z) is used to denote the set of integers. Originally, ℤ was just a handwritten version of the bold capital Z used in printing but, over time, it has come to be used more frequently in printed works too.
In chemistry, the letter Z is used to denote the Atomic number of an element (number of protons), such as Z=3 for Lithium.
Character | Z | z | ||
---|---|---|---|---|
Unicode name | LATIN CAPITAL LETTER Z | LATIN SMALL LETTER Z | ||
Encodings | decimal | hex | decimal | hex |
Unicode | 90 | U+005A | 122 | U+007A |
UTF-8 | 90 | 5A | 122 | 7A |
Numeric character reference | Z | Z | z | z |
EBCDIC family | 233 | E9 | 169 | A9 |
ASCII ^{1} | 90 | 5A | 122 | 7A |
On German typewriter- and computer keyboards (in comparison to those used in the UK/US), the positions of the letters Z and Y are swapped. (In German, Y is only used in loanwords and names.)
NATO phonetic | Morse code |
Zulu |
Signal flag | Flag semaphore | American manual alphabet (ASL fingerspelling) | Braille dots-1356 |
Zee Za-cha-ry, Zion, zeal
The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of an atom. It is identical to the charge number of the nucleus. The atomic number uniquely identifies a chemical element. In an uncharged atom, the atomic number is also equal to the number of electrons.
The sum of the atomic number Z and the number of neutrons, N, gives the mass number A of an atom. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number A.
Atoms with the same atomic number Z but different neutron numbers N, and hence different atomic masses, are known as isotopes. A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth, determines the element's standard atomic weight. Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.
The conventional symbol Z comes from the German word Zahl meaning number, which, before the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order is approximately, but not completely, consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge and a physical characteristic of atoms, did the word Atomzahl (and its English equivalent atomic number) come into common use in this context.
BeyoncéBeyoncé Giselle Knowles-Carter (; born September 4, 1981) is an American singer-songwriter. Born and raised in Houston, Texas, Beyoncé performed in various singing and dancing competitions as a child. She rose to fame in the late 1990s as lead singer of the R&B girl-group Destiny's Child. Managed by her father, Mathew Knowles, the group became one of the best-selling girl groups in history. Their hiatus saw Beyoncé's theatrical film debut in Austin Powers in Goldmember (2002), and the release of her first solo album, Dangerously in Love (2003). The album established her as a solo artist worldwide, debuting at number one on the US Billboard 200 chart and earned her five Grammy Awards. The album also featured the Billboard Hot 100 number-one singles, "Crazy in Love" and "Baby Boy".
Following the break-up of Destiny's Child in 2006, she had released her second solo album, B'Day, which contained her fourth number-one single, "Irreplaceable", as well as the top ten singles, "Déjà Vu", and "Beautiful Liar". Beyoncé also continued her acting career, with starring roles in The Pink Panther (2006), Dreamgirls (2006), and Obsessed (2009). Her marriage to rapper Jay-Z and her portrayal of Etta James in Cadillac Records (2008), influenced her third album, I Am... Sasha Fierce (2008), which saw the introduction of her alter-ego, Sasha Fierce and earned a record-setting six Grammy Awards in 2010, including Song of the Year for "Single Ladies (Put a Ring on It)". Beyoncé took a hiatus from music in 2010 and took over management of her career; her fourth album, 4 (2011), was subsequently mellower in tone, exploring 1970s funk, 1980s pop, and 1990s soul. Her critically acclaimed eponymous album, released in 2013 with no prior announcement, was distinguished from previous releases by its experimental production and exploration of darker themes. Her sixth album, Lemonade (2016), also received widespread critical acclaim, with many referring to it as her most personal and political work to date, and subsequently became the best-selling album of 2016. In 2018, she released Everything Is Love, a collaborative album with her husband Jay-Z, as The Carters.
Throughout her career, Beyoncé has sold over 100 million records worldwide as a solo artist,and is still selling. With further 60 million records with Destiny's Child, making her one of the best-selling music artists of all time. She is a multi-platinum, Grammy-Award-winning recording artist, who is acclaimed for her thrilling vocals, videos, and live concert shows. The Recording Industry Association of America recognized Beyoncé as the Top Certified Artist in America during the 2000s decade. In 2009, Billboard named her the Top Radio Songs Artist of the Decade and the Top Female Artist of the 2000s decade. Among numerous awards and accolades, Beyoncé has won 23 Grammy Awards and is the most nominated woman in the award's history. She is also the most awarded artist at the MTV Video Music Awards, with 24 wins, including the Michael Jackson Video Vanguard Award. In 2008, she was awarded the Legend Award for Outstanding Contribution to the Arts at the World Music Awards. In 2011, Beyoncé was presented with the inaugural Millennium Award at the Billboard Music Awards. In 2014, she became the highest-paid black musician in history and was listed among Time's 100 most influential people in the world for a second year in a row. Forbes ranked her as the most powerful female in entertainment on their 2015 and 2017 lists, and in 2016, she occupied the sixth place for Time's Person of the Year. In 2016, she was awarded the Fashion Icon lifetime achievement award from the Council of Fashion Designers of America. With the release of Lemonade, Beyoncé became the first and only musical act in Billboard chart history to debut at number one with their first six solo studio albums.
Cartesian coordinate systemA Cartesian coordinate system (UK: , US: ) is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.
One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.
The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.
Complex numberA complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x^{2} = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.
Complex numbers allow solutions to certain equations that have no solutions in real numbers. For example, the equation
has no real solution, since the square of a real number cannot be negative. Complex numbers provide a solution to this problem. The idea is to extend the real numbers with an indeterminate i (sometimes called the imaginary unit) that is taken to satisfy the relation i^{2} = −1, so that solutions to equations like the preceding one can be found. In this case the solutions are −1 + 3i and −1 − 3i, as can be verified using the fact that i^{2} = −1:
According to the fundamental theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. In contrast, some polynomial equations with real coefficients have no solution in real numbers. The 16th century Italian mathematician Gerolamo Cardano is credited with introducing complex numbers in his attempts to find solutions to cubic equations.
Formally, the complex number system can be defined as the algebraic extension of the ordinary real numbers by an imaginary number i. This means that complex numbers can be added, subtracted, and multiplied, as polynomials in the variable i, with the rule i^{2} = −1 imposed. Furthermore, complex numbers can also be divided by nonzero complex numbers. Overall, the complex number system is a field.
Geometrically, complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b) in the complex plane. A complex number whose real part is zero is said to be purely imaginary; the points for these numbers lie on the vertical axis of the complex plane. A complex number whose imaginary part is zero can be viewed as a real number; its point lies on the horizontal axis of the complex plane. Complex numbers can also be represented in polar form, which associates each complex number with its distance from the origin (its magnitude) and with a particular angle known as the argument of this complex number.
The geometric identification of the complex numbers with the complex plane, which is a Euclidean plane (), makes their structure as a real 2-dimensional vector space evident. Real and imaginary parts of a complex number may be taken as components of a vector with respect to the canonical standard basis. The addition of complex numbers is thus immediately depicted as the usual component-wise addition of vectors. However, the complex numbers allow for a richer algebraic structure, comprising additional operations, that are not necessarily available in a vector space; e.g., the multiplication of two complex numbers always yields again a complex number, and should not be mistaken for the usual "products" involving vectors, like the scalar multiplication, the scalar product or other (sesqui)linear forms, available in many vector spaces; and the broadly exploited vector product exists only in an orientation-dependent form in three dimensions.
Dragon BallDragon Ball (Japanese: ドラゴンボール, Hepburn: Doragon Bōru), sometimes styled as Dragonball, is a Japanese media franchise created by Akira Toriyama in 1984. The initial manga, written and illustrated by Toriyama, was serialized in Weekly Shōnen Jump from 1984 to 1995, with the 519 individual chapters collected into 42 tankōbon volumes by its publisher Shueisha. Dragon Ball was initially inspired by the classical Chinese novel Journey to the West, as well as Hong Kong martial arts films. The series follows the adventures of the protagonist, Son Goku, from his childhood through adulthood as he trains in martial arts and explores the world in search of the seven orbs known as the Dragon Balls, which summon a wish-granting dragon when gathered. Along his journey, Goku makes several friends and battles a wide variety of villains, many of whom also seek the Dragon Balls.
Toriyama's manga was adapted and divided into two anime series produced by Toei Animation: Dragon Ball and Dragon Ball Z, which together were broadcast in Japan from 1986 to 1996. Additionally, the studio has developed 20 animated feature films and three television specials, as well as two anime sequel series titled Dragon Ball GT (1996–1997) and Dragon Ball Super (2015–2018). From 2009 to 2015, a revised version of Dragon Ball Z aired in Japan under the title Dragon Ball Kai, as a recut that follows the manga's story more faithfully by removing most of the material featured exclusively in the anime. Several companies have developed various types of merchandising based on the series leading to a large media franchise that includes films, both animated and live-action, collectible trading card games, numerous action figures, along with several collections of soundtracks and a large number of video games. Dragon Ball is one of the top twenty highest-grossing media franchises of all time, having generated more than $20 billion in total franchise revenue as of 2018.Since its release, Dragon Ball has become one of the most successful manga and anime series of all time, with the manga sold in over 40 countries and the anime broadcast in more than 80 countries. The manga's 42 collected tankōbon volumes have sold over 160 million copies in Japan, and are estimated to have sold more 250–300 million copies worldwide, making it the second best-selling manga series in history, behind only One Piece. Reviewers have praised the art, characterization, and humour of the story. It is widely regarded as one of the greatest and most influential manga series ever made, with many manga artists citing Dragon Ball as a source of inspiration for their own now popular works. The anime, particularly Dragon Ball Z, is also highly popular across the world and is considered one of the most influential in boosting the popularity of Japanese animation in Western culture. It has had a considerable impact on global popular culture, referenced by and inspiring numerous artists, athletes, celebrities, filmmakers, musicians and writers across the world.
Dragon Ball ZDragon Ball Z (Japanese: ドラゴンボールZ (ゼット), Hepburn: Doragon Bōru Zetto, commonly abbreviated as DBZ) is a Japanese anime television series produced by Toei Animation. It is the sequel to the Dragon Ball anime and adapts the latter 325 chapters of the original 519-chapter Dragon Ball manga series created by Akira Toriyama which ran in Weekly Shōnen Jump from 1988-1995. Dragon Ball Z aired in Japan on Fuji TV from April 26, 1989 to January 31, 1996, before getting dubbed in territories including the United States, Canada, Australia, Europe, India, and Latin America. It was broadcast in at least 81 countries worldwide. It is part of the Dragon Ball media franchise.
Dragon Ball Z follows the adventures of Goku who, along with his companions, defend the Earth against villains ranging from aliens (Frieza), androids (Cell) and other creatures (Majin Buu). While the original Dragon Ball anime followed Goku from childhood to early adulthood, Dragon Ball Z is a continuation of his adult life, but at the same time parallels the life of his son, Gohan, as well as the development of his rival Vegeta from enemy to ally.
Due to the success of the anime in the United States, the manga chapters making up its story were initially released by Viz Media under the Dragon Ball Z title. Dragon Ball Z's popularity has spawned numerous releases which have come to represent the majority of content in the Dragon Ball franchise; including 15 movies, 2 TV specials, and 148 video games (many of them being only released in Japan), and a host of soundtracks stemming from this material. Dragon Ball Z remains a cultural icon through numerous adaptations and re-releases, including a more-recent remastered broadcast titled Dragon Ball Kai. There have also been two sequel series; Dragon Ball GT (1996–1997) and Dragon Ball Super (2015–2018).
Gamma function
In mathematics, the gamma function (represented by Γ, the capital Greek alphabet letter gamma) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers, and for any positive integer n,
Derived by Daniel Bernoulli, for complex numbers with a positive real part the gamma function is defined via a convergent improper integral:
The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except the non-positive integers, where the function has simple poles.
Other extensions of the factorial function do exist, but the gamma function is the most popular and useful. It is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics.
The gamma function has no zeroes, so the reciprocal gamma function 1/Γ(z) is a holomorphic function. In fact the gamma function corresponds to the Mellin transform of the negative exponential function:
Generation Z or Gen Z, also known by a number of other names, is the demographic cohort after the Millennials. Demographers and researchers typically use the mid-1990s to mid-2000s as starting birth years. There is little consensus regarding ending birth years. Most of Generation Z have used the Internet since a young age and are comfortable with technology and social media.
Index of law articlesThis collection of lists of law topics collects the names of topics related to law. Everything related to law, even quite remotely, should be included on the alphabetical list, and on the appropriate topic lists. All links on topical lists should also appear in the main alphabetical listing. The process of creating lists is ongoing – these lists are neither complete nor up-to-date – if you see an article that should be listed but is not (or one that shouldn't be listed as legal but is), please update the lists accordingly. You may also want to include Wikiproject Law talk page banners on the relevant pages.
IntegerAn integer (from the Latin integer meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 1/2, and √2 are not.
The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, …), also called whole numbers or counting numbers, and their additive inverses (the negative integers, i.e., −1, −2, −3, …). The set of integers is often denoted by a boldface Z ("Z") or blackboard bold (Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").
Z is a subset of the set of all rational numbers Q, in turn a subset of the real numbers R. Like the natural numbers, Z is countably infinite.
The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers.
Jay-ZShawn Corey Carter (born December 4, 1969), known professionally as Jay-Z (; stylized as JAY-Z), is an American rapper, songwriter, producer, entrepreneur, and record executive. Considered among the best rappers of all time, he is regarded as one of the world's most significant cultural icons and has been a global figure in popular culture for over two decades.Born and raised in New York City, Jay-Z first began his musical career after founding the record label Roc-A-Fella Records in 1995, and subsequently released his debut studio album Reasonable Doubt in 1996. The album was released to widespread critical success, and solidified his standing in the music industry. He has gone onto release twelve additional albums, which have all attained generally positive critical reception and universal commercial success, with The Blueprint (2001) and The Black Album (2003) albums later being heralded as modern musical classics. He has also released the full-length collaborative albums Watch the Throne (2011) and Everything Is Love (2018) with Kanye West and wife Beyoncé, respectively.Outside of his musical career, Jay-Z has also attained significant success and media attention for his career as a businessman. In 1999, he founded the clothing retailer Rocawear, and in 2003, he founded the luxury sports bar chain 40/40 Club. Both businesses have grown to become multi-million dollar corporations, and allowed Jay-Z to fund the start-up for the entertainment company Roc Nation, which was founded in 2008. In 2015, he acquired the tech company Aspiro, and took charge of their media streaming service Tidal, which has since become the world's third-largest online streaming company. His marriage to musician Beyoncé has also been a source of substantial media attention.Jay-Z is among the most critically acclaimed musicians and one of the best-selling music artists of all time, with over 100 million records sold worldwide. He has won a total of 22 Grammy Awards, the most by a rapper, and holds the record for the most number-one albums by a solo artist on the Billboard 200, with 13. He has been ranked by Billboard and fellow music publication Rolling Stone as one of the 100 greatest artists of all time. In 2017, he became the first rapper to be honored into the Songwriters Hall of Fame, and in 2018, received the commemorative "Salute to Industry Icons" award at the 60th Grammy Awards.
KrigingIn statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances. Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) need not yield the most likely intermediate values. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.
The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The English verb is to krige and the most common noun is kriging; both are often pronounced with a hard "g", following the pronunciation of the name "Krige". The word is sometimes capitalized as Kriging in the literature.
List of Dragon Ball charactersThe Dragon Ball manga series features an ensemble cast of characters created by Akira Toriyama. The series takes place in a fictional universe, the same world as Toriyama's previous series Dr. Slump, and follows the adventures of Son Goku during his boyhood years as he trains in martial arts and explores a fantastical version of Earth (地球 Chikyū) in search of the seven orbs known as the Dragon Balls that are used to summon a wish-granting dragon. The tone of the series becomes more action oriented and less comedic when Goku reaches adulthood, as he and his allies would find themselves defending Earth against various threats, overcoming seemingly insurmountable opponents and eventually emerging victorious against progressively more powerful foes.
During the course of the story, Goku encounters allies such as Bulma, Master Roshi, and Trunks, rivals such as Tien Shinhan, Piccolo, and Vegeta, and villains such as Frieza, Cell and Majin Buu. Goku's group of associates, known as the Dragon Team (ドラゴンチーム, Doragon Chīmu)[ch. 165], bolster its ranks throughout the series with the addition of former enemies and new heroes. The group is also known in Japanese as the Z Fighters (Z戦士, Zetto Senshi) or TEAM "Z" in other media, and in the English dub of Dragon Ball Z as the Earth's Special Forces.While many of the characters are humans with superhuman strength and/or supernatural abilities, the cast also includes anthropomorphic animals, extraterrestrial lifeforms, and even deities who govern the world and the universe. The series also includes depictions of the afterlife and time travel as a means of creating historical divergences. Dragon Ball Super in particular expanded the setting of the series to include parallel universes; Universe 7, or the Seventh Universe in the English dub, is designated as the universe where the vast majority of the Dragon Ball series takes place.
LogarithmIn mathematics, the logarithm is the inverse function to exponentiation (it is an example of a concave function). That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 10^{3}, the "logarithm to base 10" of 1000 is 3. The logarithm of x to base b is denoted as log_{b} (x) (or, without parentheses, as log_{b} x, or even without explicit base as log x, when no confusion is possible). More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm for any two positive real numbers b and x where b is not equal to 1, is always a unique real number y. More explicitly, the defining relation between exponentiation and logarithm is:
For example, log_{2} 64 = 6, as 2^{6} = 64.
The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e (that is b ≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. The binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.
Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors:
provided that b, x and y are all positive and b ≠ 1. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century.
Logarithmic scales reduce wide-ranging quantities to tiny scopes. For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They help describing frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting.
In the same way as the logarithm reverses exponentiation, the complex logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant; it has uses in public-key cryptography.
NasNasir bin Olu Dara Jones (; born September 14, 1973), known professionally as Nas (), is an American rapper, songwriter, entrepreneur and investor. The son of jazz musician Olu Dara, Nas has released eight consecutive platinum and multi-platinum albums and has sold over 30 million records worldwide. He is also an entrepreneur through his own record label; he serves as associate publisher of Mass Appeal magazine and the co-founder of Mass Appeal Records.
His musical career began in 1991, as a featured artist on Main Source's "Live at the Barbeque". His debut album Illmatic (1994) received universal acclaim from both critics and the hip-hop community and is frequently ranked as one of the greatest hip-hop albums of all time. Nas's follow-up It Was Written debuted at #1 on the Billboard 200, stayed on top for four consecutive weeks, went Double Platinum in two months, and made Nas internationally known. From 2001 to 2005, Nas was involved in a highly publicized feud with Jay-Z, popularized by the diss track "Ether". Nas signed to Def Jam in 2006. In 2010, he released Distant Relatives, a collaboration album with Damian Marley, donating all royalties to charities active in Africa. His 11th studio album, Life Is Good (2012) was nominated for Best Rap Album at the 55th Annual Grammy Awards.
Nas has been considered as one of the best rappers of all time. MTV ranked him at #5 on their list of "The Greatest MCs of All Time". In 2012, The Source ranked him #2 on their list of the "Top 50 Lyricists of All Time". In 2013, Nas was ranked 4th on MTV's "Hottest MCs in the Game" list. About.com ranked him first on their list of the "50 Greatest MCs of All Time" in 2014, and a year later, Nas was featured on "The 10 Best Rappers of All Time" list by Billboard. Nas has released eight consecutive platinum albums and has sold over 30 million records worldwide.
New ZealandNew Zealand (Māori: Aotearoa [aɔˈtɛaɾɔa]) is a sovereign island country in the southwestern Pacific Ocean. The country geographically comprises two main landmasses—the North Island (Te Ika-a-Māui), and the South Island (Te Waipounamu)—and around 600 smaller islands. New Zealand is situated some 2,000 kilometres (1,200 mi) east of Australia across the Tasman Sea and roughly 1,000 kilometres (600 mi) south of the Pacific island areas of New Caledonia, Fiji, and Tonga. Because of its remoteness, it was one of the last lands to be settled by humans. During its long period of isolation, New Zealand developed a distinct biodiversity of animal, fungal, and plant life. The country's varied topography and its sharp mountain peaks, such as the Southern Alps, owe much to the tectonic uplift of land and volcanic eruptions. New Zealand's capital city is Wellington, while its most populous city is Auckland.
Sometime between 1250 and 1300, Polynesians settled in the islands that later were named New Zealand and developed a distinctive Māori culture. In 1642, Dutch explorer Abel Tasman became the first European to sight New Zealand. In 1840, representatives of the United Kingdom and Māori chiefs signed the Treaty of Waitangi, which declared British sovereignty over the islands. In 1841, New Zealand became a colony within the British Empire and in 1907 it became a dominion; it gained full statutory independence in 1947 and the British monarch remained the head of state. Today, the majority of New Zealand's population of 4.9 million is of European descent; the indigenous Māori are the largest minority, followed by Asians and Pacific Islanders. Reflecting this, New Zealand's culture is mainly derived from Māori and early British settlers, with recent broadening arising from increased immigration. The official languages are English, Māori, and NZ Sign Language, with English being very dominant.
A developed country, New Zealand ranks highly in international comparisons of national performance, such as quality of life, health, education, protection of civil liberties, and economic freedom. New Zealand underwent major economic changes during the 1980s, which transformed it from a protectionist to a liberalised free-trade economy. The service sector dominates the national economy, followed by the industrial sector, and agriculture; international tourism is a significant source of revenue. Nationally, legislative authority is vested in an elected, unicameral Parliament, while executive political power is exercised by the Cabinet, led by the prime minister, currently Jacinda Ardern. Queen Elizabeth II is the country's monarch and is represented by a governor-general, currently Dame Patsy Reddy. In addition, New Zealand is organised into 11 regional councils and 67 territorial authorities for local government purposes. The Realm of New Zealand also includes Tokelau (a dependent territory); the Cook Islands and Niue (self-governing states in free association with New Zealand); and the Ross Dependency, which is New Zealand's territorial claim in Antarctica. New Zealand is a member of the United Nations, Commonwealth of Nations, ANZUS, Organisation for Economic Co-operation and Development, ASEAN Plus Six, Asia-Pacific Economic Cooperation, the Pacific Community and the Pacific Islands Forum.
Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, they become normally distributed when the number of observations is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.
The normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's t-, and logistic distributions).
The probability density of the normal distribution is
where
Standard scoreIn statistics, the standard score is the signed fractional number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores.
It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. It is a dimensionless quantity. This conversion process is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see normalization for more).
Standard scores are also called z-values, z-scores, normal scores, and standardized variables. They are most frequently used to compare an observation to a theoretical deviate, such as a standard normal deviate.
Computing a z-score requires knowing the mean and standard deviation of the complete population to which a data point belongs; if one only has a sample of observations from the population, then the analogous computation with sample mean and sample standard deviation yields the t-statistic.
ZZ TopZZ Top is an American rock band formed in 1969 in Houston, Texas. The band has, since 1970, consisted of vocalist/guitarist Billy Gibbons (the band's leader, main lyricist and musical arranger), bassist/vocalist Dusty Hill, and drummer Frank Beard. "As genuine roots musicians, they have few peers", according to critic Michael "Cub" Koda. "Gibbons is one of America's finest blues guitarists working in the arena rock idiom [...] while Hill and Beard provide the ultimate rhythm section support."The band released its first album, ZZ Top's First Album, in 1971. Beginning with blues-inspired rock, the trio later incorporated new wave, punk rock and dance-rock by using synthesizers. Their songs have a reputation for containing humorous lyrics laced with double entendres and innuendos.
The band's top-selling album is their 1983 release Eliminator, which sold more than 10 million copies in the United States. Total record sales of 25 million place ZZ Top among the top-100-selling artists in the United States, according to the Recording Industry Association of America. That includes 11 gold, seven platinum and three multi-platinum albums as of 2016, according to the RIAA. By 2014, ZZ Top had sold more than 50 million albums worldwide.ZZ Top was inducted into the Rock and Roll Hall of Fame in 2004.
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