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Topic: Standard basis

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	Standard basis -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		There is a standard basis also for the ring of (A mathematical expression that is the sum of a number of terms) polynomials in n indeterminates over a (A piece of land cleared of trees and usually enclosed) field, namely the (additional info and facts about monomial) monomials.
		The existence of other 'standard' bases has become a topic of interest in (additional info and facts about algebraic geometry) algebraic geometry, beginning with work of (additional info and facts about Hodge) Hodge from 1943 on (additional info and facts about Grassmannian) Grassmannians.
		The idea of standard basis in the (additional info and facts about universal enveloping algebra) universal enveloping algebra of a (additional info and facts about Lie algebra) Lie algebra is established by the (additional info and facts about Poincaré-Birkhoff-Witt theorem) Poincaré-Birkhoff-Witt theorem.
	www.absoluteastronomy.com /encyclopedia/s/st/standard_basis.htm (289 words)

	Gold standard - Open Encyclopedia (Site not responding. Last check: 2007-10-09)
		The gold standard may also be viewed as a monetary system in which changes in the supply and demand of gold determine the value of goods and services in relation to their supply and demand.
		Through the 1860-1871 period various attempts to resurrect bi-metallic standards were made, including one based on the gold and silver franc, however, with the rapid influx of silver from new deposits, the expectation of scarcity of silver ended.
		Bryan argued against the gold standard in his Cross of gold speech in 1896, comparing the gold standard (and specifically its effects on western farmers) to the crown of thorns worn by Jesus Christ at his crucifixion.
	open-encyclopedia.com /Gold_standard (5588 words)

	Gold standard - Wikipedia, the free encyclopedia
		The gold standard is a monetary system in which the standard economic unit of account is a fixed weight of gold and currency issuers guarantee, under specified rules, to redeem notes in that amount of gold.
		To understand the adoption of the international gold standard in the late 19th century, it is important to follow the events of the late 18th century and early 19th.
		Through the 1860–1871 period various attempts to resurrect bi-metallic standards were made, including one based on the gold and silver franc, however, with the rapid influx of silver from new deposits, the expectation of scarcity of silver ended.
	en.wikipedia.org /wiki/Gold_standard (7245 words)

	Gold standard
		The gold standard may also be viewed as a monetary system in which changes in the gold price are accepted as the sole measure of inflation/deflation and where monetary policy operates to vigourously oppose either.
		By creating a standard unit of account which was easily redeemable, relatively stable in quantity, and verifiable in its purity, the gold standard ushered in a period of dramatically expanded trade between industrializing nations, and "periphery" nations which produced agricultural goods - the so called "bread baskets".
		While much of what is written about the gold standard comes from the point of view of what are often derrisively referred to as "gold bugs", the "neo-liberal" economic policies which are currently favored by Western economists owe a great deal to the classical period gold standard.
	www.brainyencyclopedia.com /encyclopedia/g/go/gold_standard.html (4835 words)

	No Title (Site not responding. Last check: 2007-10-09)
		A set of basis vectors must be independent, because if they were not, one of them could be written as a linear combination of the others; such a vector could then be removed from the original set to form a smaller spanning set for the subspace.
		Once a basis is available for a subspace, every vector in that subspace has a unique representation as a linear combination of the basis vectors.
		The coordinates of some vector, relative to a basis, are the multipliers that would be used to express the original vector as a linear combination of the basis vectors.
	www.sci.wsu.edu /math/faculty/genz/220v/lessons/l08/l08.html (381 words)

	Spinoff of Brand Insulations, Inc. (Site not responding. Last check: 2007-10-09)
		Accordingly, such distributions are not taxable as dividends and the value thereof is to be applied to reduce the tax basis of the Standard stock held by you.
		Standard stockholders are required to allocate their tax basis in Standard stock on October 10, 1985 between the Standard stock and the Brand securities received in proportion to the fair market values of all such securities on the distribution date.
		For stockholders who held shares of Standard Shares with a remaining basis of zero, the basis of each of the Brand stocks received with respect to such zero basis shares of Standard is zero.
	www.ademco.com /pittway/spinoff_brand.htm (311 words)

	[No title]
		In case you have performed calculations in which the basis set quality was very important it may be advisable to repeat some calculations with the improved basis sets in order to check that this does not influence your conclusions.
		The standard basis sets that are provided are sufficiently flexible to accommodate the needs of almost every type of calculation of almost every user.
		After selecting the basis set for the occupied shell, the user has to specify whether additional polarization, diffuse, or contracted basis functions should be added (also tight functions for ZORA calculations can be added, but this has not been properly tested).
	www.scm.com /Doc/Doc2002.02/BasissetsSummary.doc (5492 words)

	Standard ML of NJ User's Guide (Site not responding. Last check: 2007-10-09)
		Standard ML of New Jersey (SML/NJ) is a compiler, interactive system, and programming environment for the Standard ML language.
		Standard ML of New Jersey supports some extensions to the Standard ML language, such as first-class continuations, higher-order functors, and so on.
		The Standard ML '97 language is almost, but not quite, compatible with the 1990 definition supported by earlier versions of SML/NJ; the conversion guide explains the differents, and gives examples of how to upgrade existing SML'90 programs.
	flint.cs.yale.edu /cs421/smlnj/doc (354 words)

	Rational Basis v. Intermediate Scrutiny .:.
		Lee Optical standard makes it IMPOSSIBLE to invalidate a law, because the irrational satisfies a "rational standard." Williamson is clearly not the standard in Turner, which puts some force behind the question whether the penological interest is sufficiently legitimate.
		That standard is in the intermediate range, as opposed to either end of the spectrum.
		It is not the Williamson, its only-unconstitutional-if-you-actually-die-laughing-when-you-read-it standard.
	lists.ucla.edu /pipermail/religionlaw/2005-June/018684.html (773 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The morphed orthogonal basis of the second standard head model is combined with an un-morphed expression vector of the second standard head model and the orthogonal basis of the target head to provide an animation vector for the target head.
		In general the target face basis, M', is a function of the standard face basis M and the deformation function.
		These orthogonal basis matrices may be reduced to a rank r, and hence to an m by r square matrix by removing the columns of the orthogonal basis that do not contain significant portions of information related to the images.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/99048.011227&ELEMENT_SET=DECL (5292 words)

	Standard ML Basis Library (Site not responding. Last check: 2007-10-09)
		The SML Basis Library provides interfaces and operations for basic types, such as integers and strings, support for input and output (I/O), interfaces to basic operating system interfaces, and support for standard datatypes, such as options and lists.
		The SML Basis Library is also published as a book by Cambridge University Press.
		These webpages are organized as follows: the overview page describes the different kinds of interfaces provided by the SML Basis Library as well as which components are required and optional.
	www.standardml.org /Basis (386 words)

	Re: Definitive Standard Basis Library for SML?
		There is also a basis library mailing list where implementors discuss clarifications and possible changes to the spec.
		For MLton, we keep a snapshot of the basis specification that corresponds to the latest MLton release at http://www.mlton.org/basis/ Unfortunately, because of redistribution restrictions in the basis spec license, we can not include the spec with the MLton distribution itself.
		The output is generated automatically from MLton's basis library sources, and so is guaranteed to match the version of MLton you are using.
	www.talkaboutprogramming.com /group/comp.lang.ml/messages/6754.html (488 words)

	Programming in Standard ML (Site not responding. Last check: 2007-10-09)
		The Definition of Standard ML (Revised) by Robin Milner, Mads Tofte, Robert Harper, and David MacQueen (MIT Press, 1997) constitutes the official definition of the language.
		It is supplemented by the Standard ML Basis Library, which defines a common basis of types that are shared by all implementations of Standard ML.
		Standard ML of New Jersey is a comprehensive implementation, and is the most widely used.
	www.cs.cmu.edu /People/rwh/introsml (232 words)

	Standard (Gröbner) Basis Computations (Site not responding. Last check: 2007-10-09)
		The commands in this chapter compute a standard basis and/or syzygy module of a submodule of a free module corresponding to the columns of a matrix.
		For each computation command except res and nres, the result is a matrix together with a standard basis for the corresponding submodule.
		The first matrix of the result has a standard basis computed, but the matrix is the original matrix.
	www.math.columbia.edu /online/Macaulay1-rel0994-html/node116.html (325 words)

	The phase cell representation
		For example, the standard basis consists of the cover by the tallest, thinnest patches allowed by the sampling interval.
		The Fourier transform may be regarded as the transpose of the standard basis, in the sense that the cells are transposed by interchanging time and frequency (cf.
		The wavelet basis is an octave-band decomposition of the phase plane, as in figure A.7.
	www.math.yale.edu /users/majid/manual/node25.html (409 words)

	Environmental Protection Agency > Basic Concepts in Environmental Sciences > Module 2 > Oxygen Basis Conversions
		Pollutant concentrations specified in U.S. air pollution regulations are often expressed on a 7% oxygen basis.
		The standard equation for the correction of concentration to a specific oxygen level is as follows:
		U.S. air pollution regulations often state pollution standards on a 7% oxygen basis.
	www.epa.gov /eogapti1/module2/oxygen/oxygen.htm (431 words)

	w_hw7
		Just be able to write down correctly the last example from lecture notes on 6-M showing how a linear transformation derived from a square matrix can have a simpler matrix with respect to a basis different from the standard basis, applied at both ends.
		There will be different numbers instead of 3,2,2,3 but the basis will be the same.
		One easy case you know how to do is where the first basis is the standard basis and the second is possibly ``nonstandard'': Then the columns of
	www.math.ucla.edu /~baker/115ah.1.01f/handouts/w_hw7/node1.html (367 words)

	Using Poly/ML - Chapter 2: The Standard ML Initial Basis
		This chapter describes the Initial Basis as implemented in the original 1990 definition of Standard ML.
		These are the standard mathematical functions; if the argument is outside the domain of the function or if the result is too large to represent then the corresponding exception will be raised.
		The provision of relational operators on strings is a non-standard extension to the Standard Initial Basis and may not be supported by other implementations of Standard ML.
	www.polyml.org /docs/Basis2.html (1128 words)

	Tensor Permutations in Distributed Memory
		The standard basis elements serve as address locations for the coordinates of a vector - the i-th coordinate is located in the i-th placeholder, indicated by
		, in the standard basis corresponds to listing the contents of a vector by their addresses.
		The action of a tensor permutation is determined by its action on the basis vectors, and this action is more easily computed by writing the basis as a tensor product of basis elements.
	www.mcs.drexel.edu /~jjohnson/sc98/node3.html (444 words)

	Singular Manual: Term orderings (Site not responding. Last check: 2007-10-09)
		is a general standard basis algorithm for any monomial ordering which is compatible with the natural semi-group structure of the exponents.
		The intersection of the zero-sets is the zero-set of the given ideal.
		The next commands require the input to be a standard basis.
	www.mathematik.uni-kl.de /~zca/Singular/Manual/1-3-7/sing_32.htm (756 words)

	Introduction
		By design, the Basis Library is meant to provide a fairly rich collection of general-purpose modules that can serve as the basis for applications programming or for more domain-specific libraries.
		One criterion for inclusion in the Basis Library is that a type or value requires compiler or run-time system support.
		Within the basis library, the only use of the latter convention occurs with the months and weekdays in Date.
	ei.cs.vt.edu /~cs3304/smlnj/basis/pages/intro-chapter.html (1617 words)

	Change of Basis and Coordinate Transformations (Site not responding. Last check: 2007-10-09)
		The goal of this section of the lab is to talk about linear changes of coordinates, that is, switching from one basis of a vector space to a different basis.
		Given coordinates of a point in one basis, we will be able to obtain the coordinates of that point in another basis by applying the change of coordinates matrix to it.
		Simply use the vectors in the basis and the coordinates of the vector in that basis).
	math.ucsd.edu /~math20f/Fall/Lab6F/Lab6F.html (1777 words)

	qring #tex2html_wrap_inline5607# standard basis #tex2html_wrap_inline5609# #tex2html_wrap_inline5611# result ring ... (Site not responding. Last check: 2007-10-09)
		Given a standard basis of an ideal, create a new ring where all operations in this new ring will be done modulo this ideal.
		A warning message is given if the first argument is not a standard basis.
		Creating a quotient ring where the base ring of the standard basis is already a quotient ring is legal.
	www.math.columbia.edu /online/Macaulay1-rel0994-html/node47.html (145 words)

	Definitive Standard Basis Library for SML?
		It has been some time since I used Standard ML in my daily work, but over the last couple of years I have formed the impression that the Standard Basis Library has become a moving target.
		I have formed this impression because when I download a new version of an implementation, my old programs don't always work---and inevitably the reason is because of a change in the Basis Library.
		What is worse is that my students are likely to trip over differences in the widely advertised basis specification and the actual implementations that are available to them.
	www.talkaboutprogramming.com /group/comp.lang.ml/messages/6742.html (269 words)

	Matrix Linear Transformations
		Examples 2 to 4 depend on the fact that we used the standard basis to represent the vectors in each vector space.
		Note that the difference between (d) and (e) is that the order of the basis in the range is reversed.
		The matrix is unique to the pair of bases since coordinate vectors are unique in a given basis.
	distance-ed.math.tamu.edu /Math640/chapter4/node4.html (590 words)

	8. Effective Core Potentials (Site not responding. Last check: 2007-10-09)
		Effective core potentials (ECPs) are a useful means of replacing the core electrons in a calculation with an effective potential, thereby eliminating the need for the core basis functions, which usually require a large set of Gaussians to describe them.
		All directives that are in common with the standard Gaussian basis set input have the same function and syntax.
		As for regular basis sets, ECPs may be obtained from the standard library.
	www.emsl.pnl.gov /docs/nwchem/doc/user/node10.html (1002 words)

	SML Basis Library (Site not responding. Last check: 2007-10-09)
		We are releasing this draft version of the SML Basis Library specification so that the SML community may comment on it.
		The latest versions of Moscow ML and Standard ML of New Jersey, as well as Harlequin's MLWorks, implement significant portions of this new library.
		The Standard ML Basis Library Manual (in HTML) mirrored in Denmark.
	www.smlnj.org /doc/basis (137 words)

	Roots, Coroots and Weights
		"standard" : use the standard basis for the (co)root space.
		The fundamental weights lambda_1,..., lambda_n of the root datum RD given as the rows of a matrix.
		This is the basis dual to the coroots, ie.
	www.umich.edu /~gpcc/scs/magma/text482.htm (1015 words)

	"AN ACT PROHIBITING PROPERTY AND CASUALTY INSURERS FROM CANCELING OR REFUSING TO RENEW POLICIES FOR FAILURE TO PAY ...
		Subsection (d) of section 38a-78 of the general statutes is repealed and the following is substituted in lieu thereof (Effective from passage):
		These tables shall be combined with a mortality table permitted for calculating the reserves for life insurance policies; and (5) for group life insurance, life insurance issued on the substandard basis and other special benefits, such tables as may be approved by the commissioner.
		Subsection (e) of section 38a-439 of the general statutes is repealed and the following is substituted in lieu thereof (Effective from passage):
	www.cga.ct.gov /2005/amd/s/2005SB-00031-R00HB-AMD.htm (218 words)

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