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List Of Things Named After Joseph Fourier
This is a list of things named after Joseph Fourier: Mathematics * Budan–Fourier theorem, see Budan's theorem * Fourier's theorem * Fourier–Motzkin elimination * Fourier algebra * Fourier division * Fourier method Analysis * Fourier analysis *Fourier series ** Fourier–Bessel series ** Fourier sine and cosine series ** Generalized Fourier series **Laplace–Fourier series, see Laplace series ** Fourier–Legendre series *Fourier transform ( List of Fourier-related transforms): ***Discrete-time Fourier transform (DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane ***Discrete Fourier transform (DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies ***Fast Fourier transform (FFT), a fast algorithm for computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budan–Fourier Theorem
In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan de Boislaurent. A similar theorem was published independently by Joseph Fourier in 1820. Each of these theorems is a corollary of the other. Fourier's statement appears more often in the literature of 19th century and has been referred to as Fourier's, Budan–Fourier, Fourier–Budan, and even Budan's theorem Budan's original formulation is used in fast modern algorithms for real-root isolation of polynomials. Sign variation Let c_0, c_1, c_2, \ldots c_k be a finite sequence of real numbers. A ''sign variation'' or ''sign change'' in the sequence is a pair of indices such that c_ic_j < 0, and either or for all such that . In other words, a sign variation occurs in the sequence at each place where the signs change, when ignoring zeros. For studying t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Fourier Transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced Sampling (signal processing), samples of a function (mathematics), function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex number, complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex number, complex Sine wave, sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier (other)
Fourier may refer to: People named Fourier *Joseph Fourier (1768–1830), French mathematician and physicist *Charles Fourier (1772–1837), French utopian socialist thinker * Peter Fourier (1565–1640), French saint in the Roman Catholic Church and priest of Mattaincourt Mathematics *Fourier series, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function *Fourier analysis, the description of functions as sums of sinusoids *Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series *Fourier operator, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform *Fourier inversion theorem, any one of several theorems by which Fourier inversion recovers a function from its Fourier transform * Short-time Fourier transform or short-term Fourier transform (STFT), a Fourier transform during a short term of time, used in the area of signal analysis *Frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
10101 Fourier
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Fourier University
Joseph Fourier University (UJF, french: Université Joseph Fourier, also known as Grenoble I) was a French university situated in the city of Grenoble and focused on the fields of sciences, technologies and health. It is now part of the Université Grenoble Alpes. Importance According to the 2009 ARWU, Joseph Fourier University is the sixth best university in France. Joseph Fourier University is also the fourth best university in Engineering & IT nationally and 115th globally in QS World University Rankings. The origins of this scientific university can be traced all the way back to 1811 when the scientist Joseph Fourier established a faculty of science in Grenoble. Nowadays, more than 18,000 undergraduate and graduate students participate to the life of this university. More than 2,000 are international or exchange students. Joseph Fourier University is not only famous for its alumni, but also for its commitment to fundamental as well as applied research and innovation. Part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform Spectroscopy
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of ''spectroscopy'' including optical spectroscopy, infrared spectroscopy ( FTIR, FT-NIRS), nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy. There are several methods for measuring the temporal coherence of the light (see: field-autocorrelation), including the continuous-wave and the pulsed Fourier-transform spectrometer or Fourier-transform spectrograph. The term "Fourier-transform spectroscopy" reflects the fact that in all these techniques, a Fourier transform is required to turn the raw data into the actual spectrum, and in many of the cases in optics involving interferometers, is based on the Wiener– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Optics
Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or '' superposition'', of plane waves. It has some parallels to the Huygens–Fresnel principle, in which the wavefront is regarded as being made up of a combination of spherical wavefronts (also called phasefronts) whose sum is the wavefront being studied. A key difference is that Fourier optics considers the plane waves to be natural modes of the propagation medium, as opposed to Huygens–Fresnel, where the spherical waves originate in the physical medium. A curved phasefront may be synthesized from an infinite number of these "natural modes" i.e., from plane wave phasefronts oriented in different directions in space. Far from its sources, an expanding spherical wave is locally tangent to a planar phase front (a single plane wave out of the infinite spectrum), which is transverse to the radial direction of propagation. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier's Law Of Heat Conduction
Conduction is the process by which heat is Heat transfer, transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it. In the absence of an opposing external driving energy source, within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached, temperature becoming more uniform. In conduction, the heat flow is within and through the body itself. In contrast, in heat transfer by thermal radiation, the transfer is often between bodies, which may be separated spatially. Heat can also be transferred by a combination of conduction and radiation. In solids, conduction is mediated by the combination of vibrations and collisi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Inversion Theorem
In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely. The theorem says that if we have a function f:\R \to \Complex satisfying certain conditions, and we use the convention for the Fourier transform that :(\mathcalf)(\xi):=\int_ e^ \, f(y)\,dy, then :f(x)=\int_ e^ \, (\mathcalf)(\xi)\,d\xi. In other words, the theorem says that :f(x)=\iint_ e^ \, f(y)\,dy\,d\xi. This last equation is called the Fourier integral theorem. Another way to state the theorem is that if R is the flip operator i.e. (Rf)(x) := f(-x), then :\mathcal^=\mathcalR=R\mathcal. The theorem holds if both f and its Fourier transform are absolutely integrable (in the Lebesgue sense) and f is continuous at the point x. However, even under more genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier–Mukai Transform
In algebraic geometry, a Fourier–Mukai transform ''Φ''''K'' is a functor between derived categories of coherent sheaves D(''X'') → D(''Y'') for schemes ''X'' and ''Y'', which is, in a sense, an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than i ... along a kernel object ''K'' ∈ D(''X''×''Y''). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type. These kinds of functors were introduced by in order to prove an equivalence of categories, equivalence between the derived categories of coherent sheaves on an abelian variety and its dual abelian variety, dual. That equivalence is analogous to the classical Fourier transform that gives an isomorphism between Distribution (mathematics), tempered distributions on a finite-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier–Deligne Transform
In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ''ℓ''-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29, 1976 in a letter to David Kazhdan as an analogue of the usual Fourier transform. It was used by Gérard Laumon to simplify Deligne's proof of the Weil conjectures In mathematics, the Weil conjectures were highly influential proposals by . They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory. .... References * * * Algebraic geometry {{abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
