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Topic: Region of convergence

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	Region of Convergence for the Z-transform
		The region of convergence, known as the ROC, is important to understand because it defines the region where the z-transform exists.
		The ROC for a given x[n], is defined as the range of z for which the z-transform converges.
		The Region of Convergence has a number of properties that are dependent on the characteristics of the signal, x[n].
	cnx.org /content/m10622/latest (601 words)

	Mathematical Transforms
		This data type includes information on the region of convergence and the variables involved in the transformation, which is particularly useful in stability analysis.
		In the case of the Z transform, the system is stable only if the unit circle is included in the region of convergence, while for the Laplace transform, the imaginary axis must be in the region of convergence.
		From the region of convergence, we conclude that this is stable.
	documents.wolfram.com /applications/signals/MathematicalTransforms.html (3315 words)

	What is regional inversion
		Regional inversion is a process of radical change that involves overturning the established order of territorial influence.
		Regional inversion is a long-term phenomenon occurring in multiple dimensions: economic, political, technological, social and cultural.
		Convergence theory’s analytical scope seldom goes beyond established quantitative economic parameters and general equilibrium models, thereby excluding many factors, forces and phenomena that are crucial in deciding the dynamics of regional change.
	www.regionalinversion.com /region/What_is_regional_inversion.html (2001 words)

	BIBO stability - Wikipedia, the free encyclopedia
		When the system is causal, the ROC is the open region to the right of a vertical line whose abscissa is the real part of the largest pole.
		For a causal, rational, discrete time system, the condition for stability is that the region of convergence (ROC) of the z-transform includes the unit circle.
		When the system is causal, the ROC is the open region outside a circle whose radius is the magnitude of the pole with largest magnitude.
	en.wikipedia.org /wiki/BIBO_stability (483 words)

	Characterization of the Regions of Convergence of CMA Adapted Blind Fractionally Spaced Equalizer
		Delineation of the regions of convergence of this multimodal algorithm has remained as an unresolved problem in spite of its significance with regard to CMA initialization strategies.
		The convergence regions of the local minima with low noise gain expand near the origin, while those of the local minima with high noise gain shrink.
		The convergence regions of the equalizer space of the FSE-CM for an arbitrary channel are result from this transformation, which performs rotation and dilation (determined by the singular decomposition of the channel convolution matrix).
	www.appsig.com /products/828d.htm (1733 words)

	Convergence
		convergence theory has carried a more specific connotation, referring to the hypothesized link between economic development and concomitant changes in social organization, particularly work and industrial organization, class structure, demographic patterns, characteristics of the family, education, and the role of government in assuring basic social and economic security.
		The classic and most controversial application of convergence theory has been in the study of modernization, where it is associated with the idea that the experience of developing nations will follow the path charted by western industrialized nations.
		The critique of convergence theory in the study of modernization recalls critiques of earlier theories of societal evolution advanced under the rubric of social Darwinism in the nineteenth century and structural-functionalism in the mid-twentieth century.
	www.unm.edu /~coughlin/convergnew.htm (4369 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The divergence of the mesoscale flow is small everwhere, less than f/10 (f=5e-5 at this latitude), except in a small region in the immediate lee of the island, where divergence is consistently negative.
		The curl of the mesoscale flow is also small; a region of negative (anticyclonic) curl coincides with the region of convergence described above.
		This region of convergence and anticyclonic circulation is consistent with known circulation patterns in the lee of the islands, and corresponds to Ekman convergence and anticyclonic spinup driven by windstress curl, as sketched below.
	www.satlab.hawaii.edu /hfradar/proj/adria/onr/tmp.html (406 words)

	Technological Diffusion, Spatial Spillovers And Regional Convergence In Europe
		First, the role of technology heterogeneity and diffusion in the convergence of GDP per worker observed across the European regions, in the absence of data on regional TFP.
		Second, the spatial pattern of the observed regional heterogeneity in technology and the relevance of this pattern for the econometric analysis of regional convergence in Europe.
		We first develop a growth model where technology accumulation in lagging regions depends on their own propensity to innovate and on technology diffusion from the leading region, and convergence in GDP per worker is due to both capital deepening and catch-up.
	ideas.repec.org /p/cns/cnscwp/200101.html (780 words)

	A Radical Approach to Real Analysis
		Behavior on the circle that forms the boundary between the region of convergence and the region of divergence is more complicated.
		The series might converge at all points on the circle, or it might diverge at all points on the circle, or it could converge at some points and diverge at others.
		For the power series in (1.5.1.5), these are all points on the boundary between the region of convergence and the region of divergence.
	www.macalester.edu /aratra/chapt1/chapt1_5_1.html (336 words)

	The Convergence Club
		We mean something different: we mean by "convergence" the assimilation of countries outside of northwestern Europe of the institutions, technologies, and productivity levels currently in use in northwestern Europe and in the rest of the developed industrial core of the world economy.
		So our definition of which economies are in the convergence club over a time period is not merely "did GDP per capita as a proportion of the North Atlantic level rise over the time period in question?" We require both relative income gains and a measure of industrial development as well.
		And as time passed, the process of diffusion gathered force and the size of the "convergence club"--the region to which structural change and industrial development were diffusing fast enough to reduce the relative gap vis-a-vis the core of the world economy--grew.
	www.j-bradford-delong.net /Econ_Articles/Dowrick/conv_club.html (3461 words)

	Convergence of Laurent Series
		An "annulus" is the region between two concentric circles.
		The region of convergence for the new series is x
		Hence the region of convergence for the whole series is z
	www.physicsforums.com /showthread.php?p=1133799#post1133799 (348 words)

	CORDIS: European Research Area: The activities: Regional dimension
		It is open to organisations that have already signed a contract with the Commission in the context of the 6th RTD Framework Programme - established in an Objective 1 region.
		Regions have a core role in the development of the European Research Area, a true internal market for science and knowledge.
		Dynamic regions can contribute to turning Europe into the most competitive knowledge-based economy in the world by 2010, a goal set by the March 2000 Lisbon European Council.
	cordis.europa.eu /era/regions.htm (281 words)

	Technology Convergence Consortium - Overview (Site not responding. Last check: 2007-10-09)
		The mission of TC2 is to (1) accelerate the convergence of biotechnology, nanotechnology, and information technology (2) ensure that the Bay Area expands its role as the world leader in this convergence area and (3) facilitate the transition from our current economic base to one built on this convergence.
		One of the elements of this initiative is focused on the region’s opportunities for convergence among information technology, biotechnology and nanotechnology.
		Our region is also recognized as a leader in the emerging field of nanotechnology, with major strengths at our universities and national laboratories.
	www.jointventure.org /programs-initiatives/tc2/overview.html (326 words)

	Microsoft Business Solutions Kicks Off Convergence 2003: Convergence 2003 offers a record number of Microsoft Business ... (Site not responding. Last check: 2007-10-09)
		Convergence 2003 is designed to offer attendees an opportunity to preview new applications, watch Microsoft Business Solutions technology in action, learn how Microsoft Business Solutions products and services can better serve them, meet and network with other Microsoft Business Solutions customers and participate in workshops focused on the interconnected global marketplace.
		One of the busiest places at Convergence is the usability lab, where customers give us input about adding screens for various functions or adding certain capabilities, all of which is very tangible, very valuable feedback.
		Convergence is a real opportunity to draw business value there's real return there.
	www.microsoft.com /presspass/features/2003/Mar03/03-19Convergence.mspx (1507 words)

	Telecommunications
		Convergence is a growing reality, and this is tracked locally against the backdrop of international trends.
		IDC analyses the impact of regulatory trends in its regional and country-specific telecoms sector reports.
		Convergence is a growing reality and key disruptive force - spanning networks, devices and applications.
	www.bmi-t.co.za /bmi/Content/Focus%20areas/telecommunications.htm (988 words)

	USC-SIPI REPORT #303 (Site not responding. Last check: 2007-10-09)
		We conclude that convergence is guaranteed (assuming no spurious local minima in the error function) by using a sufficiently high gain and a sufficiently low exposure energy.
		This is because this convergence condition is derived for the noise-free case and therefore does not account for the detrimental affects of detection noise on convergence.
		We conclude that for a given optical system it may not be possible to simultaneously satisfy the convergence condition while maintaining neural-space signal variances that are sufficiently small to allow the learning algorithm to converge.
	sipi.usc.edu /reports/abstracts/usc-sipi.303.html (779 words)

	Z-transform Region of convergence frequency domain Laurent series causal -n-1 n-k convolution {n} {n-p} poles (Site not responding. Last check: 2007-10-09)
		The region of convergence (ROC) is where the Z-transform of a signal has a finite sum for a region in the complex plane.
		In this case the ROC is the complex plane with a disc of radius 0.5 at the origin "punched out".
		In this case the ROC is a disc centered at the origin and of radius 0.5.
	en.powerwissen.com /4joN8XIimXM0fXo\|\|SL\|\|acvXFw==_Z-transform.html (1117 words)

	Region of Convergence (ROC)
		In general, the set of all s values satisfying the conditions for the integral of Laplace transform to converge is called the region of convergence (ROC) in the complex s-plane.
		In the first case above, the ROC is Re[s]>0, and in the second case, the ROC is Re[s]<0.
		As the Laplace integration converges independent of s, the ROC is the entire s-plane.
	fourier.eng.hmc.edu /e102/lectures/Laplace_Transform/node2.html (238 words)

	Power series - Wikipedia, the free encyclopedia
		Once a function is given as a power series, it is continuous wherever it converges and is differentiable on the interior of this set.
		Every power series with a positive radius of convergence is analytic on the interior of its region of convergence.
		On the other hand, in the interior of this region of convergence one may differentiate and integrate under the series sign, just as one may with ordinary power series.
	en.wikipedia.org /wiki/Power_series (1081 words)

	APRACA
		The fast and sustained economic growth that several major countries in the region have been experiencing now for a number of years is in itself transforming their economies and creating new business opportunities on an almost daily basis.
		Although the region as a whole may be producing enough food, it is the lack of sufficient purchasing power that causes food insecurity for those at the bottom end.
		As the region tries to grasp the enormity of the effects of poverty, the massive and debilitating 26 December 2004 earthquake and the consequent coastal floods have severely compounded the misery of several Asian countries around the Indian Ocean, in terms of death and injury, livelihood disruption and unemployment, loss of assets and outward migration.
	www.fao.org /world/regional/rap/speeches/2005/20050525.html (1980 words)

	Hurricanes (Site not responding. Last check: 2007-10-09)
		Surface convergence occurs on the east side of this wave and surface divergence occurs on the west side.
		Convergence at the surface leads to convergence of moisture.
		The Eye is the central region of the hurricane.
	www.ux1.eiu.edu /~jpstimac/1400/hurricanes_outline.html (767 words)

	5.1 Trust Region
		The convergence of the algorithm is quite insensitive to their exact values.
		However the values of the parameters affect how accurately the controller follows the trajectory, and they are selected differently for coarse transportation and fine manipulation moves, trading accuracy for time.
		The above trust region modification to the quasi-Newton method is guaranteed to converge to a minimum.
	www.cs.rochester.edu /~jag/PercAct/thesis/node19.html (351 words)

	PACS-SONET Original Proposal for more observing sites
		The Intertropical Convergence Zone (ITCZ) over the eastern Pacific Ocean, as the region of convergence between the northern Hemisphere easterly trade wind flow and the southeast trades of the southern Hemisphere, is the locus of some of the highest precipitation values found anywhere on the globe.
		Since the observations over this region are from mobile platforms (ships, aircraft) or observations that otherwise vary irregularly in space and time (cloud-drift winds), there are no independent long-term observations that can be used to validate the accuracy of the mean fields derived from the assimilation-based analyses.
		This region is quite close, in relative terms, to a region of substantial data (Central America) and uncertainties farther offshore are likely to be higher.
	www.nssl.noaa.gov /projects/pacs/html_files/pacs-prop.html (3054 words)

	Application of the flow convergence region method to the determination of stroke volume and cardiac output in patients ...
		Application of the flow convergence region method to the determination of stroke volume and cardiac output in patients with mitral stenosis
		Aliasing velocities of 20 to 23 cm/s were used to record the flow convergence region proximal to the stenotic mitral orifice.
		No significant difference existed between the cardiac output obtained using the flow convergence region method and that obtained using Fick method in 12 patients with pure mitral stenosis.
	www.pulsus.com /cardiol/12_04/hori_ed.htm (660 words)

	Payments Innovation in SE Asia - Through the Looking Glass
		Overview of the key centers of innovation in the SE Asia region and the key initiatives in place 2.
		Is the grass actually greener or is it that the looking glass through which we view this region is green tinted.
		Due to the extremely high cost of telecommunications in the region, Japan and other innovators had to take an alternative evolutionary path to compensate for this.
	www.emediawire.com /releases/2004/5/emw127767.htm (696 words)

	GNU Scientific Library -- Reference Manual - Multidimensional Root-Finding
		They require an initial guess for the location of the root, but there is no absolute guarantee of convergence -- the function must be suitable for this technique and the initial guess must be sufficiently close to the root for it to work.
		The components of D are computed internally, using the column norms of the Jacobian to estimate the sensitivity of the residual to each component of x.
		This is a modified version of Newtons method which attempts to improve global convergence by requiring every step to reduce the Euclidean norm of the residual, f(x).
	nereida.deioc.ull.es /html/gsl/gsl-ref_23.html (2599 words)

	Himalayas and Andes (Site not responding. Last check: 2007-10-09)
		Once convergence has thickened the crust over a broad region, the available plate forces to overcome spreading forces, rather than forces within individual thrust sheets, determines the evolution of an orogen.
		The orogen can grow wider by thickening crust over a broader region and convergence between the major plates of the orogen can continue as major strike-slip ``indentor'' faults allow parts of the colliding plates to move laterally from the collision zone without widening it.
		The north-south convergence associated with plate motions occurs within the Himalayas and on indentor faults.
	www.agu.org /revgeophys/sleep00/node5.html (377 words)

	Tampa Bay Region Chooses Convergence Communications to Develop Emergency Management Portal
		Convergence will deploy its E-Sponder(SM) solution to develop a customized portal for the Tampa Bay Region including Hillsborough and Pinellas Counties and the cities of Tampa, Clearwater and St. Petersburg.
		In addition to Tampa, Convergence Communications' E-Sponder was selected this summer to provide emergency management software to the State of Wisconsin Emergency Management, Department of Military Affairs.
		Convergence was named Microsoft Worldwide Partner of the Year - Information Worker at the 2005 Microsoft Worldwide Partner Event.
	www.prnewswire.com /cgi-bin/stories.pl?ACCT=104&STORY=/www/story/12-05-2005/0004227704&EDATE= (458 words)

	Physics 137, Assignment 13 key (Site not responding. Last check: 2007-10-09)
		This combination of convergence and more dense air usually results in sinking air which is warmed by compression as it sinks so it is warmer near the surface than would be expected.
		(a) On the chart, mark where regions of convergence and divergence are occurring.
		To strenghthen an anticyclone requires that the convergence aloft must be greater than the surface divergence.
	maxwell.byu.edu /~spencerr/phys137/Assignment13key.html (544 words)

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