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Topic: Univalent

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	PlanetMath: univalent analytic function
		Definition 1 An analytic function on an open set is called univalent if it is one-to-one.
		For example mappings of the unit disc to itself
		This is version 3 of univalent analytic function, born on 2004-02-26, modified 2005-03-07.
	planetmath.org /encyclopedia/Univalent.html (85 words)

	The NADPH:O2 oxidoreductase of human neutrophils. Stoichiometry of univalent and divalent reduction of O2. (Site not responding. Last check: 2007-10-26)
		Univalent flux rates of less than 40% were observed with exposure of the enzyme to concentrations of deoxycholate in excess of 0.1% or to pH values below 6.0 or above 8.0.
		The capacity of the enzyme to carry out univalent reduction fell with increasing NADPH concentrations in a manner resembling that previously reported with increasing concentrations of xanthine in the case of xanthine oxidase (Fridovich, I. Biol.
		Its capacity to affect univalent reduction of O2 depends upon the concentration of electron donor (NADPH) supplied as well as conditions of storage and assay of the native enzyme.
	www.arclab.org /medlineupdates/abstract_3009441.html (290 words)

	Springer Online Reference Works
		In the study of univalent functions one of the fundamental problems is whether there exists a univalent mapping from a given domain
		The first substantial results in the theory of univalent functions were obtained using the area principle.
		This method enables one to solve many problems in the theory of functions quite simply, in particular extremal problems in classes of functions that can be represented by means of Stieltjes integrals: convex functions, close-to-convex functions, star-like functions, typically-real functions, and functions with positive real part (see Carathéodory class).
	eom.springer.de /u/u095620.htm (1483 words)

	PlanetMath: schlicht functions
		Definition 1 The class of univalent functions on the open unit disc in the complex plane such that for any
		A basic result on these gives that this set is in fact compact in the space of analytic functions on the unit disc.
		Alternatively this theorem can be stated for all univalent functions by the above remark, but there a sequence of univalent functions can converge either to a univalent function or to a constant.
	planetmath.org /encyclopedia/SchlichtFunctions.html (186 words)

	Derivatized metallic surfaces, composites of functionalized polymers with such metallic surfaces and processes for ...
		difunctional substantially linear fluoroaliphatic acid or univalent salt thereof is a bis-oxyacid of phosphorus or a univalent salt thereof.
		The process of claim 2 wherein the bis-oxyacid of phosphorus or univalent salt thereof is a fluoro bis-phosphate or a univalent salt thereof.
		difunctional substantially linear fluoroaliphatic acid or univalent salt thereof having 8 to less than 30 carbon linkages in the fluoroaliphatic chain with a liquid comprising a polymer having a functional group associative with said difunctional acid or salt thereof to form a mixture; and coating the mixture onto a surface of a metal substrate.
	www.freepatentsonline.com /6299983.html (9199 words)

	Comparison of univalent behavior in desynaptic, asynaptic and several trisomics (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-26)
		Observations have been made in this laboratory of univalent behavior at metaphase I, anaphase I and prophase II in microsporocytes of plants which were trisomic for chromosome 5, 9, 10 or a maize-Tripsacum interchange chromosome, as well as of plants which were homozygous for asynaptic or desynaptic.
		Univalents of all the trisomics studied show more variable behavior than the synaptic mutants, sometimes separating freely after lagging and sometimes apparently sticking together and remaining in the plate region until very late.
		At prophase II in the trisomics, some cells contain 10 normal dyads plus two monads (thought to have arisen from the premature separation of the chromatids of a univalent which had been distributed intact to a pole at the first division).
	www.agron.missouri.edu.cob-web.org:8888 /mnl/51/62maguire.html (359 words)

	Crisp Volume 6 No 1
		Univalent negative searches were shorter than univalent positive searches (p <.0001), confirming a negativity effect.
		Likewise, the univalent negative/unicategorical appearance, univalent positive/unicategorical trait, and univalent negative/unicategorical trait decks consisted of the 20 negative appearance items, 20 positive trait items, and 20 negative trait items respectively, also shown in Table 1.
		The expectation that bivalent searches would be longer than univalent negative searches was confirmed overall, though closer inspection of the data revealed that the effect obtained only for unicategorical trait searches.
	www.uiowa.edu /~grpproc/crisp/crisp.6.1.htm (5921 words)

	Lecture19-Monosomics
		The univalent often shows retarded movements which first become evident at metaphase I. While all the bivalents move to the equatorial plate, the univalent lies away from the plate.
		The later behavior of the univalent is quite variable: (1) it may pass to one of the poles undivided where it may or may not be included in the telophase I nucleus; (2) it may divide equationally with sister chromatids going to opposite poles or the same pole; or (3) it may misdivide.
		During the second division, the univalent may divide normally if it has passed to one of the poles undivided during the first division.
	www.hort.wisc.edu /instruction/cytogenetics/lecture19monosomics.htm (865 words)

	Nonrandom Segregation of the Mouse Univalent X Chromosome: Evidence of Spindle-Mediated Meiotic Drive -- LeMaire-Adkins ...
		Schematic of oocyte containing a univalent X chromosome at metaphase I (top), illustrating the two types of segregation that can occur (bottom).
		Intact segregation: Both X chromatids segregate intact to one spindle pole and, at MII metaphase, both X chromatids are either aligned on the MII spindle (bottom left) or in the polar body (bottom center).
		univalent X chromosome remained in the oocyte (Fig 2, a and
	www.genetics.org /cgi/content/full/156/2/775 (5154 words)

	Springer Online Reference Works
		Univalent function), based on the study of the variation of a function
		Quadratic differential) in the solution of extremal problems in the theory of univalent functions clear, since
		-th diameter in a family of continua of a given capacity; the solution of a number of extremal problems of univalent conformal mappings of doubly-connected domains; distortion theorems for multiply-connected domains, which at the same prove existence theorems of univalent conformal mappings of a given multiply-connected domain onto canonical domains, etc.
	eom.springer.de /b/b017410.htm (403 words)

	A COEFFICIENT PROBLEM FOR UNIVALENT FUNCTIONS RELATED TO TWO-POINT DISTORTION THEOREMS (Site not responding. Last check: 2007-10-26)
		We discuss a class of coefficient functionals over the set of normalized univalent functions on the unit disk.
		These functionals are related to symmetric, linearly invariant two-point distortion theorems for univalent functions due to Kim and Minda.
		In the same fashion, two-point distortion theorems for bounded univalent functions are obtained.
	math.la.asu.edu /~rmmc/rmj/VOL31-1/GRE (96 words)

	Poles near the origin produce lower bounds for coefficients of meromorphic univalent functions, F. G. Avkhadiev, K.-J. ...
		A. Baernstein II and G. Schober, Estimates for inverse coefficients of univalent functions from integral means, Israel J. Math.
		J. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math.
		Z. Lewandowski and E. Zlotkiewicz, On the domain of variability of the second coefficient for a class of meromorphic univalent functions, Bull.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.mmj/1080837738 (361 words)

	Cell adhesion molecules: detection with univalent second antibody -- Springer and Barondes 87 (3): 703 -- The Journal ...
		Cell adhesion molecules: detection with univalent second antibody -- Springer and Barondes 87 (3): 703 -- The Journal of Cell Biology
		Cell adhesion molecules: detection with univalent second antibody
		univalent second antibody blocks agglutination induced by the rabbit
	www.jcb.org /cgi/content/abstract/87/3/703 (282 words)

	Univalent function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-26)
		In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is one-to-one.
		is a univalent function such that f(G) = Ω (that is, f is onto), then the derivative of f is never zero, f is invertible, and its inverse f
		This article incorporates material from univalent analytic function on PlanetMath, which is licensed under the GFDL.
	en.wikipedia.org /wiki/Univalent_function (180 words)

	Valence (chemistry) - Wikipedia, the free encyclopedia
		The maximum number of univalent atoms (originally hydrogen or chlorine atoms) that may combine with an atom of the element under consideration, or with a fragment, or for which an atom of this element can be substituted.
		Fluorine is the element for which the largest number of atoms combine with atoms of other elements: it is univalent in all compounds except the ion [H
		In fact, the IUPAC definition can only be resolved by fixing the valences of hydrogen and fluorine as one, a convention which has been followed here.
	en.wikipedia.org /wiki/Univalent (657 words)

	Citebase - Chordal Loewner families and univalent Cauchy transforms
		In both cases the correspondence is being given by solving the chordal Loewner equation.
		We use this to show that any probability measure on the real line with finite variance and mean zero has univalent Cauchy transform if and only if it belongs to some chordal Loewner family.
		If the probability measure has compact support we give two further necessary and sufficient conditions for the univalence of the Cauchy transform, the first in terms of the transfinite diameter of the complement of the image domain of the reciprocal Cauchy transform, and the second in terms of moment inequalities corresponding to the Grunsky inequalities.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0306130 (229 words)

	univalent - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "univalent" is defined.
		Univalent : Online Plain Text English Dictionary [home, info]
		Univalent : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=univalent (187 words)

	Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions (via ... (Site not responding. Last check: 2007-10-26)
		For the classes S and K of (normalized) univalent and convex analytic functions, respectively, a number of authors conjectured interesting extensions of certain known distortion inequalities in terms of a fractional derivative operator.
		While examining and investigating the validity of these conjectures, many subsequent works considered various generalizations of the distortion inequalities relevant to each of these conjectures.
		Distortion inequalities, analytic functions, fractional derivatives, univalent functions, convex functions, hypergeometric function.
	jipam-old.vu.edu.au.cob-web.org:8888 /v2n2/038_00.html (341 words)

	CJM - Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations
		CJM - Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations
		In this article we characterize the univalent harmonic mappings from the exterior of the unit disk, $\Delta$, onto a simply connected domain $\Omega$ containing infinity and which are solutions of the system of elliptic partial differential equations $\fzbb = a(z)f_z(z)$ where the second dilatation function $a(z)$ is a finite Blaschke product.
		At the end of this article, we apply our results to nonparametric minimal surfaces having the property that the image of its Gauss map is the upper half-sphere covered once or twice.
	journals.cms.math.ca /cgi-bin/vault/view/bshouty0815 (111 words)

	univalent - French-English Dictionary WordReference.com
		We found no French translation for 'univalent' in our English to French Dictionary.
		Or did you want to translate 'univalent' from French to English?
		Forum discussions with the word(s) 'univalent' in the title:
	www.wordreference.com /enfr/univalent (49 words)

	Note on the zeros of functions with univalent derivatives (Site not responding. Last check: 2007-10-26)
		Note on the zeros of functions with univalent derivatives
		Keywords and phrases: univalent functions, close-to-convex functions, entire functions.
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	www.hindawi.com /GetArticle.aspx?doi=10.1155/S0161171286000108 (76 words)

	Rule A-1. Saturated Unbranched-chain Compounds and Univalent Radicals (ACYCLIC HYDROCARBONS) (Site not responding. Last check: 2007-10-26)
		Saturated Unbranched-chain Compounds and Univalent Radicals (ACYCLIC HYDROCARBONS)
		1.2 - Univalent radicals derived from saturated unbranched acyclic hydrocarbons by removal of hydrogen from a terminal carbon atom are named by replacing the ending "-ane" of the name of the hydrocarbon by "-yl".
		Look up structures of trivial and trade names with ACD/Dictionary
	www.acdlabs.com /iupac/nomenclature/79/r79_34.htm (227 words)

	Rule A-2. Saturated Branched-chain Compounds and Univalent Radicals (ACYCLIC HYDROCARBONS) (via CobWeb/3.1 ... (Site not responding. Last check: 2007-10-26)
		Saturated Branched-chain Compounds and Univalent Radicals (ACYCLIC HYDROCARBONS) (via CobWeb/3.1 planetlab2.tamu.edu)
		2.25 - Univalent branched radicals derived from alkanes are named by prefixing the designation of the side chains to the name of the unbranched alkyl radical possessing the longest possible chain starting from the carbon atom with the free valence, the said atom being numbered as 1.
		The following names may be used for the unsubstituted radicals only:
	www.acdlabs.com.cob-web.org:8888 /iupac/nomenclature/79/r79_36.htm (553 words)

	VinylBand.net - A univalent hydrocarbon radical of the ethylene series
		VinylBand.net - A univalent hydrocarbon radical of the ethylene series
		A univalent hydrocarbon radical of the ethylene series
		Monday, December 11 2006 @ 08:18 AM CST
	www.vinylband.net (335 words)

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