Double Lagrangian Grassmannian
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Double Lagrangian Grassmannian
A double is a look-alike or doppelgänger; one person or being that resembles another. Double, The Double or Dubble may also refer to: Film and television * Double (filmmaking), someone who substitutes for the credited actor of a character * The Double (1934 film), ''The Double'' (1934 film), a German crime comedy film * The Double (1971 film), ''The Double'' (1971 film), an Italian film * The Double (2011 film), ''The Double'' (2011 film), a spy thriller film * The Double (2013 film), ''The Double'' (2013 film), a film based on the Dostoevsky novella * ''Kamen Rider W, Kamen Rider Double'', a 2009–10 Japanese television series ** List of Kamen Rider W characters#Kamen Rider W, Kamen Rider Double (character), the protagonist in a Japanese television series of the same name Food and drink * Doppio, a double shot of espresso * Dubbel, a strong Belgian Trappist beer or, more generally, a strong brown ale * A drink order of two shots of distilled beverage, hard liquor in one glass ...
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Look-alike
A look-alike, double, or doppelgänger is a person who bears a strong physical resemblance to another person, excluding cases like twins and other instances of family resemblance. Some look-alikes have been notable individuals in their own right, such as Britain's King George V and Russia's Tsar Nicholas II, who bore a striking resemblance to each other (they were first cousins). Other notable look-alikes have been notable solely for resembling well-known individuals, such as Clifton James, who acted as a double for British Field Marshal Bernard Montgomery during World War II. Some look-alikes who have resembled celebrities have worked as entertainers, impersonating them on stage and screen, or at venues like parties and corporate functions. Professional look-alikes have often been represented by talent agencies specializing in celebrity impersonators. Close physical resemblance between two or more individuals is also a common plot point in works of fiction. Notable look-a ...
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The Double (Dostoevsky Novel)
''The Double: A Petersburg Poem'' (russian: Двойник. Петербургская поэма, Dvoynik. Peterburgskaya poema) is a novel written by Fyodor Dostoevsky. It was first published on 30 January 1846 in the ''Otechestvennye zapiski''. It was subsequently revised and republished by Dostoevsky in 1866. Plot summary In Saint Petersburg, Yakov Petrovich Golyadkin works as a titular councillor (rank 9 in the Table of Ranks established by Peter the Great.), a low-level bureaucrat struggling to succeed. Golyadkin has a formative discussion with his Doctor Rutenspitz, who fears for his sanity and tells him that his behaviour is dangerously antisocial. He prescribes "cheerful company" as the remedy. Golyadkin resolves to try this, and leaves the office. He proceeds to a birthday party for Klara Olsufyevna, the daughter of his office manager. He was uninvited, and a series of ''faux pas'' lead to his expulsion from the party. On his way home through a snowstorm, he encounte ...
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Double Variation
The double variation (also known as alternating variations) is a musical form used in classical music. It is a type of theme and variations that employs two themes. In a double variation set, a first theme (to be called A here) is followed by a second theme (B), followed by a variation on A, then a variation on B, and so on with alternating A and B variations. Often there is a coda at the end. The double variation is strongly associated with the composer Joseph Haydn, who wrote many such movements during his career. The double variation in Haydn The double variation first appears Haydn's work of the 1770s. Haydn may have been inspired by an earlier example of Carl Philipp Emanuel Bach, the sixth of that composer's ''Sonatas with Varied Reprises'', (W. 50/6, H. 140), in C minor (1760). Elaine Sisman, an authority on variations, notes "This set of sonatas was advertised in Vienna several times in the period in which Haydn wrote his first oublevariations."Sisman (1990) While ...
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Doubling (voicing)
In music theory, voicing refers to two closely related concepts: # How a musician or group distributes, or spaces, notes and chords on one or more instruments # The simultaneous vertical placement of notes in relation to each other; this relates to the concepts of spacing and doubling It includes the instrumentation and vertical spacing and ordering of the musical notes in a chord: which notes are on the top or in the middle, which ones are doubled, which octave each is in, and which instruments or voices perform each note. Vertical placement The following three chords are all C-major triads in root position with different voicings. The first is in close position (the most compact voicing), while the second and third are in open position (that is, with wider spacing). Notice also that the G is doubled at the octave in the third chord; that is, it appears in two different octaves. : Examples Many composers, as they developed and gained experience, became more enterpr ...
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Double Album
A double album (or double record) is an audio album that spans two units of the primary medium in which it is sold, typically either records or compact disc. A double album is usually, though not always, released as such because the recording is longer than the capacity of the medium. Recording artists often think of double albums as being a single piece artistically; however, there are exceptions such as John Lennon's ''Some Time in New York City'' (which consisted of one studio record and one live album packaged together) and OutKast's ''Speakerboxxx/The Love Below'' (effectively two solo albums, one by each member of the duo). Since the advent of the compact disc, albums are sometimes released with a bonus disc featuring additional material as a supplement to the main album, with live tracks, studio out-takes, cut songs, or older unreleased material. One innovation was the inclusion of a DVD of related material with a compact disc, such as video related to the album or DVD-A ...
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Double (manifold)
In the subject of manifold theory in mathematics, if M is a manifold with boundary, its double is obtained by gluing two copies of M together along their common boundary. Precisely, the double is M \times \ / \sim where (x,0) \sim (x,1) for all x \in \partial M. Although the concept makes sense for any manifold, and even for some non-manifold sets such as the Alexander horned sphere, the notion of double tends to be used primarily in the context that \partial M is non-empty and M is compact. Doubles bound Given a manifold M, the double of M is the boundary of M \times ,1/math>. This gives doubles a special role in cobordism. Examples The ''n''-sphere is the double of the ''n''-ball. In this context, the two balls would be the upper and lower hemi-sphere respectively. More generally, if M is closed, the double of M \times D^k is M \times S^k. Even more generally, the double of a disc bundle over a manifold is a sphere bundle over the same manifold. More concretely, the ...
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Ordered Pair
In mathematics, an ordered pair (''a'', ''b'') is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a'') unless ''a'' = ''b''. (In contrast, the unordered pair equals the unordered pair .) Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors. (Technically, this is an abuse of terminology since an ordered pair need not be an element of a vector space.) The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered ''n''-tuples (ordered lists of ''n'' objects). For example, the ordered triple (''a'',''b'',''c'') can be defined as (''a'', (''b'',''c'')), i.e., as one pair nested in another. In the ordered pair (''a'', ''b''), the object ''a'' is called the ''first entry'', and the object ''b'' the '' ...
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defined inductively using the construction of an ordered pair. Mathematicians usually write tuples by listing the elements within parentheses "" and separated by a comma and a space; for example, denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "nbsp; or angle brackets "⟨ ⟩". Braces "" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term ''tuple'' can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebr ...
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Split-complex Number
In algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components and , and is written z=x+yj, where j^2=1. The ''conjugate'' of is z^*=x-yj. Since j^2=1, the product of a number with its conjugate is N(z) := zz^* = x^2 - y^2, an isotropic quadratic form. The collection of all split complex numbers z=x+yj for forms an algebra over the field of real numbers. Two split-complex numbers and have a product that satisfies N(wz)=N(w)N(z). This composition of over the algebra product makes a composition algebra. A similar algebra based on and component-wise operations of addition and multiplication, where is the quadratic form on also forms a quadratic space. The ring isomorphism \begin D &\to \mathbb^2 \\ x + yj &\mapsto (x - y, x + y) \end relates proportional quadratic forms, but the mapping is an isometry since the multiplicative identity of is at a distance from 0, which is normalized in . S ...
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Double-precision Floating-point Format
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754-2008 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 ''single precision'' and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and ...
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2 (number)
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. Evolution Arabic digit The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method. The Gupta script rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic Ghubar writing, the bottom line was completely vertical, and the digit looked like a dotless closing question mark. Restoring the bottom line to its original horizonta ...
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Multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ...
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