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Topic: Spectral radius

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	Olympus FluoView Resource Center: Interactive Java Tutorials
		Spectral Bleed-Through (Crossover) in Confocal Microscopy - Bleed-through (often termed crossover) of fluorescence emission, due to the broad spectral profiles exhibited by common fluorophores, is a fundamental problem that must be addressed in both widefield and laser scanning confocal fluorescence microscopy.
		The blue-violet spectral line is useful for a host of common fluorophores and fluorescent proteins in single, double, or triple labeling experiments.
		The spectral properties of fluorescent proteins are dependent upon the structure of the fluorophore as well as the localized interactions of amino acid residues in the immediate vicinity, and in some cases, residues far removed from the fluorophore.
	www.olympusfluoview.com /java (2347 words)

	PlanetMath: Gelfand spectral radius theorem
		"Gelfand spectral radius theorem" is owned by Andrea Ambrosio.
		Cross-references: Hilbert space, bounded operators, algebra, infinite-dimensional, matrix norm, norm, Banach algebra, algebras, operator, theory, dimensions, infinite, spectral radius, square matrix, self-consistent matrix norm
		This is version 6 of Gelfand spectral radius theorem, born on 2003-05-27, modified 2007-10-08.
	planetmath.org /encyclopedia/GelfandSpectralRadiusTheorem.html (142 words)

	PlanetMath: proof of Gelfand spectral radius theorem
		"proof of Gelfand spectral radius theorem" is owned by Andrea Ambrosio.
		Cross-references: spectral radius, lower bound, norm, bounded, natural number, definition, limit, sequence, powers, matrix
		This is version 4 of proof of Gelfand spectral radius theorem, born on 2005-11-06, modified 2006-09-11.
	www.planetmath.org /encyclopedia/ProofOfGelfandSpectralRadiusTheorem.html (138 words)

	PlanetMath: spectral radius
		More generally, the spectrum and spectral radius can be defined for Banach algebras with identity element: If is a Banach algebra over
		Spectral radius formula by lupin on 2005-07-29 09:10:52
		Are there any elaborate descriptions on the generation and interpretation of such spectral portraits?
	www.planetmath.org /encyclopedia/SpectralRadius.html (140 words)

	Imagine the Universe! Dictionary
		The supplementary SI unit of angular measure, defined as the central angle of a circle whose subtended arc is equal to the radius of the circle.
		Similar to spatial resolution except that it applies to frequency, spectral resolution is the ability of the telescope to differentiate two light signals which differ in frequency by a small amount.
		The supplementary SI unit of solid angle defined as the solid central angle of a sphere that encloses a surface on the sphere equal to the square of the sphere's radius.
	imagine.gsfc.nasa.gov /docs/dict_qz.html (3025 words)

	Spectral Radius (Site not responding. Last check: )
		The spectral radius of a matrix is the radius of the smallest circle in the complex plane that contains all its eigen values.
		Conversely, assume the spectral radius is less than 1, and use the binomial theorem to see that the subdiagonal elements of a simple jordan block become n times the eigen value raised to the n-1.
		If it converges, the terms must approach 0, hence the spectral radius of m is less than 1.
	www.mathreference.com /la-mpoly,srad.html (313 words)

	[No title] (Site not responding. Last check: )
		The essential spectral radius of $\calL$ on $C^r$, $r=0,1,\dots$ is less than or equal to $\exp \sup_{\nu\in\calM} \{h_\nu+\lambda_\nu-r\cdot \chi_\nu\}.$ \end{thm} \begin{thm}\label{thm1'} Assume $f$ is expanding.
		Since $\ophi$ in $\calL$ is triangular, it is possible to apply the scalar ($m=1$) result for the spectral radius of transfer operator from, e.g, \cite{Bo,RuBo} to estimate the spectral radius of $\overline\calL$ in terms of $\of$-pressure for the diagonal elements of $\ophi$.
		General facts on the stability of Fredholm spectrum under compact perturbations imply that the essential spectral radius of $\calL$ on $C^1_X(E)$ is dominated by the spectral radius of $\calK$ on $C^0_{\calX}(\calE)$.
	www.ma.utexas.edu /mp_arc/papers/95-406 (5241 words)

	Implementation of the generalized VIP representation
		Although obvious, the stability of the generalized VIP representation is illustrated based on a spectral analysis of the amplification matrix.
		The spectral radius of the amplification matrix must be strictly less than one:
		for different values of the damping ratio (see Figure 17) shows that the spectral radius is less than one for all values of the frequency and decreasing with the increase in frequency.
	www-users.cs.umn.edu /~xiangmin/arc/node35.html (739 words)

	Spectral gap of a graph
		The spectral radius of the graph has several definitions (depending on how negative eigenvalues [which corresponds to almost-bipartite graphs] are taken into account).
		The one we use is the following one: the spectral radius is the largest modulus of an eigenvalue of M distinct from
		For the spectral gap the situation is reversed: the lower bound is proved, whereas the upper bound is probabilistic.
	www.yann-ollivier.org /specgraph/specgraph.html (757 words)

	The Spectral Radius of Infinite Graphs - ECS EPrints Repository
		The Spectral Radius of Infinite Graphs - ECS EPrints Repository
		Biggs, N. L., Mohar, B. and Shawe-Taylor, J. The Spectral Radius of Infinite Graphs.
		EPrints is free software developed by the University of Southampton to facilitate Open Access to research.
	eprints.ecs.soton.ac.uk /9831 (68 words)

	Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard - Blondel, Gaubert, Tsitsiklis ...
		Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard (2000)
		The logarithm of the average spectral radius is traditionally called Lyapunov exponent.
		Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard.
	citeseer.ist.psu.edu /385133.html (725 words)

	Matrix Norm, spectral radius and Condition Number
		The spectral radius is used in the calculation of the matrix 2-norm, but in general, it is not the same as the matrix norm.
		This is an important example to show how the matrix norm differs from the spectral radius.
		For the other norms, the relationship between spectral radius and matrix norm is not as explicit, but we always have the inequality
	www.physics.arizona.edu /~restrepo/475A/Notes/sourcea/node53.html (533 words)

	[No title]
		Ullrich claimed Lounesto was wrong about "spectral radius".
		You stated that the spectral radius is a norm.
		radius than I. Silly me, I didn't even know it was a norm.
	www.mathforum.org /kb/plaintext.jspa?messageID=267919 (611 words)

	Black Holes
		At this radius, the escape speed is equal to the speed of light, and once light passes through, even it cannot escape.
		Its companion star, HDE 226868 is a B0 supergiant with a surface temperature of about 31,000 K. Spectroscopic observations show that the spectral lines of HDE 226868 shift back and forth with a period of 5.6 days.
		From the mass-luminosity relation, the mass of this supergiant is calculated as 30 times the mass of the Sun.
	imagine.gsfc.nasa.gov /docs/science/know_l2/black_holes.html (1394 words)

	Proceedings of the American Mathematical Society
		A formula for the spectral radius of a subdivision operator, in terms of the moduli of eigenvalues, is derived under a mild condition.
		T. Goodman, C. Micchelli, and J. Ward, Spectral radius formulas for subdivision operators, Recent Advances in Wavelet Analysis (L. Schumaker and G. Webb, eds.), Academic Press, Boston, MA, 1994, pp.
		Keywords: Subdivision operator, spectral radius, joint spectral radius
	www.ams.org /proc/2004-132-04/S0002-9939-03-07194-6/home.html (360 words)

	The minimal spectral radius of graphs with a given diameter (Site not responding. Last check: )
		The spectral radius of a graph (i.e., the largest eigenvalue of its corresponding adjacency matrix) plays an important role in modeling virus propagation in networks.
		In fact, the smaller the spectral radius, the larger the robustness of a network against the spread of viruses.
		In general, communication networks are designed such that the diameter is small, because the larger the number of nodes traversed on a connection, the lower the quality of the service running over the network.
	ideas.repec.org /p/dgr/kubcen/2006102.html (330 words)

	University of Maryland A. James Clark School of Engineering: Clark School Events
		This question can be formalized by introducing the concept of joint spectral radius that measures the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from a set.
		The joint spectral radius appears in a number of application contexts but is notoriously difficult to compute and to approximate.
		The algorithm approximates the joint spectral with arbitrary high accuracy and is polynomial in the size of the matrices once the desired accuracy is fixed.
	www.engr.umd.edu /events/index.php?mode=4&id=331 (583 words)

	WCOM Spring 2000: Jim Burke
		A spectral function on the linear space of complex n by n matrices is an extended real valued function the that can be represented as the composition of a permutation invariant extended real valued function with the mapping that takes an n by n matrix to its spectrum counting multiplicities.
		The maximum modulus of the spectrum (the spectral radius) is an example of such a function.
		The spectral radius has importance in the discrete case, while the spectral abscissa is important in the continuous case.
	oldweb.cecm.sfu.ca /events/WCOM00S/burke.html (223 words)

	On the design of an L-stable second-order accurate explicit time discretized operator representation
		The curves of spectral radius of the L-stable second-order accurate stabilized explicit time discretized operator representation with different artificial damping ratios are shown in Figure 43 (a - b).
		It is evident that: 1) The spectral radii are less than unity for dynamic problems with various physical damping ratio cases; 2) The spectral radius tends to zero as
		The comparison of dissipation and dispersion characteristics with the central difference method are given in Figures 44(a) and 44(b).
	www-users.cs.umn.edu /~xiangmin/arc/node53.html (284 words)

	University of Maryland \| Electrical and Computer Engineering Department
		This question can be formalized by introducing the concept of joint spectral radius that measures the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from a set.
		The joint spectral radius appears in a number of application contexts but is notoriously difficult to compute and to approximate.
		The algorithm approximates the joint spectral with arbitrary high accuracy and is polynomial in the size of the matrices once the desired accuracy is fixed.
	www.ee.umd.edu /calendar/index.php?mode=4&id=331 (635 words)

	Spectral gap of a graph (Site not responding. Last check: )
		The spectral radius of the graph has several definitions (depending on how negative eigenvalues [which corresponds to almost-bipartite graphs] are taken into account).
		The one we use is the following one: the spectral radius is the largest modulus of an eigenvalue of M distinct from
		For the spectral gap the situation is reversed: the lower bound is proved, whereas the upper bound is probabilistic.
	www.eleves.ens.fr /home/ollivier/specgraph/specgraph.html (757 words)

	Stars and Habitable Planets
		Even the largest, possibly suitable stars -- i.e., spectral type F0-4 (Kasting et al, 1993; abstract) -- may only be able to support Earth-type life for around two billion years, and so planets in favorable orbits may not have sufficient time to develop complex life on land such as trees.
		On the opposite extreme, stars with less than half of Sol's mass (e.g., smaller spectral type M dwarfs like Proxima Centauri) are likely to tidally lock planets that are orbiting close enough to have liquid water on their surface too quickly, before life can develop (Peale, 1977).
		Differences in the spectral type of the host stars, orbital eccentricity (degree of elliptical deviation from perfect circularity), and stellar age did not appear to have significant correlations, but in hierarchial multiple systems, noncoplanarity may exist at small separations.
	www.solstation.com /habitable.htm (3208 words)

	ANS : Store : Electronic Articles
		A spectral analysis of the resulting acceleration schemes demonstrates their excellent spectral properties for model problem configurations, characterized by a uniform mesh of infinite extent and homogeneous material composition, each in its own cell-size regime.
		Thus, the spectral radius of KAP vanishes as the computational cell size approaches infinity, but it exceeds unity for very thin cells, thereby implying instability.
		For this reason, and to avoid potential complication in the case of cells that are thin in one dimension and thick in another, NAP is adopted in the remainder of this work.
	www.ans.org /store/index.cgi?i=E110000-nse-136-2-202-226 (444 words)

	Spectral Radius Formula
		AMCA: Spectral radius for sampling operator by Mark C. Ho...
		Gelfand Transform and Spectral Radius Formulæ for Ultrametric Banach Algebras...
		A sharp formula for the essential spectral radius of the...
	www.scienceoxygen.com /math/649.html (272 words)

	[No title]
		is "spectral radius" and it is not a norm at all.
		(Try it; hint: the sum of two nilpotent matrices need not be nilpotent.) In some textbooks, the expression "spectral norm" is used to denote the maximal singular value of A. This is indeed a norm, and I don't like the use of "spectral" in this context.
		To be precise the spectral norm of a matrix A is the positive square root of the the maximum eigenvalue of A'*A where the prime indicates conjugation and transposition.
	www.math.niu.edu /~rusin/known-math/01_incoming/spec_rad (654 words)

	publ2005.htm
		Spectral mapping theorems for semigroups of operators, Acta Sci.
		Operators with the spectral decomposition property are decomposable, Studia Sci.
		On the spectral singularities of the truncated shift, Acta Math.
	www.math.bme.hu /~bnagy/2003publ.htm (964 words)

	[No title] (Site not responding. Last check: )
		Analysed with maximum numerial damping (spectral radius = 0.0).
		Analysed with less numerial damping (spectral radius = 0.2).
		Analysed with maximum numerial damping (spectral radius = 0.2).
	www.topopt.dtu.dk /crash/index_seat.html (381 words)

	Atlas: Analytic joint spectral radius in a solvable Lie algebra of operators by Daniel Beltita (Site not responding. Last check: )
		The algebraic joint spectral radius of a set of operators (introduced by G.-C. Rota and G. Strang) has proved recently its usefulness in the solution of an important open problem concerning the existence of invariant subspaces for semigroups of compact quasinilpotent operators, cf.
		On the other hand, several mathematicians have studied a geometric joint spectral radius for commuting tuples of operators (defined by means of the Taylor spectrum) and compared it with the algebraic one.
		This spectral radius is compared with the algebraic and geometric ones when the operators belong to some finite-dimensional solvable Lie algebra (extending the framework of commutativity by means of the recently introduced Cartan-Taylor joint spectrum).
	atlas-conferences.com /cgi-bin/abstract/caeo-12 (250 words)

	Analytic joint spectral radius in a solvable Lie algebra of operators (Site not responding. Last check: )
		Analytic joint spectral radius in a solvable Lie algebra of operators
		One introduces the concept of analytic spectral radius for a family of operators indexed by some finite measure space.
		This spectral radius is compared with the algebraic and geometric ones when the operators belong to a finite-dimensional solvable Lie algebra.
	www.imar.ro /~dbeltita/jsrabs.html (82 words)

	[No title] (Site not responding. Last check: )
		This special issue aims to highlight the advances that have been achieved in recent times and to generate a state of the art account of the developments in algebraic and analytic theory of the joint spectral radius, computational aspects and application areas.
		In order to make the broad scope of methods visible we encourage submissions from all areas that have an impact on the understanding of the joint spectral radius ranging from matrix analysis, numerical analysis, algebraic theory of matrix semigroups, computational complexity theory, stability theory of switched linear systems, spectral theory of semigroups of matrices.
		We note that depending on the authors the joint spectral radius is also known as the maximal Lyapunov exponent or Lyapunov indicator, the Bohl exponent or the exponential growth rate and we encourage the submission of papers that create links to fields where notions similar to the joint spectral radius are studied, e.g.
	www.math.wisc.edu /~hans/jsr-call-new.txt (372 words)

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