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Topic: Isolated singularity

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	PlanetMath: isolated singularity
		is not analytic, the isolated singularities are exactly the isolated points of
		Cross-references: essential singularities, poles, removable singularities, isolated points, points, analytic, open set, function, open, Riemann sphere
		This is version 6 of isolated singularity, born on 2003-10-15, modified 2007-04-15.
	planetmath.org /encyclopedia/IsolatedSingularity.html (73 words)

	Singularity theory - Wikipedia, the free encyclopedia
		In mathematics, singularity theory is the study of the failure of manifold structure.
		That implies the breakdown of parametrization of points; it is prominent in cosmology, where a gravitational singularity, at which the gravitational field is strong enough to change the very structure of space-time, is identified with a fl hole.
		Such singularities in algebraic geometry are the easiest in principle to study, since they are defined by polynomial equations and therefore in terms of a coordinate system.
	en.wikipedia.org /wiki/Singularity_theory (1082 words)

	Isolated singularity - Wikipedia, the free encyclopedia
		In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it.
		Formally, a complex number z is an isolated singularity of a function f if there exists an open disk D centered at z such that f is holomorphic on D − {z}, that is, on the set obtained from D by taking z out.
		has a singularity at 0 which is not isolated, since there are additional singularities at the reciprocal of every integer which are located arbitrarily close to 0 (though the singularities at these reciprocals are themselves isolated).
	en.wikipedia.org /wiki/Isolated_singularity (181 words)

	Singularity theory (Site not responding. Last check: 2007-11-01)
		In mathematics, singularity theory is the study of thefailure of manifold structure.
		That implies the breakdown of parametrization of points; it is prominent in cosmology,where a gravitational singularity, at which the gravitational field is strong enough to change the verystructure of space-time, is identified with a fl hole.
		Such singularities in algebraic geometry are the easiest inprinciple to study, since they are defined by polynomialequations and therefore in terms of a coordinate system.
	www.therfcc.org /singularity-theory-3596.html (1008 words)

	Isolated singularity (Site not responding. Last check: 2007-11-01)
		In complex analysis, a branch of mathematics, an isolated singularity is a singularity of a function ''f at a point z such that there exists an open disk centered at z within which f is analytic at every point except z.
		Surviving the Singularity Steve Alan Edwards interviews five transhumanists on the Singularity.
		Singularity Institute for Artificial Intelligence Nonprofit organization devoted to creating, discussing and coordinating singularity-related efforts, and publish introductory material and research papers on the topic.
	www.serebella.com /encyclopedia/article-Isolated_singularity.html (464 words)

	Microsoft Research Singularity Project
		Singularity is a research project focused on the construction of dependable systems through innovation in the areas of systems, languages, and tools.
		In the current Singularity prototype SIPs are extremely cheap; they run in ring 0 in the kernel’s address space.
		Singularity uses these advances to build more reliable systems and applications.
	research.microsoft.com /os/singularity (640 words)

	singularity theory (Site not responding. Last check: 2007-11-01)
		A finite-time singularity occurs when a kinematic variable increases towards infinity at a finite time.
		If idealized motion is considered, in which the same fraction of kinetic energy is lost on each bounce, the frequency of bounces becomes infinite as the ball comes to rest in a finite time.
		Technically this involves group actions of Lie groups on spaces of jetss; in less abstract terms Taylor expansions are examined up to change of variable, pinning down singularities with enough derivatives.
	www.yourencyclopedia.net /singularity_theory.html (1104 words)

	Isolated singularity - Definition, explanation
		Formally, a complex number z is an isolated singularity of a function f if there exists an open disk D centered at z such that f is holomorphic on D−{z}, that is, on the set obtained from D by taking z out.
		Every singularity of a meromorphic function is isolated, but isolation of singularities is not alone sufficient to guarantee a function is meromorphic.
		has a singularity at 0 which is not isolated, since there are additional singularities at the reciprocal of every integer which are located arbitrarily close to 0 (though the singularities at these reciprocals are themselves isolated).
	www.calsky.com /lexikon/en/txt/i/is/isolated_singularity.php (185 words)

	Daniel Barlet
		An interesting consequence of the local study along $S^$ is the corollary showing that for a germ with an isolated* singularity, the largest sub-(a,b)-module having a simple p\^ole in its Brieskorn-(a,b)-module is independant of the choice of a reduced equation for the corresponding hypersurface germ.
		An analoguous of the Brieskorn module of an isolated singularity is defined and a finitness theorem is proved using Kashiwara's constructibility theorem.
		Abstract: The aim of this first part is to introduce, for an rather large class of hypersurface singularities with 1 dimensionnal locus, the analog of the Brieskorn lattice at the origin (the singular point of the singular locus).
	www.iecn.u-nancy.fr /~barlet (1970 words)

	Isolated singularity (Site not responding. Last check: 2007-11-01)
		Every singularity of a meromorphic function is isolated,but isolation of singularities is not alone sufficient to guarantee a function is meromorphic.
		Many important tools of complexanalysis such as Laurent series and the residue theorem require that all relevant singularities of the function be isolated.
		The function csc (1/(π z)) has a singularity at 0 which is not isolated, since there are additionalsingularities at the reciprocal of every integer which are located arbitrarily close to 0(though the singularities at thesereciprocals are themselves isolated).
	www.therfcc.org /isolated-singularity-33127.html (161 words)

	Isolated singularity -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-01)
		Every singularity of a (Click link for more info and facts about meromorphic function) meromorphic function is isolated, but isolation of singularities is not alone sufficient to guarantee a function is meromorphic.
		The function has 0 as an isolated singularity.
		The (Ratio of the hypotenuse to the opposite side of a right-angled triangle) cosecant function csc(πz) has every (Any of the natural numbers (positive or negative) or zero) integer as an isolated singularity.
	www.absoluteastronomy.com /encyclopedia/i/is/isolated_singularity.htm (125 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Hence in this paper we deal with singularities whose projectivized tangent cone at the singular point $D$ is a non-reduced divisor in $\pp^2.$ Let $\dre$ be the reduced divisor in $\pp^2$ related to $D$ and $p$ its degree.
		First section of the paper is devoted to preliminary results, we write down another formula for the Milnor number in terms of the multiplicity of the singularity and some generalized Milnor numbers of its projectivized tangent cone at the singular point $D.$ In sections 2 and 3 we prove Theorems 2 and 3 respectively.
		Let $(V,0)\subset (\cc^{n},0)$ be an isolated hypersurface singularity defined by the zero locus of a complex analytic function $f.$ By \cite{17} for studying topological properties of $(V,0)$ we may assume that $f=f_d+f_{d+1}+\ldots+f_r$ is a polynomial of degree $r$ large enough.
	home.imf.au.dk /esn/preprints/063 (2989 words)

	CMB - Characterizations of Simple Isolated Line Singularities
		A line singularity is a function germ $f\colon(\CC ^{n+1},0) \lra\CC$ with a smooth $1$-dimensional critical set $\Sigma=\{(x,y)\in \CC\times \CC^n \mid y=0\}$.
		An isolated line singularity is defined by the condition that for every $x \neq 0$, the germ of $f$ at $(x,0)$ is equivalent to $y_1^2 +\cdots+y_n ^2$.
		Simple isolated line singularities were classified by Dirk Siersma and are analogous of the famous $A-D-E$ singularities.
	journals.cms.math.ca /cgi-bin/vault/view/zaharia7401?size=2 (93 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		In singularity theory, the most common equivalence relation of hypersurface singularities is the ${\cal R}$ (=right)-equivalence.\\ {\bf 1.2.\ Definition.}\ Two germs $g$, \f are called ${\cal R}$-equivalent, if there exists a biholomorphic germ $\varphi: ({\bf C}^{n+1},0)\to ({\bf C}^{n+1},0)$ such that $f=g\circ \varphi$.
		The singular locus of the space--germ $(V_f,0)$ is given by $Sing(V_f):= \{z:\partial f(z)=0\}$.
		Therefore, $S_0=(\mu+\sigma)/4$ is the measure of the non--rationality of the singularity $(f^{-1}(0),0)$ (cf.
	home.imf.au.dk /esn/preprints/088 (9464 words)

	Singularity Theory Abstracts
		Given any stable perturbation of such a map, there are various multi-germ singularity types that arise, and the object is to count the number of each type of isolated singularity that occurs.
		We extend this result to the case where the source is a complete intersection with an isolated singularity.
		The purpose of this expository article is to describe in an elementary and homogeneous manner, the relationship between the geometric and algebraic multiplicities of isolated critical points of holomorphic functions.
	www.maths.manchester.ac.uk /~jm/Research/sing_abstracts.html (892 words)

	Isolated Singularities (Site not responding. Last check: 2007-11-01)
		Isolated Singularities of Solutions of Fully Nonlinear Elliptic Equations...
		Instability of pole singularities for the Chazy equation...
		Classi cation of singularities at in nity of...
	www.scienceoxygen.com /math/470.html (106 words)

	JARCS 2005 Australian-Japanese Real and Complex Singularities Workshop
		The link with singularity theory is a recent result by Henning Krause, which exhibits the derived category of a singularity, in the sense of Kontsevich, as the compact objects in an infinite derived category.
		A complex curve singularity can be viewed as a complex codimension 1 condition on a family of curves - count the number of times the singularity appears on curves in the family - and thus a second cohomology class in the compactified moduli space M
		Complex plane curve singularities can be studied using the link of the singularity, a topological invariant which is a link in the 3-sphere obtained by intersecting the curve with the boundary of a very small ball around the singularity.
	www.maths.usyd.edu.au /u/laurent/RCSW/abstracts (2001 words)

	Mixed Hodge Structures and Singularities - Cambridge University Press
		This book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying of singularities by means of differential forms.
		The author introduces the Gauss–Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure.
		The period map of a m-constant deformation of an isolated hypersurface singularity associated to Brieskorn lattices and mixed Hodge structures.
	www.cambridge.org /catalogue/catalogue.asp?isbn=9780521620604 (201 words)

	IUM10 conference: S.Gussein-Zade (Site not responding. Last check: 2007-11-01)
		There are some generalizations of the classical Eisenbud-Levine-Khimshiashvili formula for the index of a singular point of an analytic vector field on $R^n$ to vector fields on singular varieties.
		For a variety with an isolated singularity, we define an index of a (real) 1-form on it.
		In the complex setting we define an index of a holomorphic 1-form on a complex isolated complete intersection singularity (icis) and express it as the dimension of a certain algebra.
	www.mccme.ru /ium/ium10/gzade.html (113 words)

	Barbelith Underground > Head Shop > What is "this"? And does the nothing noth?
		Two different uses of the same word, a singular phenomena is a 'sense datum' or a 'qualia', for example an instance of redness or a feeling of pain.
		I am temporarily adopting the stance that all properties are relational and that things cannot exist in isolation in order to have a common ground to thrash this out in.
		Moreover, no isolated bit, which does not at least talk to itself, can be said to be communicating information, or more strongly, it can not be said to be “encoded” with information; therefore, it is nothing, empty.
	www.barbelith.com /topic/12262/from/35 (12863 words)

	Singularity Theory Abstracts
		Given any stable perturbation of such a map, there are various multi-germ singularity types that arise, and the object is to count the number of each type of isolated singularity that occurs.
		The purpose of this expository article is to describe in an elementary and homogeneous manner, the relationship between the geometric and algebraic multiplicities of isolated critical points of holomorphic functions.
		We make use of singularity theory to define the contact between submanifolds of a manifold, whether or not the submanifolds are of complementary dimension.
	www.ma.umist.ac.uk /~jm/Research/sing_abstracts.html (836 words)

	Citations: Singular points of complex hypersurfaces - Milnor (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		concerning isolated hypersurface singularities: There is a fibration of (S Gamma L f) Gamma Gamma S whose fiber F is an open manifold that is homotopy equivalent to a bouquet of n spheres S Delta Delta Delta S : The Milnor number of L f is the number of S s in the.
		) of a germ F : C ; 0) C ; 0) of isolated singularity is the C dimension of E=Jac(F) where Jac(F) is the ideal generated by the two partial derivatives of F.
		The germs of the non singular curves fF = g (6= 0 and small) have the homotopy type of a bouquet of circles (the vanishing....
	citeseer.ist.psu.edu /context/70501/0 (2116 words)

	Singularity III: Revenge of the SIP
		Instead, we've modelled a conventional systems as a version of Singularity in which the kernel and device drivers run in one hardware domain and application and system processes each run in their own domain.
		Right now, Singularity is a small system (a few hundred thousand lines of code), and the real challenge would only arise if it grew and was maintained by a larger, less cohesive team.
		Since Singularity won't reach a mature state (mature = can be used by a lot people, without going back to the DOS UI and knowing much about OS internals) in the next couple of years, emulation could be an interesting alternative.
	channel9.msdn.com /Showpost.aspx?postid=227259 (3536 words)

	Singularities, Zeros, and Poles
		Thus, the origin and each point on the negative real axis is a singularity of
		Functions with isolated singularities have a Laurent series because the punctured disk
		We now look at this special case of Laurent's theorem in order to classify three types of isolated singularities.
	math.fullerton.edu /mathews/c2003/SingularityZeroPoleMod.html (299 words)

	Recent Publications (Site not responding. Last check: 2007-11-01)
		S. Taliaferro, On the growth of superharmonic functions near an isolated singularity I, J. Differential Equations 158 (1999), 28-47.
		S. Taliaferro, On the growth of superharmonic functions near an isolated singularity II, Comm.
		S. Taliaferro, Isolated singularities of nonlinear elliptic inequalities, Indiana Univ. Math.
	www.math.tamu.edu /~steven.taliaferro/selpubs.html (216 words)

	Isolated Singularities and Series Expansions
		A function f has an isolated singularity at z
		Here are the definitions of three functions, each with an isolated singularity at 0:
		An isolated singularity that is not removable and not a pole is called an essential singularity.
	www.math.duke.edu /education/ccp/materials/engin/series/series2.html (318 words)

	Session 13 \\ {\bf Singularities and Residues }
		A branch point is a special type of singularity such that if a circuit is described around it, the function after the circuit assumes a different value.
		Once and if all branch points have been suitably removed by cutting the only remaining singularities are points wher df/dz does not exist.
		A third kind of singularity consists of non-removable isolated singularities.
	www.rh.edu /~ernesto/C_S2000/mes/Notes/mes13.html (1136 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		The link of an isolated singularity carries a natural contact structure.
		Ohta and I classified of symplectic fillings of the link, when the singularity is either a simple singularity of dimension 2 (Kleinian singularity) or a simple elliptic singularity.
		Based on it, Bhupal and I studied the case that the singularity is a quotient surface singularity and a rational determinantal singularity with reduced fundamental cycle.
	www.ipam.ucla.edu /abstract.aspx?tid=2948 (96 words)

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