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related and transform
The conjugation trick can also be used to define a new transform, closely related to the DFT, that is involutary — that is, which is its own inverse.
In the case of the San Andreas fault continental transform, many earthquakes occur away from the plate boundary and are related to strains developed within the broader zone of deformation caused by major irregularities in the fault trace ( e. g., the " Big bend " region ).
The inverse transform, known as Fourier series, is a representation of s < sub > P </ sub >( t ) in terms of a summation of a potentially infinite number of harmonically related sinusoids or complex exponential functions, each with an amplitude and phase specified by one of the coefficients:
The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration ( frequencies ), the Laplace transform resolves a function into its moments.
A delicate analysis of this equation and related properties of the zeta function, using the Mellin transform and Perron's formula, shows that for non-integer x the equation
As derived below, the electron density within the crystal and the diffraction patterns are related by a simple mathematical method, the Fourier transform, which allows the density to be calculated relatively easily from the patterns.
The Fourier transform F ( q ) is generally a complex number, and therefore has a magnitude | F ( q )| and a phase φ ( q ) related by the equation
In spectroscopy the term is used in a related sense to indicate that the experiment is performed with a mixture of frequencies at once and their respective response unravelled afterwards using the Fourier transform principle.
Two related transforms are the discrete sine transform ( DST ), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform ( MDCT ), which is based on a DCT of overlapping data.
The kernel is related to the transform by the equation.
* Discrete cosine transform, a mathematical transform related to the Fourier transform
An encryption algorithm is malleable if it is possible for an adversary to transform a ciphertext into another ciphertext which decrypts to a related plaintext.
( The sequence and its differences are related by a binomial transform.
A related transform is the discrete cosine transform ( DCT ), which is equivalent to a DFT of real and even functions.
A discrete Hartley transform ( DHT ) is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform ( DFT ), with analogous applications in signal processing and related fields.

related and modified
In this geometric description, tidal effects — the relative acceleration of bodies in free fall — are related to the derivative of the connection, showing how the modified geometry is caused by the presence of mass.
These species would become modified over time, but would still be related to species found on the continent, and Darwin observed that this was a common pattern.
Under the Individuals with Disabilities Education Act, special educational support is limited to children and youth falling into one of a dozen disability categories ( e. g., specific learning disability ) and adds that, to be eligible, students may require both special education ( modified instruction ) and related services ( supports such as speech and language pathology ).
It is related to a more general concept called mediated reality, in which a view of reality is modified ( possibly even diminished rather than augmented ) by a computer.
Monsanto admitted a senior manager at Monsanto directed an Indonesian consulting firm to give a $ 50, 000 bribe to a high-level official in Indonesia's environment ministry in 2002 related to the agency's assessment on its genetically modified cotton.
The Court further modified the punishment prong by holding that punishment could survive scrutiny if it was rationally related to other, nonpunitive goals.
Like the related orders Thelyphonida, Amblypygi, and Solifugae, the schizomids use only six legs for walking, having modified their first two legs to serve as sensory organs.
Like the related orders Schizomida, Amblypygi, and Solifugae, the vinegarroons use only six legs for walking, having modified their first two legs to serve as antennae-like sensory organs.
Twin studies have estimated that approximately 20-30 % of an individual ’ s lifespan is related to genetics, the rest is due to individual behaviors and environmental factors which can be modified.
Typically this greeting remains mainly Islam related while Christians have modified it to " Salam ".
The boundaries of this time scale are related to large impact events that have modified the lunar surface, changes in crater form that occur through time, and the size-frequency distribution of craters superposed on geological units.
A related window function is the Kaiser-Bessel derived ( KBD ) window, which is designed to be suitable for use with the modified discrete cosine transform ( MDCT ).
More recently, the main fats concerned have been shown to comprise low density lipoproteins, which contain cholesterol, and accumulate in the vessel wall in oxidised and related modified forms ( oxLDL ).
As the Nahan's " Francolin " is related to the Stone Partridge rather than the true francolins and spurfowl, its name is sometimes modified to Nahan's Partridge.
* Minimal subtraction ( MS ) scheme and the related modified minimal subtraction ( MS-bar ) scheme
requires a thesis of about 45, 000 words and is usually related to the student's institution-focused study, while the Ph. D. thesis requires 80, 000 words and must be suitable for publication in an abridged or modified form.
For example, an adjective can be negated by using the prefix un-( e. g. unable ), in-( e. g. inappropriate ), dis-( e. g. dishonest ), or a-( e. g. amoral ), or through the use of one of a myriad related but rarer prefixes, all modified versions of the first four.
To account for gain compression due to the high power densities in semiconductor lasers, the gain equation is modified such that it becomes related to the inverse of the optical power.
The notion of " interaction " is closely related to that of " moderation " that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the explanatory variable has been moderated or modified by the environmental variable.
* The primary key data can always be modified, even with databases that do not support cascading updates across related foreign keys.
In 2005, the Constitutional Court of Hungary struck down the yearly national budget law in its entirety, because almost half of the paragraphs were not related to state fiscals at all, but modified 44 other existing pieces of legislation, which concerned health regulations, public education and foreign relations.
Several species exhibit adaptations for mutualism with ants by providing modified leaves for domatia (" homes "), much as in the related genus Dischidia ; H. imbricata has leaves that form a concave cup over the tree trunk it climbs up to shelter ants, and H. darwinii has arrangements of bullate leaves on its stems to form shelters.
Based on a modified version of the Mk5 Golf's PQ46 platform, the B6 featured a transverse rather than longitundinal engine layout of its predecessor, like the previous B3 and B4 generations, which were related to the A2 ( Golf ) platform.

related and discrete
The work factor for breaking Diffie-Hellman is based on the discrete logarithm problem, which is related to the integer factorization problem on which RSA's strength is based.
As Hox genes code for transcription factors, this causes different activated combinations of both Hox and other genes in discrete anteroposterior transverse segments of the neural tube ( neuromeres ) and related patterns in surrounding tissues, such as branchial arches, lateral mesoderm, neural crest, skin and endoderm, in the head to tail direction.
" Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
However, complex-data FFTs are so closely related to algorithms for related problems such as real-data FFTs, discrete cosine transforms, discrete Hartley transforms, and so on, that any improvement in one of these would immediately lead to improvements in the others ( Duhamel & Vetterli, 1990 ).
File: Niels Bohr. jpg | Niels Bohr ( 1885-1962 ): used quantum mechanical model ( known as the Bohr model ) of the atom which theorized that electrons travel in discrete orbits around the nucleus, showed how electron energy levels are related to spectral lines, received the Nobel Prize in Physics in 1922.
relies on the similar and related high level of difficulty of the discrete logarithm problem, as does the closely related DSA, which was developed at the US National Security Agency ( NSA ) and published by NIST as a proposed standard.
In particular, most of the popular public key ciphers are based on the difficulty of factoring integers ( or the related discrete logarithm problem, which can also be solved by Shor's algorithm ), including forms of RSA.
Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order.
Einstein explained this conundrum by postulating that the electrons can receive energy from electromagnetic field only in discrete portions ( quanta that were called photons ): an amount of energy E that was related to the frequency f of the light by
This is related to the operation of discrete convolution in two ways.
Its security depends upon the difficulty of a certain problem in related to computing discrete logarithms ( see below ).
Moreover, if the discrete step is not related to object's relative speed, the collision could go undetected, resulting in an object which passes through another, if fast enough.
A related implication of the cosmological principle is that the largest discrete structures in the universe are in mechanical equilibrium.
Functions related to the hardness of the discrete logarithm problem ( either modulo a prime or in a group defined over an elliptic curve ) are not known to be trapdoor functions, because there is no known " trapdoor " information about the group that enables the efficient computation of discrete logs.

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