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Topic: Sufficiently large

	Sufficiently Large
		Often the audience is not quite aware just how large, 'sufficiently large' really is. It can be as large, or considerably larger than the number of fundamental particles (atoms, (baryons, leptons)) in the universe.
		Sufficiently large can be really big in the way that space is not.
		For those with sufficient experience it serves as a marker to ask the question "How large are we talking about?" For example, HeapSort is faster than BubbleSort for sufficiently large N - how large, when does the change-over occur?
	c2.com /cgi/wiki?SufficientlyLarge (237 words)

	Sufficiently large - Wikipedia, the free encyclopedia
		In mathematics, the phrase sufficiently large is used in contexts such as:
		The phrase "sufficiently large" should not be confused with the phrases "arbitrarily large" or "infinitely large".
		"Sufficiently large" is sometimes the subject of mathematical humor; for example, as in the mathematician's joke "π = 3, for sufficiently large values of 3".
	en.wikipedia.org /wiki/Sufficiently_large (113 words)

	Arbitrarily large - Wikipedia, the free encyclopedia
		This should not be confused with the phrase "sufficiently large".
		For instance, it is true that prime numbers can be arbitrarily large, but it is not true that all sufficiently large numbers are prime.
		It is also worth noting that "arbitrarily large" does not mean "infinitely large" - for instance, while prime numbers can be arbitrarily large, there is no such thing as an infinitely large prime, since all prime numbers (as well as all other integers) are finite.
	en.wikipedia.org /wiki/Arbitrarily_large (240 words)

	California - Wikipedia, the free encyclopedia
		With dredging, several rivers have become sufficiently large and deep that several inland cities (notably Stockton and Sacramento) are seaports.
		Large, settled populations lived on the West Coast and hunted sea mammals, fished for salmon, and gathered shellfish, while more mobile hunters and gathering groups in the California interior hunted terrestrial game and gathered nuts, acorns, and berries.
		There are large Korean Communities in Koreatown of Los Angeles as well as East San Gabriel Valley, Cerritos, South Bay, Los Angeles, and in North Orange County.
	en.wikipedia.org /wiki/California (6733 words)

	United States Patent Application: 0030031442
		In particular, the doping levels are very high, such that the gain g makes a sufficiently large contribution to an imaginary part of the complex-valued V.sub.c-parameter to define at least one gain-guided mode, e.g., the fundamental mode or several low-order modes of radiation in the optical fiber.
		The large cladding permits high pump energies to be injected into the ends of the fiber, and permits this pump energy to be supplied by spatially incoherent pump sources such as spatially incoherent diode laser arrays.
		At the same time the cladding region 14 will always be of sufficiently large diameter that the outer cladding 16 will have negligible effects on the propagation of the laser radiation 22 that is guided within the core 12 of the fiber.
	www.stanford.edu /~siegman/gain_guided_fiber_patent.html (8506 words)

	Virus Evolution Workgroup: 1999 Workshop Abstract
		The bias against large advantageous mutations results because large mutations (in general) are more likely to have deleterious pleiotropic (side) effects, and the bias increases with the number of phenotypic dimensions, which presumably is correlated with the complexity of the genome (see Burch and Chao 1999).
		As a result, in a population that is sufficiently large to harbor advantageous mutations of both large and small effect, evolution should proceed by large steps due to the higher probability of fixation of large mutations.
		A concern had been raised as to whether pleiotropy was sufficiently strong in any organism for Fisher’s explanation to apply (Orr and Coyne 1992), and whether an RNA virus would have a sufficiently complex genetic system to generate the required pleiotropy was uncertain.
	www.noble.org /virusevolution/abstracts/LinChao.htm (1119 words)

	Chandra Press Room :: More About Black Holes (Site not responding. Last check: 2007-11-04)
		The bottom line is that the observations must imply that a sufficiently large amount of matter is compressed into a sufficiently small region of space so that no other explanation is possible.
		The best places to look for fl holes are regions where large supplies of gas are available, such as double star systems, star forming regions, or the centers of galaxies.
		The discovery of a large, mid-mass fl hole away from the galaxy's center shows that somehow -- and it is not an easy task theoretically – fl holes much more massive than ordinary stellar fl holes can form in dense star clusters.
	chandra.harvard.edu /press/kits/m82kit/m82fact.html?set=large (619 words)

	California-Accomodations.com. California City Guide, your Guide to Tourist and Visitor Information Online
		Down the center of the state lies the Central Valley, a huge, fertile valley bounded by the coastal mountain ranges in the west, the Sierra Nevada to the east, the Cascade Range in the north and the the Tehachapi Mountains in the south.
		In the south lie the San Bernardino Mountains and a large salt lake, the Salton Sea.
		With dredging, several of these rivers have become sufficiently large and deep that several inland cities, notably Stockton, California, are seaports.
	www.california-accommodations.com /California-city-guide.html (824 words)

	CATHOLIC ENCYCLOPEDIA: Altar Canopy
		It should be square in form, sufficiently large to cover the altar and the predella on which the celebrant stands, and if it can easily be done, the colour of the material, silk velvet or other cloth, with which it is covered, should vary with the colour of the ornaments of the altar.
		It may also be a stationary structure, and this is usually the case in large churches, and then it is made of marble, stone, metal, or wood beautifully carved and overlaid with gold or silver, in the form of a cupola erected on four pillars.
		The canopy or ciborium is, according to the decision of the Cong.
	www.newadvent.org /cathen/01351a.htm (337 words)

	Large Bird Cages - Presented by BirdsComfort.com
		If you have large birds such as African Greys, Amazons, parrots, cockatoos, and macaws as pets, you should go for a large bird cages.
		A large bird cages should have a bar spacing of one or more inches.
		* Since most large pet birds have considerable beak strength and are prone to chewing, it is best to invest in all-steel or metal constructed large bird cages for your pets.
	www.birdscomfort.com /large_bird_cages.html (316 words)

	William B. Morgan Large Cavitation Channel (LCC)
		The William B. Morgan Large Cavitation Channel (LCC) is one of the world's largest and most technically advanced water tunnel facilities.
		It is capable of testing all types of ship and submarine propellers and propeller-hull interactions with model scales sufficiently large to match the largest towing and turning basins in the world.
		Large test chamber with 10 ft by 10 ft cross-section and a 13.1 m (43 ft) working length.
	www.globalsecurity.org /military/facility/presidents-island.htm (758 words)

	Large Numbers
		But historically, a large number was whatever the prevailing culture deemed it to be an intrinsically circular definition.
		For example, 1,799,257 factors into 7,001 x 257, but to decompose a sufficiently large number into its prime factors can be so problematic that computer scientists have harnessed this difficulty to encrypt data.
		LARGE NUMBERS- such as the 100-digit, or googol-size, ones running across the tops of these pages - have become more accessible over time thanks to advances in computing.
	www.fortunecity.com /emachines/e11/86/largeno.html (3119 words)

	lapack-d/dlabad.html (Site not responding. Last check: 2007-11-04)
		This subroutine is intended to identify machines with a large exponent range, such as the Crays, and redefine the underflow and overflow limits to be the square roots of the values computed by DLAMCH.
		This subroutine is needed because DLAMCH does not compensate for poor arithmetic in the upper half of the exponent range, as is found on a Cray.
		LARGE (input/output) DOUBLE PRECISION On entry, the overflow threshold as computed by DLAMCH.
	www.math.utah.edu:8080 /software/lapack/lapack-d/dlabad.html (115 words)

	Members of these large groups sufficiently proved identification in libel suits (Site not responding. Last check: 2007-11-04)
		Male models at a Neiman-Marcus department store were called "fags." A court determined that the 25 or so men concerned were known as models at the store, and the slur defamed each of them.
		Identification was sufficient for individual members of a college football team to establish identification.
		Although more than 60 players were on the team, their association with the team was well known within the community.
	excellent.com.utk.edu /~bowles/group-examples.html (160 words)

	lapack-s/slabad.html (Site not responding. Last check: 2007-11-04)
		This subroutine is intended to identify machines with a large exponent range, such as the Crays, and redefine the underflow and overflow limits to be the square roots of the values computed by SLAMCH.
		This subroutine is needed because SLAMCH does not compensate for poor arithmetic in the upper half of the exponent range, as is found on a Cray.
		LARGE (input/output) REAL On entry, the overflow threshold as computed by SLAMCH.
	www.math.utah.edu /software/lapack/lapack-s/slabad.html (113 words)

	[No title]
		The importance of the central limit theorem is that we can use the normal distribution to approximate the sampling distribution of the sample mean y bar as long as the population possesses a finite mean and variance, and the number n of measurements in the sample is sufficiently large.
		How large the sample size must be will depend on the nature of the sampled population.
		Although the chance of a large difference between the percentage of successes and the chance of success gets smaller and smaller as n grows, nothing prevents the difference from being large in some sequences of trials.
	www.eng.morgan.edu /~slh/410CLT.html (3053 words)

	SGI - Developer Central Open Source \| XFS
		This may seem to be an extremely large address space, but it is needed to plan for the exponential disk density improvements observed in the storage industry in recent years.
		As disk capacity grows, not only does the address space need to be sufficiently large, but the structures and algorithms need to scale.
		Efficiency when dealing with large amounts (terabytes) of main memory and hence large numbers of active files and large amounts of cached file data are areas demanding continual improvements.
	oss.sgi.com /projects/xfs (1645 words)

	Price taking equilibrium in club economies with multiple memberships and unbounded club sizes
		Clubs may be large, as large as the total agent set.
		With some additional standard sorts of assumptions on preferences, we demonstrate that for all sufficiently large economies, the core is non-empty and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy).
		Together these two results imply that, given the communication costs, for all sufficiently large economies there exists Edgeworth states of the economy and every Edgeworth state can be supported as a price-taking equilibrium.
	ideas.repec.org /p/mse/wpsorb/b04109.html (799 words)

	Conservation
		As we were riding along one of the many trails on the farm, Beto suddenly stopped and stared at the ground beside his horse.
		The highest level of tropical conservation is to have the habitat be sufficiently large and sufficiently natural and undisturbed that the entire original bird and animal population returns, all the way up to the top of the food chain.
		In the Americas, the endangered jaguar is at the very top, requiring a large area of natural habitat and abundant natural food.
	tropicalhardwoods.com /htm/main/conservation.htm (993 words)

	Conclusions (Site not responding. Last check: 2007-11-04)
		The first and perhaps the most important challenge is to deliver a sufficiently large quantum register with individually addressable qubits and individually controllable couplings.
		The decoherence time for the register should be sufficiently long to allow for a sizeable computation of the order of at least thousands or tens of thousands of gates.
		Our discussion in the previous chapter showed that in order to make such a register a basis for fault-tolerant computation, it would have to be very large indeed, at least of the order of 13 physical qubits per one logical qubit.
	beige.ucs.indiana.edu /B679/node122.html (1355 words)

	Encyclopaedia Britannica entry (Site not responding. Last check: 2007-11-04)
		In 1920 Viggo Brun introduced a sieve method to prove that every sufficiently large even integer is a sum of two integers, each of which has no more than nine prime factors.
		In 1950 Alfréd Rényi proved an inequality demonstrating that every sufficiently large even integer is the sum of a prime and an integer that is the product of a bounded number of prime factors.
		Bombieri extended Rényi's work, developing a density theorem that allowed him to prove his results on the primes in arithmetic progressions and to treat problems like those listed above, where earlier proofs had required the assumption of the extended Riemann hypothesis or other powerful means from analytic number theory.
	www.aam314.vzz.net /EB/Bombieri.html (346 words)

	Mittuniversitetet. - Home
		Mid Sweden University has partnerships with a number of Universities around the world for the exchange of students and staff.
		Our special commitment to priority areas is primarily concerned with research and postgraduate programmes but this also presupposes a sufficiently large undergraduate programme linked to these areas.
		Mid Sweden University Phone: +46 771-975 000
	www.miun.se /default____22057.aspx (108 words)

	Overview of the Kepler Mission (Site not responding. Last check: 2007-11-04)
		The results from this mission are meant to test the hypotheses and to determine the characteristics of a wide variety of planetary systems.
		The sample size of stars for this mission is large enough to capture the richness of the unexpected.
		The Kepler Mission is by far the best and quickest method for the detection and characterization of a large number of Earth-size planets.The proposed (not yet selected) Kepler Mission, a Discovery-class Mission, is designed to discover and characterize hundreds of terrestrial planets.
	www.kepler.arc.nasa.gov /summary.html (1425 words)

	Introduction
		This work is intended for the layman and is largely oriented toward the aesthetic appeal of tilings.
		For the figures in the Encyclopedia, a sufficiently large number of generations has been created to illustrate the general form of the infinite tiling.
		The resultant tiling is often very difficult to predict, and can be quite unexpected, from which derives the pleasure in discovering these tilings.
	members.cox.net /fractalenc/Introduction.html (1318 words)

	Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes
		0, for all sufficiently large economies, the core is non-empty and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy).
		Moreover, for any given economy, every state of the economy that is in the core for all replications of that economy can be supported as a price-taking equilibrium with communication costs.
		With some additional standard sorts of assumptions on preferences, we demonstrate that, given communication costs parameterized by ε > 0, for all sufficiently large economies, the core is non-empty and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy).
	ideas.repec.org /p/qmw/qmwecw/wp513.html (916 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		SUBROUTINE PDLABAD(ICTXT, SMALL, LARGE) * * -- ScaLAPACK auxiliary routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley.
		This subroutine is intended * to identify machines with a large exponent range, such as the Crays, * and redefine the underflow and overflow limits to be the square roots * of the values computed by PDLAMCH.
		This subroutine is needed because * PDLAMCH does not compensate for poor arithmetic in the upper half of * the exponent range, as is found on a Cray.
	www.netlib.org /scalapack/html/src/pdlabad.f (322 words)

	AMCA: CEP-subgroups of free Burnside groups of sufficiently large odd exponents. by Dmitriy Sonkin
		AMCA: CEP-subgroups of free Burnside groups of sufficiently large odd exponents.
		L \cap H = N. In this case H is called a CEP-subgroup of G. For sufficiently large odd exponent n we construct a CEP-subgroup isomorphic to a free Burnside group B(\infty, n) with infinite number of generators in the free Burnside group B(2, n) on two generators.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/j/a/14.htm (145 words)

	Learnables.com: Curriculum - German Advanced
		Completion of the intermediate programs enables an individual to acquire a sufficiently large vocabulary to engage in conversation.
		In addition, the script for Book 5 is available for students who wish to read while listening.
		The use of pictures enables students to acquire and remember a large number of words without the use of a dictionary.
	www.learnables.com /curr_germanadv.html (888 words)

	: Class Dlabad (Site not responding. Last check: 2007-11-04)
		For each array argument, the Java version will include an integer offset parameter, so the arguments may not match the description exactly.
		This subroutine is intended to * identify machines with a large exponent range, such as the Crays, and * redefine the underflow and overflow limits to be the square roots of * the values computed by DLAMCH.
		This subroutine is needed because * DLAMCH does not compensate for poor arithmetic in the upper half of * the exponent range, as is found on a Cray.
	www.cs.utk.edu /~seymour/f2j/docs/org/netlib/lapack/Dlabad.html (216 words)

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