moment

The best place for building a dam is a narrow part of a deep river valley; the valley sides can then act as natural walls. The primary function of the dam's structure is to fill the gap in the natural reservoir line left by the stream channel. The sites are usually those where the gap becomes a minimum for the required storage capacity. The most economical arrangement is often a composite structure such as a masonry dam flanked by earth embankments. The current use of t ...

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Dam, Dam - History, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams, Dam - Notes

Read more here: » Dam: Encyclopedia II - Dam - Other considerations

In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are given by the sum extending over all sequences j1, j2, j3, ..., jn−k+1 of positive integers such that Bell polynomials - Convolution identity. For sequences xn, yn, n = 0, 1, 2, ..., define a sort of convolution by Let be the nth term of the sequence See also:

Bell polynomials, Bell polynomials - Definition, Bell polynomials - Convolution identity, Bell polynomials - Complete Bell polynomials, Bell polynomials - Combinatorial meaning, Bell polynomials - Examples, Bell polynomials - Stirling numbers and Bell numbers, Bell polynomials - Where do Bell polynomials occur?, Bell polynomials - Composition of formal power series and Fàa di Bruno's formula, Bell polynomials - Moments and cumulants, Bell polynomials - Representation of polynomial sequences of binomial type

Read more here: » Bell polynomials: Encyclopedia II - Bell polynomials - Definition

One use for white noise is in the field of architectural acoustics. Here in order to submerge distracting, undesirable noises (for example conversations, etc.,) in interior spaces, a constant low level of noise is generated and provided as a background sound. White noise is used by some sirens for emergency vehicles, due to its ability to cut through background noise (e.g. urban traffic noise). White noise has also been used in electronic music, where it is used either directly or as an input for a filter to create other types of nois ...

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White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal, White noise - External link

Read more here: » White noise: Encyclopedia II - White noise - Applications

The sum is sometimes called the nth complete Bell polynomial. In order to contrast them with complete Bell polynomials, the polynomials Bn, k defined above are sometimes called "partial" Bell polynomials. The complete Bell polynomials satisfy the following identity ...

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Bell polynomials, Bell polynomials - Definition, Bell polynomials - Convolution identity, Bell polynomials - Complete Bell polynomials, Bell polynomials - Combinatorial meaning, Bell polynomials - Examples, Bell polynomials - Stirling numbers and Bell numbers, Bell polynomials - Where do Bell polynomials occur?, Bell polynomials - Composition of formal power series and Fàa di Bruno's formula, Bell polynomials - Moments and cumulants, Bell polynomials - Representation of polynomial sequences of binomial type

Read more here: » Bell polynomials: Encyclopedia II - Bell polynomials - Complete Bell polynomials

The term white noise is also commonly applied to a noise signal in the spatial domain which has zero autocorrelation with itself over the relevant space dimensions. The signal is then "white" in the spatial frequency domain (this is equally true for signals in the angular frequency domain, e.g. the distribution of a signal across all angles in the night sky). The image to the right displays a finite length, discrete time realizati ...

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White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal, White noise - External link

Read more here: » White noise: Encyclopedia II - White noise - Statistical properties

A spillway is a section of a dam designed to pass water from the upstream side of a dam to the downstream side. Many spillways have floodgates designed to control the flow through the spillway. A service spillway or primary spillway passes normal flow. An auxiliary spillway releases flow in excess of the capacity of the service spillway. An emergency spillway is designed for extreme conditions, such as a serious malfunction of the service spillway. A fuse-plug spillway is a low embankment designed to be overtopped and washed aw ...

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Dam, Dam - History, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams, Dam - Notes

Read more here: » Dam: Encyclopedia II - Dam - Spillways

The joint cumulant of several random variables X1, ..., Xn is where π runs through the list of all partitions of { 1, ..., n }, and B runs through the list of all blocks of the partition π. For example, The joint cumulant of just one random variable is its expected value, and that of two random variables is their covariance. If some of the random variables are independent of all of the others, then the joint cumulant is zero. If all n random variables are the same, then the joint c ...

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Cumulant, Cumulant - Cumulants of probability distributions, Cumulant - Some properties of cumulants, Cumulant - Invariance and equivariance, Cumulant - Homogeneity, Cumulant - Additivity, Cumulant - Cumulants and moments, Cumulant - Cumulants and set-partitions, Cumulant - Cumulants of particular probability distributions, Cumulant - Joint cumulants, Cumulant - Conditional cumulants and the law of total cumulance, Cumulant - History, Cumulant - Formal cumulants, Cumulant - One well-known example, Cumulant - Cumulants of a polynomial sequence of binomial type, Cumulant - Free cumulants, Cumulant - External references

Read more here: » Cumulant: Encyclopedia II - Cumulant - Joint cumulants

More generally, the cumulants of a sequence { mn : n = 1, 2, 3, ... }, not necessarily the moments of any probability distribution, are given by where the values of κn for n = 1, 2, 3, ... are found formally, i.e., by algebra alone, in disregard of questions of whether any series converges. All of the difficulties of the "problem of cumulants" are absent when one works formally. The simplest example is that the second cumulant of a probability distribution must always be nonnegative, and is zero only if all of the higher cumulants are zero. Formal ...

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Cumulant, Cumulant - Cumulants of probability distributions, Cumulant - Some properties of cumulants, Cumulant - Invariance and equivariance, Cumulant - Homogeneity, Cumulant - Additivity, Cumulant - Cumulants and moments, Cumulant - Cumulants and set-partitions, Cumulant - Cumulants of particular probability distributions, Cumulant - Joint cumulants, Cumulant - Conditional cumulants and the law of total cumulance, Cumulant - History, Cumulant - Formal cumulants, Cumulant - One well-known example, Cumulant - Cumulants of a polynomial sequence of binomial type, Cumulant - Free cumulants, Cumulant - External references

Read more here: » Cumulant: Encyclopedia II - Cumulant - Formal cumulants

One use for white noise is in the field of architectural acoustics. Here in order to submerge distracting, undesirable noises (for example conversations, etc.,) in interior spaces, a constant low level of noise is generated and provided as a background sound. White noise is used by some sirens for emergency vehicles, due to its ability to cut through background noise (e.g. urban traffic noise). White noise has also been used in electronic music, where it is used either directly or as an input for a filter to create other types of nois ...

See also:

White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal

Read more here: » White noise: Encyclopedia II - White noise - Applications

The term white noise is also commonly applied to a noise signal in the spatial domain which has zero autocorrelation with itself over the relevant space dimensions. The signal is then "white" in the spatial frequency domain (this is equally true for signals in the angular frequency domain, e.g. the distribution of a signal across all angles in the night sky). The image to the right displays a finite length, discrete time realizati ...

See also:

White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal

Read more here: » White noise: Encyclopedia II - White noise - Statistical properties

It appears that Larry Niven created the Pak Protectors partly to show that high intelligence is simply an evolutionary tool. There have been some movements in SF that equate high intelligence with selflessness, civilization and altruism. Pak protectors are slaves to their instincts, which hard-wire their goals and priorities. Their intelligence serves evolutionary goals in order to preserve their species in a hostile environment. Niven has stated in other writings that he invented the Protectors as a thought experiment to explain the ...

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Pak Protector, Pak Protector - The Pak species, Pak Protector - Tree Of Life, Pak Protector - Protector behaviour, Pak Protector - The Pak and Humanity, Pak Protector - Narrative purpose

Read more here: » Pak Protector: Encyclopedia II - Pak Protector - Narrative purpose

White noise - White random vector. A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following: I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation.

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White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal

Read more here: » White noise: Encyclopedia II - White noise - Mathematical definition

Two theoretical applications using a white random vector are the simulation and whitening of another arbitrary random vector. To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix. We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating. To whiten an arbitrary random vector, we transform it by a different carefully chosen matr ...

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White noise, White noise - Statistical properties, White noise - Colors of noise, White noise - Applications, White noise - Mathematical definition, White noise - White random vector, White noise - White random process white noise, White noise - Random vector transformations, White noise - Simulating a random vector, White noise - Whitening a random vector, White noise - Random signal transformations, White noise - Simulating a continuous-time random signal, White noise - Whitening a continuous-time random signal

Read more here: » White noise: Encyclopedia II - White noise - Random vector transformations

ζ(1) is infinite as the harmonic series, and so the case when s = 1 is not meaningful. However, if A is any set of positive integers that has a density, i.e. if exists where N(A, n) is the number of members of A less than or equal to n, then is equal to that density. The latter limit can also exist in some cases in which A does not have a density. For example, if A is the set of all positive integers whose first ...

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Zeta distribution, Zeta distribution - Moments, Zeta distribution - Moment generating function, Zeta distribution - The case s = 1

Read more here: » Zeta distribution: Encyclopedia II - Zeta distribution - The case s = 1

Torque has dimensions of force times distance and the SI units of torque are stated as "newton-metres". Even though the order of "newton" and "metre" are mathematically interchangeable, the BIPM (Bureau International des Poids et Mesures) specifies that the order should be N·m not m·N[1]. The joule, the SI unit for energy or work, is also defined as 1 N·m, but this unit is not used for torque. Since energy can be thought of as the result of "force dot distance", energy is always a scalar whereas torque is "force cross distance" and ...

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Torque, Torque - Units, Torque - Special cases and other facts, Torque - Moment arm formula, Torque - Force at an angle, Torque - Static equilibrium, Torque - Torque as a function of time, Torque - Machine torque, Torque - Relationship between torque and power, Torque - Conversion to other units, Torque - Derivation

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Humans are descended from Pak breeders that were stranded on Earth 2.5 million years ago. The protectors that built the colony ship died out from lack of food. The reason why humans evolved beyond the original Pak breeder form (Homo habilis) is that the Tree-of-Life virus requires thallium in the soil to survive and Earth is not adequately thallious; all our Pak Protectors died out mill ...

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Pak Protector, Pak Protector - The Pak species, Pak Protector - Tree Of Life, Pak Protector - Protector behaviour, Pak Protector - The Pak and Humanity, Pak Protector - Narrative purpose

Read more here: » Pak Protector: Encyclopedia II - Pak Protector - The Pak and Humanity

Pak Protectors have an in-built need to look after (or protect, hence the name) their "parent" breeder species. Protectors recognize their own breeder family line by scent, and are instinctively compelled to act in the best interests of breeder relatives. Pak Protectors will fight among themselves to procure land and resources for their respective breeder populations, often leading to the violent deaths of entire Pak family lines. A Pak Protector with no breeders to protect will generally stop eating and quickly starve, although some breeder ...

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Pak Protector, Pak Protector - The Pak species, Pak Protector - Tree Of Life, Pak Protector - Protector behaviour, Pak Protector - The Pak and Humanity, Pak Protector - Narrative purpose

Read more here: » Pak Protector: Encyclopedia II - Pak Protector - Protector behaviour

In the identity one sums over all partitions of the set { 1, ..., n }. If instead, one sums only over the noncrossing partitions, then one gets "free cumulants" rather than conventional cumulants treated above. These play a central role in free probability theory. In that theory, rather than considering independence of random variables, defined in terms of Cartesian products of algebras of random variables, one considers instead "freeness" of random variables, defined in terms of free products of algebras ...

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Cumulant, Cumulant - Cumulants of probability distributions, Cumulant - Some properties of cumulants, Cumulant - Invariance and equivariance, Cumulant - Homogeneity, Cumulant - Additivity, Cumulant - Cumulants and moments, Cumulant - Cumulants and set-partitions, Cumulant - Cumulants of particular probability distributions, Cumulant - Joint cumulants, Cumulant - Conditional cumulants and the law of total cumulance, Cumulant - History, Cumulant - Formal cumulants, Cumulant - One well-known example, Cumulant - Cumulants of a polynomial sequence of binomial type, Cumulant - Free cumulants, Cumulant - External references

Read more here: » Cumulant: Encyclopedia II - Cumulant - Free cumulants

For any sequence { κn : n = 1, 2, 3, ... } of scalars in a field of characteristic zero, being considered formal cumulants, there is a corresponding sequence { μ ′ : n = 1, 2, 3, ... } of formal moments, given by the polynomials above. For those polynomials, construct a polynomial sequence in the following way. Out the polynomial make a new ...

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Cumulant, Cumulant - Cumulants of probability distributions, Cumulant - Some properties of cumulants, Cumulant - Invariance and equivariance, Cumulant - Homogeneity, Cumulant - Additivity, Cumulant - Cumulants and moments, Cumulant - Cumulants and set-partitions, Cumulant - Cumulants of particular probability distributions, Cumulant - Joint cumulants, Cumulant - Conditional cumulants and the law of total cumulance, Cumulant - History, Cumulant - Formal cumulants, Cumulant - One well-known example, Cumulant - Cumulants of a polynomial sequence of binomial type, Cumulant - Free cumulants, Cumulant - External references

Read more here: » Cumulant: Encyclopedia II - Cumulant - Cumulants of a polynomial sequence of binomial type

When placed in an electric (E) or magnetic (B) field, equal but opposite forces arise on each side of the dipole creating a torque τ: for an electric dipole moment p (in coulomb-meters), or for a magnetic dipole moment m (in ampere-square meters). The resulting torque will tend to align the dipole with the applied field. ...

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Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation

Read more here: » Dipole: Encyclopedia II - Dipole - Alignment of a dipole to an applied field

Dam - Failed dams. Baldwin Hills Dam - 1963 Banqiao and Shimantan Dams - 1975 Big Bay Dam, Mississippi - 2004 Buffalo Creek Flood - 1972 Camará Dam - 2004 South Fork Dam - 1889 Kelly Barnes Dam - 1977 Lawn Lake Dam - 1982 Malpasset, Côte d'Azur, France - 1959 Opuha Dam - 1997 Shakidor Dam - 2005 St. Francis Dam, Los Angeles, California - 1928 Taum Sauk reservoir - 2005 Teton Dam - 1976 ...

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Dam, Dam - History, Dam - Types of dams, Dam - Diversionary dams, Dam - Timber dams, Dam - Embankment dams, Dam - Masonry dams, Dam - Cofferdams, Dam - Spillways, Dam - Other considerations, Dam - Environmental impacts, Dam - Stream flow, Dam - Barrier to migration, Dam - Water quality impacts, Dam - Examples of dams, Dam - Failed dams, Dam - Notes

Read more here: » Dam: Encyclopedia II - Dam - Examples of dams

Torque - Moment arm formula. A very useful special case, often given as the definition of torque in fields other than physics, is as follows: The construction of the "moment arm" is shown in the figure below, along with the vectors r and F mentioned above. The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. If the force is perpendicular to the displacemen ...

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Torque, Torque - Units, Torque - Special cases and other facts, Torque - Moment arm formula, Torque - Force at an angle, Torque - Static equilibrium, Torque - Torque as a function of time, Torque - Machine torque, Torque - Relationship between torque and power, Torque - Conversion to other units, Torque - Derivation

Read more here: » Torque: Encyclopedia II - Torque - Special cases and other facts