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	Spectral sequence - Wikipedia, the free encyclopedia
		Spectral sequences are a generalization of exact sequences, and since their introduction by Jean Leray in 1946, they have become an important research tool, particularly in homotopy theory.
		Spectral sequences were found in diverse situations, and they gave intricate relationships among homology and cohomology groups coming from geometric situations such as fibrations and from algebraic situations involving derived functors.
		A doubly graded spectral sequence has a tremendous amount of data to keep track of, but there is a common visualization technique which makes the structure of the spectral sequence clearer.
	en.wikipedia.org /wiki/Spectral_sequence (2657 words)

	Stellar classification - Wikipedia, the free encyclopedia
		The Yerkes spectral classification, also called the MKK system from the authors' initials, is a system of stellar spectral classification introduced in 1943 by William Wilson Morgan, Phillip C. Keenan and Edith Kellman of Yerkes Observatory.
		This classification is based on spectral lines sensitive to stellar surface gravity which is related to luminosity, as opposed to the Harvard classification which is based on surface temperature.
		Since the radius of a giant star is much larger than a dwarf star while their masses are roughly comparable, the gravity and thus the gas density and pressure on the surface of a giant star are much lower than for a dwarf.
	en.wikipedia.org /wiki/Spectral_classification (2611 words)

	Encyclopedia :: encyclopedia : Integer sequence (Site not responding. Last check: 2007-11-01)
		An integer sequence is a definable sequence, if there exists some statement P(x) which is true for that integer sequence x and false for all other integer sequences.
		The set of computable integer sequences and definable integer sequences are both countable, with the computable sequences a proper subset of the definable sequences.
		The set of all integer sequences is uncountable; thus, almost all integer sequences are uncomputable and cannot be defined.
	www.hallencyclopedia.com /Integer_sequence (202 words)

	A Users Guide to Spectral Sequences (Cambridge Studies in Advanced Mathematics) (Site not responding. Last check: 2007-11-01)
		Spectral sequences have generally been thought of as being complicated, esoteric constructions, due mainly to the way they are presented in the mathematical literature.
		The "two-index" property of spectral sequences in this case arises from the fact that the associated graded vector space to the filtered graded vector space is in fact `bigraded.
		More formally, the spectral sequence is a sequence of differential bigraded vector spaces, where each bigraded vector space in the sequence is equipped with a linear mapping that is also a differential.
	www.programming-reviews.com /A_Users_Guide_to_Spectral_Sequences_Cambridge_Studies_in_Advanced_Mathematics_0521567599.html (1109 words)

	Spectral Sequences Book (Site not responding. Last check: 2007-11-01)
		An introduction to the Serre spectral sequence, with a number of applications, mostly fairly standard.
		What is written so far is just the derivation of the basic spectral sequence (additive structure only), after the necessary preliminaries on spectra, and illustrated by a few computations of stable homotopy groups of spheres.
		At present all that is written is the construction of the spectral sequences, without any applications.
	www.math.cornell.edu /~hatcher/SSAT/SSATpage.html (140 words)

	Books on Spectral Sequences (Site not responding. Last check: 2007-11-01)
		Spectral Sequences are among the most elegant and powerful methods of computation in mathematics.
		The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence.
		This book is devoted to Spectral Sequences related to cobordism theory: the spectral sequence of a singularity, the Adams-Novikov spectral sequence, and applications of these and other sequences to the investigation of cobordism rings.
	books.bankhacker.com /Spectral+Sequences (602 words)

	The Spectral Sequence as a Temperature Sequence (Site not responding. Last check: 2007-11-01)
		On the other hand, spectral lines associated with molecules are only found for spectral classes K and M. This is because these correspond to low surface temperatures, and molecules can only hold together in stars with relatively low surface temperatures.
		Generally, the above sequence is a surface temperature sequence, with high temperatures toward the left (O and B stars) and low temperatures to the right (K and M stars).
		Since the color index is also a measure of surface temperature, this sequence may also be interpreted in terms of color index, with algebraically smaller values of the color index to the left and larger values to the right.
	csep10.phys.utk.edu /astr162/lect/stars/spectra.html (397 words)

	PlanetMath: spectral sequence
		Cohomology spectral sequences are identical, except that all the arrows go in the other direction.)
		Most interesting spectral sequences are upper right quadrant, meaning that
		This is version 5 of spectral sequence, born on 2003-08-21, modified 2005-03-02.
	planetmath.org /encyclopedia/SpectralSequence.html (150 words)

	Properties of Stars
		The spectral lines seen for different types of stars are summarized in the Main Sequence Star Properties table below.
		Each spectral type is subdivided into 10 intervals, e.g., G2 or F5, with 0 hotter than 1, 1 hotter than 2, etc. About 90% of the stars are called main sequence stars.
		Notice the trends in the table: as the temperature of the main sequence star increases, the mass and size increase.
	www.astronomynotes.com /starprop/s12.htm (1409 words)

	Spectral classification of late-type dwarfs
		Spectral classification is astronomical botany: it is an ordering and organisation of observations based solely on appearance.
		A spectral classification system tied to physical parameters must change with each revision of the theoretical models, and a changing system makes it very difficult to establish the readily-understood common reference system which is essential for spectral types to be of any use.
		Spectral class M is characterised by the presence of strong absorption bands due to the diatomic molecule titanium oxide, TiO (Morgan, Keenan \& Kellman, 1943).
	www-int.stsci.edu /~inr/ldwarf.html (2629 words)

	PlanetMath: Leray spectral sequence
		The Leray spectral sequence is a special case of the Grothendieck spectral sequence regarding composition of functors.
		Cross-references: direct image, spectral sequence, abelian groups, sheaf, topological spaces, continuous map, functors, composition, Grothendieck spectral sequence
		This is version 3 of Leray spectral sequence, born on 2001-12-12, modified 2004-03-31.
	www.planetmath.org /encyclopedia/LeraySpectralSequence.html (89 words)

	Amazon.com: A User's Guide to Spectral Sequences (Cambridge Studies in Advanced Mathematics): Books: John McCleary (Site not responding. Last check: 2007-11-01)
		The author introduces spectral sequences as a tool for computing the homology or cohomology (which he labels as H*) of a space or an algebraic invariant assigned to a space or algebraic object.
		The Eilenberg-Moore spectral sequence also arises in the study of fibrations, when the cohomology of the base space and the cohomology of the total space are known and one wants to compute the cohomology of the fiber.
		The Bockstein spectral sequence arose in the study of Lie groups, and the author gives the details of the construction of this spectral sequence and its application to H-spaces.
	www.amazon.com /exec/obidos/tg/detail/-/0521561418?v=glance (1946 words)

	Sky Publishing - The Spectral Types of Stars (Site not responding. Last check: 2007-11-01)
		Appended to the basic spectral type may be letters for chemical peculiarities, an extended atmosphere, unusual surface activity, fast rotation, or other special characteristics.
		Spectral types on the blue end were called "early" and those on the red end "late." These terms are still used today, though the incorrect idea of stellar evolution they embody -- that stars simply cool with age -- has been obsolete for generations.
		Stars arrive on the main sequence soon after they are born, and this is where they spend most of their lives.
	www.wwnorton.com /astro21/sandt/startypes.html (2238 words)

	Search Results for Sequence*
		Then the "curious property" is that each member of the sequence is equal to the rational whose numerator is the sum of the numerators of the fractions on either side, and whose denominator is the sum of the denominators of the fractions on either side.
		In 1907 Ernst Fischer studied orthonormal sequences of functions and gave necessary and sufficient conditions for a sequence of constants to be the Fourier coefficients of a square integrable function.
		Serre uses spectral sequences to the study of the relations between the homology groups of fibre, total space and base space in a fibration.
	www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=Sequence*&CONTEXT=1 (5617 words)

	Spectra
		It was noted very early that the spectral sequence in this form correlates with color, ranging from a blue tint for O and B stars to reddish for class M. Since color depends on surface temperature, so must the spectral class.
		Decimal subdivisions of the spectral classes go toward lower temperature, for example, A0 lies at the hot end of class A near a temperature of 10,000 K, while A9 is at the cool end near 7200 K. The Sun, with a temperature of 5800 K, is class G2.
		The differences in stellar spectra, at least for main sequence stars, are caused almost entirely by differences in ionization (after all, if sodium is all ionized, the absorptions of neutral sodium will not be present) and the by the way in which the absorption efficiencies change with temperature.
	www.astro.uiuc.edu /~kaler/sow/spectra.html (5857 words)

	[No title]
		From the phantom projective class we derive a generalized Milnor sequence for filtered diagrams of finite spectra, and from this it follows that the group of phantom maps from X to Y can always be described as a lim 1 group.
		And in the third part, we show that the Adams spectral sequence with respect to the ghost projective class in a category of A1 modules over an A1 ring is in fact a universal coefficient spectral sequence, and we explain how this gives new lower bounds on the ghostlength of a spectrum.
		Then the phantom spectral sequence abutting to D(M;N) is the same as the spectral se quence (9.4) described in the previous part of this section.
	jdc.math.uwo.ca /papers/ideals.txt (14824 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		(Here is the origin of the term spectral and where the real question lies.) Koszul made a remarkable clarification of the algebra of a spectral sequence which he termed a sequence of homologies.
		Serre coined suite spectrale to cover the case of a homology spectral sequence.
		The inventor of the spectral sequence, before writing out the full proofs that it did what it was supposed to exclaimed "I 'spect it'll work" (you have to say it to make "I expect it will" sound like "spectral".
	www.lehigh.edu /~dmd1/il214.txt (406 words)

	#5 - Color-Magnitude Diagrams
		However, from spectral types G to K to M (the "late" spectral types) it appeared that the luminosity increased while the temperature continued to decrease, indicating the existence of giant, cool, yellowish and reddish stars.
		While the dwarf red stars continued the sequence of decreasing temperature and luminosity all the way from B to K, the giant stars formed a divergent group, beginning at class K. Henry Norris Russell at Princeton was at the same time also investigating the co-relations between spectral type and other properties of stars.
		One important difference, however, was the tendency for open cluster main sequence stars to be of earlier spectral type (brighter, and higher up on the main sequence) than those in the solar neighborhood.
	astrowww.phys.uvic.ca /astrocourses/a120/A120/lab5.html (2232 words)

	A User's Guide to Spectral Sequences - Cambridge University Press
		Spectral sequences are among the most elegant, most powerful, and most complicated methods of computation in mathematics.
		The heart of the book is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence.
		Spectral sequences in algebra, algebraic geometry and algebraic K-theory; 12.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521567599 (278 words)

	[No title]
		A spectral sequence for string cohomology Marcel Bökstedt & Iver Ottosen* 5 December 2002 Abstract Let X be a 1-connected spaces with free loop space X. We in- troduce two spectral sequences converging towards H(X; Z=p) and H((X)hT; Z=p).
		This is a remarkable spectral sequence that under fortunate circumstances converges to the homology of the total space of a cosimplicial space.
		In order to handle the other spectral sequence we need some results on cosimplicial spaces which are presented in the next section.
	www.math.purdue.edu /research/atopology/Bokstedt-Ottosen/stringV4.txt (9403 words)

	The Webfooted Astronomer: Secrets of the Harvard Classification Revealed
		Strong spectral lines of hydrogen begin to appear a B0 and increase in strength as the spectral class reaches B9.
		Spectral lines due to hydrogen begin to weaken, the K line of calcium continues to get stronger, and characteristic spectral lines (neutral and ionized) of such as Fe, Mn, and Na begin to appear.
		The range of this numeric code is from 0 to 9 and indicates how far to the left or right a star is in its spectral sequence.
	www.seattleastro.org /webfoot/feb00/pg2.htm (767 words)

	PlanetMath: Grothendieck spectral sequence
		then there is a spectral sequence for each object
		Cross-references: theory, algebra, Leray spectral sequence, sheaf, sequence, acyclic, injectives, global section, direct image, functor, continuous map, abelian groups, sheaves, category, topological spaces, spectral sequence, objects, injective objects, abelian categories, left exact functors
		This is version 5 of Grothendieck spectral sequence, born on 2001-12-12, modified 2003-07-19.
	planetmath.org /encyclopedia/GrothendieckSpectralSequence.html (157 words)

	A Spectral Sequence for Motivic Cohomology, by Spencer Bloch and Steve Lichtenbaum
		The purpose of this paper is to construct a spectral sequence from the motivic cohomology of a field F to its algebraic K-theory: Here we define motivic cohomology via higher Chow groups.
		We show that, assuming a rather innocuous looking "moving lemma" called Theorem A, this complex is an exact couple, and the resulting spectral sequence has the desired form.
		Sections 2 through 6 of the paper are devoted to proving theorem A. Finally, in section 7, we prove that the higher Chow complex shifted to the right 4 steps and then truncated so the resulting complex is supported in degrees 1 and 2, is quasi-isomorphic to the complex Gamma(2) introduced by Lichtenbaum.
	www.mathematik.uni-osnabrueck.de /K-theory/0062 (232 words)

	The Harvard Spectral Sequence (Site not responding. Last check: 2007-11-01)
		By late in the last century it was realized that the spectra of stars (in particular, their patterns of absorption lines) had systematic features that could be classified into what came to be known as the Harvard Spectral Sequence.
		The sequence was denoted by a series of letters O, B, A,...
		For even finer gradation in the spectral sequence, each category in this classification can be subdivided into 10 subclasses using numbers from 0 to 9.
	csep10.phys.utk.edu /astr162/lect/stars/harvard.html (126 words)

	Dwyer: Exotic convergence... (Site not responding. Last check: 2007-11-01)
		This paper uses machinery from Strong convergence of the Eilenberg-Moore spectral sequence to study the ordinary homology Eilenberg-Moore spectral sequence (EMSS) of a fibration in some cases in which the spectral sequence does not converge strongly.
		This does not mean that at E-infinity the spectral sequence displays exactly the graded object associated to the filtration of the homology of F by powers of I, but it does mean that the topology on each homology group of F induced by the abutment filtration is equivalent to the I-adic topology.
		The exact statement is easiest to express in terms of towers of abelian groups: the natural map from the I-adic completion tower of each homology group of F to the corresponding abutment tower of the spectral sequence is a pro-isomorphism.
	www.nd.edu /~wgd/Html/Exotic.Convergence.EMSS.html (228 words)

	[No title]
		The E_{2}-term of this spectral sequence consists of the right derived functors of product in the category of E_{}E-comodules, and the spectral* sequence always converges (with a horizontal vanishing line at E_{infty}) when E is the Johnson-Wilson theory E(n) and each factor of the product is L_{n}-local.
		This spectral sequence is relevant to the chromatic splitting conjecture.
		The computation is based on the Koschorke's exact singularity sequence for groups of normal bordisms and the remarkable properties of the essentially unique, balanced binary Gray code in dimension 4.
	www.lehigh.edu /~dmd1/mh110.txt (643 words)

	Dwyer: Strong convergence... (Site not responding. Last check: 2007-11-01)
		This paper proves that the ordinary homology Eilenberg-Moore spectral sequence (EMSS) of a fibration converges strongly if and only if the monodromy action of the fundamental group of the base on the homology of the fibre is nilpotent.
		The proof of the other implication proceeds by showing that the abutment of the EMSS fits into a spectral sequence equation: there is a Serre spectral sequence converging from the homology of the base with coefficients in the EMSS abutment to the homology of the total space.
		The techniques used here are applied again in Exotic convergence of the Eilenberg-Moore spectral sequence to obtain some information about the abutment of the EMSS in cases in which it does not converge strongly.
	www.nd.edu /~wgd/Html/Strong.Convergence.EMSS.html (382 words)

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