Though a pH value has no unit, it is not an arbitrary scale; the number arises from a definition based on the activity of hydrogen ions in the solution. The formula for calculating pH is: [H+] denotes the activity of H+ ions (or more accurately written, [H3O+], the equivalent hydronium ions), measured in moles per litre (also known as molarity). In dilute solutions (like river or tap water) the activity is approximately equal to the concen ...

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PH, PH - Definition, PH - Measuring, PH - pOH, PH - Calculation of pH for weak and strong acids, PH - Indicators, PH - References

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The octonions can be thought of as octets (or 8-tuples) of real numbers. Every octonion is a real linear combination of the unit octonions {1, i, j, k, l, li, lj, lk}. That is, every octonion x can be written in the form x = x0 + x1 i + x2 j + x3 k + x4 l + x5 li + x6 lj + x7 lk. with real co ...

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Octonion, Octonion - History, Octonion - Definition, Octonion - Cayley-Dickson construction, Octonion - Fano plane mnemonic, Octonion - Conjugate norm and inverse, Octonion - Properties, Octonion - Automorphisms, Octonion - Quotes

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Even though the concept of phases is widely-used in the physical sciences, it is not easy to define precisely. Before presenting the general definition, we will provide two common examples of phase phenomena: firstly, the ordinary solid, liquid, and gas phases of matter; secondly, the paramagnetic and ferromagnetic phases of magnetic materials. Phase matter - Example 1: Solid liquid and gas phases. Water (H2O) is composed of water molecules, each of which is an oxygen atom attached to two hydrog ...

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Phase matter, Phase matter - Definition, Phase matter - Example 1: Solid liquid and gas phases, Phase matter - Example 2: Magnetic phases, Phase matter - General definition of phases, Phase matter - Other examples of phases, Phase matter - Phase diagrams, Phase matter - Metastable phases, Phase matter - Phase equilibrium, Phase matter - Emergence and universality

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The power spectral density, PSD, describes how the power (or variance) of a time series is distributed with frequency. If f(t) is a signal, the spectral density Φ(ω) of the signal is the square of the magnitude of the continuous Fourier transform of the signal. where ω is the angular frequency (2π times the cyclic frequency) and F(ω) is the conti ...

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Spectral density, Spectral density - Definition, Spectral density - Properties, Spectral density - Related concepts, Spectral density - Applications, Spectral density - Colorimetry

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The constant is defined as the exponential rate at which the average absolute value of a random Fibonacci sequence increases. A "random Fibonacci sequence" is a sequence of numbers fn with the following recursive definition: f0 = 1, f1 = 1, and In other words, the decision whether to add or subtract the previous two elements of the sequence to get the next element, is taken at random with a probability of 0.5 favour ...

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Viswanath's constant, Viswanath's constant - Definition, Viswanath's constant - Explication, Viswanath's constant - Significance

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For any (topologically) discrete set S of points in Euclidean space and for almost any point x, there is one point of S to which x is closer than x is to any other point of S. The word "almost" is occasioned by the fact that a point x may be equally close to two or more points of S. If S contains only two points, a and b, then the set of all points equidistant from a and b is a hyperplane — an affine subspace of codimension 1. That hyperplane ...

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Voronoi diagram, Voronoi diagram - Definition, Voronoi diagram - History, Voronoi diagram - Examples, Voronoi diagram - Generalizations

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Let I be a (possibly infinite) index set and suppose Xi is a topological space for every i in I. Set X = Π Xi, the Cartesian product of the sets Xi. For every i in I, we have a canonical projection pi : X → Xi. The product topology on X is defined to be the coarsest topology (i.e. the topology with the fewest open sets) for which all the projections pi are continuous. The product topology is ...

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Product topology, Product topology - Definition, Product topology - Examples, Product topology - Properties, Product topology - Relation to other topological notions

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The most widely held common definition is "a reasonable belief that a crime has been committed". An alternative definition has been proposed, "reason to believe that an injury had criminal cause", which is claimed to be more protective of individual rights as was intended by the authors of the Bill of Rights. See the critique below. In the context of warrants, the Oxford Companion to American Law defines probable cause as "information sufficient to warrant a prudent person's belief that the wanted individual had committed a cri ...

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Probable cause, Probable cause - Definition, Probable cause - Related cases, Probable cause - Probable cause hearings, Probable cause - Critique

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Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X. If μ is a positive measure, then N is null if its measure μ(N) is zero. If μ is not a positive measure, then N is μ-null if N is |μ|-null, where |μ| is the total variation of μ; equivalently, if every measurable subset A of N satisfies μ(A)=0. For positives measures, this is equivalent to the definition given above; but for signed measures, this is stronger th ...

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Null set, Null set - Definition, Null set - Properties, Null set - In Lebesgue measure, Null set - Uses

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The nitrite ion is NO2-. A nitrite compound is one that contains this group, either an ionic compound, or an analogous covalent one. These may be considered salts or esters of nitrous acid. ...

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Nitrite, Nitrite - Definition, Nitrite - Examples, Nitrite - Discussion

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A model is formally defined in the context of some language L, which consists of a set of constant symbols, a set of relation symbols each of valence some positive integer, and a set of function symbols each of valence some positive integer. A model of the language L consists of several things: A universe set A which contains all the objects of interest (the "domain of discourse"), and An element of A for each constant symbol of L. A function from ASee also:

Model theory, Model theory - Definition, Model theory - Theorems of model theory

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From Shannon's Mathematical Theory of Communication (1949) we know that in an optimal code, the message length (in binary) of an event E, , where E has probability P(E), is given by . From Bayes's theorem we know that the probability of a hypothesis (H) given evidence (E) is proportional to P(E | H) ...

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Minimum message length, Minimum message length - Definition, Minimum message length - Continuous valued parameters, Minimum message length - Key features of MML

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A metric space is a 2-tuple (X,d) where X is a set and d is a metric on X, that is, a function d : X × X → R such that d(x, y) ≥ 0     (non-negativity) d(x, y) = 0   if and only if   x = y     (identity of indiscernibles) d(x, y) = d(y, x)     ...

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Metric space, Metric space - History, Metric space - Definition, Metric space - Examples, Metric space - Metric spaces as topological spaces, Metric space - Boundedness and compactness, Metric space - Separation properties and extension of continuous functions, Metric space - Distance between points and sets, Metric space - Equivalence of metric spaces, Metric space - Quotient metric space

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Because of inconsistencies in the use of SI-derived prefixes such as kilo- and mega-, the exact number can be any one of the following: 1,000,000 bytes (10002, 106): This is the definition recommended by IEC. It is used primarily in networking contexts and most storage media, particularly hard drives and DVDs. This definition of 'mega-' as a "binary prefix is consistent with the other SI prefixes, and with many other uses of the prefix in computing, such as CPU clock speeds or measures of performance. ...

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Megabyte, Megabyte - Definition, Megabyte - Megabytes in use

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A category C is given by two pieces of data: a class of objects and a class of morphisms. There are two operations defined on every morphism, the domain (or source) and the codomain (or target). Morphisms are often depicted as arrows from their domain to their codomain, e.g. if a morphism f has domain X and codomain Y, it is denoted f : X → Y. The set of all morphisms from X to Y is denoted homC(X,Y) or simply hom(X, Y). (Some authors write MorC(X ...

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Morphism, Morphism - Definition, Morphism - Types of morphisms, Morphism - Examples

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As for what multiplication means, the product of two whole numbers n and m is: This is just a shorthand for saying, "Add m to itself n times." Expanding the above to make its meaning more clear: m × n = m + m + m + ... + m such that there are n m's added together. So for instance: 5 × 2 = 5 + 5 = 10 2 × 5 = 2 + 2 + 2 + 2 + 2 = 10 4 × 3 = 4 + 4 + 4 = 12 m × 6 = m + m + ...

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Multiplication, Multiplication - Notation, Multiplication - Definition, Multiplication - Computation

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The nitride ion is N3- (a nitrogen atom plus three electrons). A nitride (compound) is a compound that has nitrogen with more electropositive elements. ...

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Nitride, Nitride - Definition, Nitride - Examples, Nitride - Discussion

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If X is a topological space and p is a point in X, a neighbourhood of p is a set V, which contains an open set U containing p. Note that the neighbourhood V need not be an open set itself. If V is open it is called an open neighbourhood. Some authors require that neighbourhoods be open; be careful to note conventions. If S is a subset of X, a neighbourhood of S is a set V, which contains an open s ...

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Neighbourhood mathematics, Neighbourhood mathematics - Definition, Neighbourhood mathematics - In a metric space, Neighbourhood mathematics - Examples, Neighbourhood mathematics - Topology from neighbourhoods, Neighbourhood mathematics - Uniform neighbourhoods, Neighbourhood mathematics - Significance of neighbourhoods in analysis of real functions

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In order to consider mythology, it is first necessary to consider what is meant by the term myth. Myths are generally narratives passed down traditionally intended to explain the universal and local beginnings ("creation myths" and "founding myths"), natural phenomena, inexplicable cultural conventions, and anything else for which no simple explanation presents itself. Not all myths need have this explicatory purpose, however. Myths are by definition sacred and usually involve a supernatural force or deity. Many legends and narratives passed down orally from gener ...

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Mythology, Mythology - Definition, Mythology - Religion and mythology, Mythology - Classifications, Mythology - Related concepts, Mythology - Formation of myths, Mythology - Myths as depictions of historical events, Mythology - Other theories, Mythology - Modern mythology, Mythology - Myths by region, Mythology - Africa, Mythology - Asia non-Middle East, Mythology - Australia and Oceania, Mythology - Europe, Mythology - Middle East, Mythology - North America, Mythology - South America and Mesoamerica, Mythology - Mythological archetypes, Mythology - Mythological creatures, Mythology - Books on mythology

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There is a wide range of Muslim politicians, from male dictators like Saddam Hussain to female democratic leaders like Benazir Bhutto or theoctratic leaders like Khomeini. Some of the have been labeled as terrorists like the male Osama bin Laden or female Maryam Rajavi, while other have been praised as freedom fighters, like the female Shirin Ebadi or the male Husayn ibn Ali. Some of them are non-leader politicians, like the members of the unicameral Iranian parliament, named "the Islamic Consultative Assembly" or "Majles-e Shura-ye Eslami", consisting of 290 members elected to a 4-year term.< ...

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Muslim politicians, Muslim politicians - Definition

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The US Census Bureau defines an urbanized area as: "Core census block groups or blocks that have a population density of at least 1,000 people per square mile and (386 per square kilometer) and surrounding census blocks that have an overall density of at least 500 people per square mile (193 per square kilometer)." Definitions vary somewhat in other nations. The minimum density requirement is generally 400 persons per square kilometer. In Australia, the minimum density is 200 people per square kilometer. In Japan urbanized areas are defined ...

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Urbanized Area, Urbanized Area - Definition

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There are two layers of encoding that make up Unix time, and they can be usefully separated. The first layer encodes a point in time as a scalar real number, and the second encodes that number as a sequence of bits or in some other manner. Unix time - Encoding time as a number. Modern Unix time is based strictly on UTC. UTC counts time using SI seconds, and breaks up the span of time into days. UTC days are mostly 86400 s long, but are occasionally 86401 s and could be 86399 s long (though the la ...

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Unix time, Unix time - Definition, Unix time - Encoding time as a number, Unix time - Representing the number, Unix time - UTC basis, Unix time - History, Unix time - 32-bit overflow, Unix time - time_t parties

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