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Topic: Relative compactness

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	Relative Compactness from the Bitopological Point of View (Site not responding. Last check: 2007-10-31)
		The notion of relative compactness based on the relation of two topologies on the same set and used by Z. Balogh instead of the above-mentioned idea clearly reveals, even at first glance, the bitopological essence of this notion.
		Thus we are able to choose different kinds of bitopological local compactness leading to the relative compactness.
		Besides, the strengthening of relative compactness makes it possible to connect the resulting strong compactness with a special type local compactness by the equivalence relation.
	www.pmf.ukim.edu.mk /mathematics/dvalishvili.htm (282 words)

	SHK - Shakbazian Compact Groups of Galaxies
		The name of the Shakhbazian compact group of galaxies as constructed from the sequence number (listed in the original references and in the originating CDS Catalog) combined with the prefix `SHK' which is recommended by the Dictionary of Astronomical Nomenclature.
		The number of galaxies in the compact group: in the published lists, this number was frequently stated as a range, notice, and these ranges were apparently converted (by the authors) to their median values when the machine-readable version was created.
		The coefficient of relative compactness of the group of galaxies: this coefficient is the ratio of the sum of the diameters of all the galaxies of the group to the diameter of the group as a whole.
	heasarc.gsfc.nasa.gov /W3Browse/all/shk.html (613 words)

	Portable emergency breathing apparatus - Patent 4798203
		relative to the axis of the supply container, thus optimizing compactness and lightness of weight of the housing and thus the overall apparatus.
		Furthermore, the improved operating characteristics are achieved with a structure which promotes radial and axial compactness of the valve assembly and thus the desired compactness with respect to the apparatus in its entirety.
		A further object is the provision of apparatus of the foregoing character wherein the housing has a radially outer surface relative to the container axis which is within the cylindrical plane of the outer surface of the side wall of the container, thus to optimize protection for the connection between the housing and container.
	www.freepatentsonline.com /4798203.html (5226 words)

	Compactness Criteria in Function Spaces, (by M.Dörfler, H.G.Feichtinger and K.Gröchenig)
		Thus for $L^2$ the relative compactness can be characterized by tightness in the time as well as in the frequency variable.
		As special cases for the compactness criterion developed in this context one obtains a characterzation of compact subsets in modulation spaces by means of tightness of their STFT in phase space, or in a similar way the characterization of relative compactness in homogeneous Besov spaces by means of wavelet transforms.
		As a final example of the general principle a compactness criterion for the Bergmann-Fock space is stated.
	www.mat.univie.ac.at /~nuhag/Gabor/archive/abstracts/9999/dfgXX.html (302 words)

	Iowa Code 1997SUPPLEMENT: Section 42.4
		The compactness of a district is greatest when the length of the district and the width of the district are equal.
		The measure of a district's compactness is the absolute value of the difference between the length and the width of the district.
		The population center of the district is defined by computing the population-weighted average of the "x" co-ordinates and "y" co-ordinates of each geographic unit center assigned to the district, it being assumed for the purpose of this calculation that each population data unit possesses uniform density of population.
	www.legis.state.ia.us /IACODE/1997SUPPLEMENT/42/4.html (1678 words)

	Appendix G - State Districting Principles
		When it is necessary to compare the relative compactness of two or more districts, or of two or more alternative districting plans, the tests prescribed by paragraphs “b” and “c” of this subsection shall be used.
		In determining the relative compactness of a district, consideration should be given to overall geographical and demographic compactness.
		Legislative districts shall consist of compact, contiguous territory and shall have population as nearly equal as is practicable, based on the last preceding federal census.
	www.senate.leg.state.mn.us /departments/scr/redist/red2000/Tab5appx.htm (8984 words)

	City of Brentwood (Site not responding. Last check: 2007-10-31)
		One method of evaluating relative compactness, or the severity of soil compaction, is to measure the soil’s weight per volume, or its density.
		Conversely, when a tree is planted into compacted soil and drainage is impeded through the crushing of soil macro pores, water may remain around the root zone depriving the roots of needed oxygen.
		Compaction is often specified as a percentage of a peak density from a standard moisture-density curve (such as Proctor density) or a specified testing protocol (such as AASHTO T-99).
	www.ci.brentwood.ca.us /department/parks/urban_trees/structural_soils.cfm (4321 words)

	Developing an Equal Area Global Grid by Small Circle Subdivision
		After the relative co-latitudes of the nine small circles are computed, the poles and the arc lengths of all the small circles can be calculated the same way as in the four-fold case.
		The compactness of grid cells is an important geometrical property, as the ideal global grid would have identically shaped cells (zero compactness variation) at the highest possible compactness.
		The general pattern is that the higher compactness sub-triangles at the next lower recursion level are partitioned similarly, with center triangles of lower compactness surrounded by three higher compactness outer triangles.
	www.ncgia.ucsb.edu /globalgrids-book/song-kimmerling-sahr (6683 words)

	XML Binary Characterization Measurement Methodologies (Site not responding. Last check: 2007-10-31)
		Measurement of compactness consists of encoding the same data using the major combinations of methods which are categorized by: tokenization, document optimization (compression), schema-based encoding, the combination of document and schema-based optimization, deltas, and lossy compression.
		Compactness: This is the additional space required for the application of an update or the typical overhead of supporting different kinds of changes to a format instance.
		For compactness, this percentage is overhead over a linear creation of an instance with the same data in the candidate format, along with an estimated (for analytical) or actual (for empirical) standard deviation.
	www.w3.org /TR/2005/NOTE-xbc-measurement-20050331 (12437 words)

	Galaxy Collisions: 2. Some Phenomenology: What's Out There?
		Most collisions are relatively quick and impulsive, but the magnitude of the effects does depend on the relative velocity at closest approach (see e.g.
		The scale length of the various components, or relative compactness, is another important parameter.
		Another two are the dimensionless impact parameter, and a dimensionless measure of the compactness of the companion.
	www.public.iastate.edu /~curt/cg/section2.html (2618 words)

	Confocal Single-Mode-Fiber-Optic Raman Microspectrometer
		The spectrometer portion of the apparatus would be compact, relative to prior Raman spectrometers of equivalent spectral resolution.
		The light diverging from the output end of this fiber would be focused by the objective lens onto a small spot on the surface of a specimen (or, optionally in the case of a semitransparent specimen, into a small subsurface volume).
		This compactness would be achieved by a novel design featuring only two reflective surfaces, one of which would be a convex diffraction grating shaped and blazed by electron-beam lithography in poly(methyl methacrylate).
	www.nasatech.com /Briefs/Apr01/NPO20932.html (860 words)

	Bush v. Vera, 517 U.S. 952 (1996). (Site not responding. Last check: 2007-10-31)
		These findings--that the State substantially neglected traditional districting criteria such as compactness, that it was committed from the outset to creating majority minority districts, and that it manipulated district lines to exploit unprecedentedly detailed racial data--together weigh in favor of the application of strict scrutiny.
		We have, however, already found that all three districts are bizarrely shaped and far from compact, and that those characteristics are predominantly attributable to gerrymandering that was racially motivated and/or achieved by the use of race as a proxy.
		If, because of the dispersion of the minority population, a reasonably compact majority minority district cannot be created, §2 does not require a majority minority district; if a reasonably compact district can be created, nothing in §2 requires the race based creation of a district that is far from compact.
	supct.law.cornell.edu /supct/html/94-805.ZO.html (7520 words)

	Abstracts (Site not responding. Last check: 2007-10-31)
		The theory of relative boundedness or compactness plays a useful role in the spectral theory of linear operators.
		For example, the Kato-Rellich theorem states that if A is self-adjoint and B is a symmetric A-bounded operator with relative bound less than one, then A+B is self-adjoint; further A+B is bounded below if A is. Relative compactness preserves the essential spectrum and Fredholm index.
		In the case of a limit-circle endpoint, it is found that the criteria have a somewhat different structure than for the limit-point endpoint.
	www.cs.cf.ac.uk /Gregynog99/hinton.html (125 words)

	An Introduction to Banach Space Theory
		The section includes a short discussion of topological groups, primarily to be able to obtain a characterization of relative compactness in topological groups in terms of the accumulation of nets that does not always hold in arbitrary topological spaces.
		The goal of optional Section 2.9 is to obtain James's characterization of weakly compact subsets of a Banach space in terms of the behavior of bounded linear functionals.
		Schauder's theorem relating the compactness of a bounded linear operator to that of its adjoint is presented, as is the characterization of operator compactness in terms of the bounded-weak*-to-norm continuity of the adjoint.
	www.math.lsa.umich.edu /~meggin/ibst.html (2875 words)

	Access to DNA secrets yields better understanding of genes, possible tool for disease diagnosis
		When DNA is highly compacted, like a closed accordion, it's not as accessible to transcription proteins, and cannot make RNA, said Dr. Harold "Skip" Garner, professor of biochemistry and internal medicine at UT Southwestern and senior author of the study.
		Using the chromatin array, UT Southwestern researchers can detect the relative compactness of several stretches of DNA at a time with very high resolution, allowing them to determine which genes have the propensity for making RNA.
		Other techniques have be used to examine the compactness of DNA, but only a small piece of DNA at a time, said Ryan Weil, a UT Southwestern biophysics graduate student and the study's lead author.
	www.eurekalert.org /pub_releases/2004-07/uots-atd070704.php (794 words)

	AMCA: On relative countable paracompactness by Yoshikazu Yasui (Site not responding. Last check: 2007-10-31)
		Gordienko etc. and studies of relative compactness were done in A.V. Arhangel'skii, I.V. Jaschenko and J. Tartir etc..
		In this talk, we shall discuss the relative version of countable paracompactness and study their characterizations etc..
		A.V. Arhangel'skii and I.V. Jaschenko, Relatively compact spaces and separation properties, Comm.
	at.yorku.ca /c/a/b/y/18.htm (213 words)

	Comparison of HTML Produced by Several HATs
		Recently, there was a lively discussion on the Help Authoring Tools and Techniques (HATT) mailing list about the relative compactness and efficiency of the HTML code produced by various Help authoring tools.
		Compact HTML is important for a variety of reasons.
		The test we performed is not an overall evaluation of any of the authoring tools, nor are the results of the test intended as an endorsement of any of the authoring tools involved.
	www.knopf.com /resources/hatcomp/index.html (1074 words)

	EMSL: Ab Initio Methods Benchmark Report -- Overview
		Since relative computational performance can vary significantly from program to program and from machine to machine, researchers at the Environmental Molecular Sciences Laboratory (EMSL) and elsewhere are confronted with a complex set of choices when trying to determine what works best for them.
		We have since learned that this failure was the result of near linear dependency in the basis, due to the diffuse s functions on hydrogen and the relative compactness of the particular Ci conformation we used.
		This is in spite of the relatively slow clock on the 590 (66 MHz vs. 300 MHz for the DEC 900).
	www.emsl.pnl.gov /docs/tms/abinitio/Benchmarks.html (7884 words)

	Apollo Moon Landing hoax accusations - Wikipedia, the free encyclopedia
		Detailed comparison of the backgrounds said to be identical in fact show significant changes in the relative positions of the hills that are consistent with the claimed locations that the images were taken from.
		The regolith was estimated to be several meters thick and is highly compacted with depth.
		Sibrel made repeated demands over several years that Apollo 11 Lunar Module Pilot 'Buzz' Aldrin swear an oath on the Bible that he had walked on the Moon, or admit that it was all a hoax.
	en.wikipedia.org /wiki/Apollo_moon_landing_hoax_accusations (12015 words)

	Disprot - Database of Protein Disorder
		Application of intrinsic fluorescence to the study of protein conformational analysis relies on the fact that the parameters of tryptophan emission (intensity and wavelength of maximal fluorescence) depend essentially on environmental factors, including solvent polarity, pH, and presence or absence of quenchers.
		The viscosity of a sample, which is the degree to which it resists flow under an applied force, is affected by the molecular weight of a protein and its shape and conformation.
		By comparing the behavior of a protein to those of known structure and similar size, the relative disorder of a protein can be determined.
	www.ist.temple.edu /disprot/view_detection.php?detection_id=BF (1728 words)

	GEM-SET
		The compact Fugu genome contains the same basic vertebrate blueprint as the human genome in a sequence seven times shorter.
		This difference is primarily due to the scarcity in Fugu of the large repeat-filled tracts that litter the human genome.
		If you were to run an internet search on "fugu" you will find a lot of information about the human genome project in general, and may find a more direct reponse to your question.
	www.uic.edu /orgs/gem-set/archive030715q1.htm (219 words)

	CPF Campus Participation
		The relative compactness of the campus, proximity of similar campus functions to each other and to residence halls, and the integration of downtown Iowa City are positive qualities.
		Workshop participants cite the lack of trees, shrubs and flowers, and the diminishing of greenspace as weaknesses of the campus.
		The relative compactness of the campus that is seen as a strength is also a weakness when compactness leads to a lack of open space between buildings.
	www.uiowa.edu /~cpc/cpf/manual/partic.htm (846 words)

	WEAK CONVERGENCE METHODS FOR SEMILINEAR ELLIPTIC EQUATIONS
		The main difficulty in examining the compactness of Palais—Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains.
		In this book we develop the concentration—compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences.
		This tool, combined with some basic methods from the Lusternik—Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions.
	www.worldscibooks.com /mathematics/4225.html (190 words)

	JGI - Why Sequence the Pufferfish??
		The compact Takifugu genome contains the same basic vertebrate blueprint as the human genome in a sequence seven times shorter.
		This difference is primarily due to the scarcity in Takifugu of the large repeat-filled tracts that litter the human genome.
		The relative compactness of the Takifugu genome simplifies the detection and analysis of both gene sequences and gene regulatory elements.
	www.jgi.doe.gov /sequencing/why/pufferfish.html (279 words)

	Galactic discovery
		Charmandaris and other astronomers believed that a possible explanation might be that this diffuse atomic gas is located, not in vast, very dilute clouds, but rather around smaller, much denser molecular clouds, such as those detected in our own galaxy, the Milky Way.
		But due to their relative compactness, said Charmandaris, these molecular clouds would be expected to be found at significant distances from the remnants of galactic collisions.
		To test this idea, the astronomers decided to look for the possible presence in the shells around some nearby elliptical galaxies of specific molecules that are typical of dense gas clouds.
	www.news.cornell.edu /Chronicle/00/4.6.00/Vassilis-galaxy.html (508 words)

	Volume 25, Number 2, 1999
		Here we study the integers (d,g,r) such that on a smooth projective curve of genus g there exists a rank $r$ stable vector bundle with degree d and spanned by its global sections.
		) endowed with the weak* topology is not a Valdivia compact.
		Namely, it yields an example of an affine continuous image of a convex Valdivia compact (in the weak* topology of a dual Banach space) which is not Valdivia, and shows that the property of the dual unit ball being Valdivia is not an isomorphic property.
	www.math.bas.bg /~serdica/n2_99.html (556 words)

	Publications of the SPACES team
		Regular systems possess the projection property, are relatively easy to compute, and often have a compact form.
		In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z. Li.
		When all the polynomials have the same degree, the complexity of this algorithm is polynomial relative to the generic number of solutions.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	Array convergence of functions of the first Baire-class
		of elements in a pointwise compact subset of the Baire-1 functions on a Polish space, whose iterated pointwise limit
		In angelic spaces the notions of (relative) compactness, (relative) countable compactness and (relative) sequential compactness coincide.
		A device of R. Whitley's applied to pointwise compactness in spaces of continuous functions, Proc.
	www.math.utep.edu /Faculty/helmut/baire/baire.html (753 words)

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