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In mathematics, the '''Bockstein spectral sequence''' is a [[spectral sequence]] relating the homology with mod&nbsp;''p'' coefficients and the h This gives the first page of the spectral sequence: we take <math>E_{s,t}^1 = H_{s+t}(C \otimes \Z/p)</math> with the ...

{{short description|On when a morphism of spectral sequences in homological algebra is an isomorphism}} ...her Zeeman]],{{sfnp|Zeeman|1957}} gives conditions for a [[morphism]] of [[spectral sequence]]s to be an isomorphism. ...

...[mathematics]], the '''Čech-to-derived functor spectral sequence''' is a [[spectral sequence]] that relates [[Čech cohomology]] of a [[sheaf (mathematics)|shea ...to the cover <math>\mathfrak{U}</math>. Then the Čech-to-derived functor spectral sequence is:{{sfn|Godement|1973|loc=Théorème 5.4.1}} ...

[[Image:DPSS figure.svg|thumb|230px|The three leading Slepian sequences for T=1000 and 2WT=6. Note that each higher order sequence has an extra zer ...maximally localized on a given [[frequency]] interval, as measured by the spectral concentration. ...

In [[mathematics]], the '''Freudenthal spectral theorem''' is a result in [[Riesz space|Riesz space theory]] proved by [[Ha ...operator]]s can all be shown to follow as special cases of the Freudenthal spectral theorem. ...

...]]''' (named after [[Alfred Frölicher]], who actually discovered it). This spectral sequence describes the precise relationship between the [[Dolbeault cohom ==Description of the spectral sequence== ...

...math> with the following [[decomposition of spectrum (functional analysis)|spectral decomposition]]: ...ta}^{X^{n}}</math> to refer also to the set of <math>\delta</math>-typical sequences: ...

...onal homotopy theory]], the '''Halperin conjecture''' concerns the [[Serre spectral sequence]] of certain fibrations. It is named after the [[Canadian]] mathem ...<math> F </math> has non-zero [[Euler characteristic]]), then the [[Serre spectral sequence]] associated to the fibration collapses at the <math> E_2 </math> ...

...Spectrum (topology)|spectra]] yielding a tool for constructing the [[Adams spectral sequence]]. Essentially, the idea is to take a connective spectrum of finit ...um <math>MU</math>, and is used in the construction of the [[Adams–Novikov spectral sequence]]<ref name=":0" />^{pg 49}. ...

...by performing [[Fourier analysis]] on signals derived from segments of DNA sequences. Because of its predictive power, it has been used as a preliminary indicat ...em after the symbolic string is properly mapped to one (or more) numerical sequences. The reason for this periodicity is due to the biased distribution towards ...

...n fiber]]s. It also naturally arises in many [[spectral sequence]]s; see [[spectral sequence#Edge maps and transgressions]]. ...

...he fiber <math>f^{-1}(X)</math>, which is a subcategory, consists of exact sequences whose third term is ''X''. This makes ''E'' a [[fibered category|category f ...and <math>H_p(X, \Z ) \simeq H_p(Y, \Z ), p \ge 0</math>. Now, the [[Serre spectral sequence]]s for <math>Ff \to X \to Y</math> and <math>* \to Y \to Y</math> ...

...ence space of an operator ideal to taking [[Cesàro mean]]s. This explicit spectral characterisation reduces problems and questions about commutators and [[sin </ref> As a student American mathematician Gary Weiss began to investigate spectral conditions for commutators of [[Hilbert–Schmidt operators]].<ref name="GW1" ...

...braic topology, he specialised in [[homotopy theory]]. The ''Bousfield-Kan spectral sequence'', [[Bousfield localization]] of [[spectrum (topology)|spectra]] a | title=The homotopy spectral sequence of a space with coefficients in a ring ...

...matrix''' is a graphical representation of [[similarity measure|similar]] sequences in a data series. ...nce matrix]]), [[correlation]], or comparison of local [[histogram]]s or [[spectral properties]] (e.g. IXEGRAM<ref>{{cite journal|author1= M. A. Casey |author2 ...

...ecially continuous processes with high frequency components to their power spectral densities, may have multiple upcrossings or multiple peaks in rapid success ...'')}} with [[variance]] {{math|σ_''y''²}} and [[power spectral density]] {{math|Φ_''y''(''f'')}}, where {{mvar|f}} is a frequenc ...

...djoint Jacobi operators acting on the [[Hilbert space]] of square summable sequences over the [[positive integers]] <math>\ell^2(\mathbb{N})</math>. In this cas ...gree ''n'' and these polynomials are [[orthonormal]] with respect to the [[spectral measure]] corresponding to the first basis vector <math>\delta_{1,n}</math> ...

...ery nonzero <math>\lambda\in\sigma(T)</math> is an eigenvalue. This same "spectral theorem" consisting of (i)-(iv) is satisfied for inessential operators in ' ...math>, is strictly singular. Here <math>c_0</math> is the Banach space of sequences converging to zero. This is a corollary of Pitt's theorem, which states th ...

The '''spectral test''' is a statistical test for the quality of a class of [[pseudorandom }}</ref> The spectral test compares the distance between these planes; the further apart they are ...

...of [[Lp space#The p-norm in countably infinite dimensions|square-summable sequences]] and spaces of [[Hilbert space#Examples|square-integrable functions]]. Lin Singular traces measure the asymptotic spectral behaviour of operators and have found applications in the [[noncommutative ...