
	Where results make sense

Topic: Sieve methods

	Sieve theory - Wikipedia, the free encyclopedia
		Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers.
		One of the original purposes of sieve theory was to try to prove conjectures in number theory such as the twin prime conjecture.
		Sieve theory is somewhat related to sieve algorithms such as the general number field sieve, used for factoring large numbers, although sieve theory and sieve algorithms serve different purposes.
	en.wikipedia.org /wiki/Sieve_methods (587 words)

	Cardiff University School of Mathematics Home Page
		Sieve methods were created to attack the well-known Goldbach and twin-prime problems.
		It turns out that there are excellent reasons why sieve methods alone cannot solve these problems, but they give partial information on these and many other problems where the `deeper' methods of analytic number theory, such as exponential sums will not work.
		Sieve methods can be purely combinatorial like the "sieve of Eratosthenes", or partly combinatorial and partly analytic: finding an inequality by rearranging a sum of squares which must be positive - even the modulus squared of an exponential sum in the so-called "large sieve".
	www.cf.ac.uk /maths/numbertheory/sieves.html (174 words)

	Sieve - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-09-17)
		A sieve is a device for segregating aggregate based on particle size.
		Sieves commonly consist of a wire mesh on which the aggregate is placed.
		A sieve used in cooking is a colander.
	encyclopedia.worldsearch.com /sieve.htm (212 words)

	PlanetMath: sieve of Eratosthenes
		The sieve of Eratosthenes is the number-theoretic version of the principle of inclusion-exclusion.
		The obtained bound is clearly inferior to the prime number theorem, but the method applies to problems that are not tractable by the other techniques.
		This is version 5 of sieve of Eratosthenes, born on 2004-01-24, modified 2004-05-16.
	www.planetmath.org /encyclopedia/SieveOfEratosthenes2.html (237 words)

	PlanetMath: Brun's pure sieve
		The sieve of Eratosthenes is based on the principle of inclusion-exclusion in the form
		This inequality is stronger than the one obtained by an application of the sieve of Eratosthenes.
		This is version 6 of Brun's pure sieve, born on 2004-02-21, modified 2004-07-31.
	planetmath.org /encyclopedia/BrunsPureSieve.html (541 words)

	General number field sieve (Site not responding. Last check: 2007-09-17)
		In mathematics, the general number field sieve is the most efficient algorithm known for factoring integers.
		When the term "number field sieve" is used without qualification, it refers to the general number field sieve.
		It is better than the general number field sieve when factors are of small size, as it works by finding smooth values of order of the smallest prime divisor of n, and its running time depends on the size of this divisor.
	www.serebella.com /encyclopedia/article-General_number_field_sieve.html (852 words)

	Sieve theory - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-09-17)
		Nevertheless, the more advanced sieves can still get very intricate and delicate (especially when combined with other deep techniques in number theory), and entire textbooks have been devoted to this single subfield of number theory; a classic reference is.
		Sieve Methods, Exponential Sums, and their Applications in Number Theory (London Mathematical Society Lecture Note Series)
		The sieve method in group theory: Application of the sieve method to the word problem for certain types of groups.
	encyclopedia.worldsearch.com /sieve_theory.htm (665 words)

	sieve methods (Site not responding. Last check: 2007-09-17)
		Sieve samples to an appropriate size for mineral separates approximately 800-500 microns and 500-250 microns.
		Running two sets of sieves will let you clean one while the other set is shaking.
		Remove sieves from shaker and disassemble stack carefully.
	www.uvm.edu /cosmolab/lab/sievemeth.html (143 words)

	Cornell Math - MATH 735, Spring 2000
		Of the numerous methods available for the study of the natural numbers, we shall discuss at least three: elementary methods, sieve methods and the theory of the Riemann zeta function and related functions.
		Sieve methods have their origin in the Sieve of Eratosthenes.
		In their modern incarnation they are methods for estimating the size of a set of integers given some information about how that set is distributed among congruence classes.
	www.math.cornell.edu /~www/Courses/GradCourses/SP00/735.html (385 words)

	Special number field sieve (Site not responding. Last check: 2007-09-17)
		The special number field sieve (SNFS) is a special-purpose integer factorization algorithm.
		The general number field sieve (GNFS) was derived from it.
		sieve field special special needs field parking special finance field workouts field wallpaper field turf special floor special forces field trip field training
	www.serebella.com /encyclopedia/article-Special_number_field_sieve.html (381 words)

	Water Resources Division (WRD) Policy on Publication of Sediment Size Data Determined by use of the Sedigraph
		Methods for producing data describing selected properties of fluvial sediment have evolved since 1993 when Office of Surface Water (OSW) Technical Memorandum 93.11, "Water Resources Division Policy on Publication of Sediment Size Data Determined by use of the Sedigraph," was released.
		Method codes related to field determinations or for analyses performed locally in the absence of the SLEDS software must be entered into the database by the data collector or provider.
		Method codes for historical data may be entered at the discretion of the individual District.
	water.usgs.gov /admin/memo/SW/sw04.01.html (1116 words)

	Sieve Methods (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		Sieve methods can yield valuable clues about these distributions and hence allow us to bound the running times of these algorithms.
		In this treatise we survey the major sieve methods and their important applications in number theory.
		1 an elementary method in the theory of primes (context) - Selberg - 1947
	citeseer.ist.psu.edu /charles00sieve.html (295 words)

	AASV News archive - Development of a 3-sieve method to determine particle size in the field
		The sieve was shaken by hand until it appeared that all the small particles had fallen through the screen.
		Of the 44 samples used in Exp 2, the one-sieve method was only able to predict 11 (25%) of the samples within 75 µm of their actual size, using the regression equation provided by the manufacturer (Table).
		While the three-sieve method predicts the average particle sizes more accurately than the one-sieve, it is still not as precise as the standard Ro-tap tester and 13-sieve stack.
	www.aasp.org /news/story.php?id=73 (938 words)

	Elementary Topics in Analytic Number Theory: Ross 2003 (Site not responding. Last check: 2007-09-17)
		Introduction to Sieves and the Sieve of Eratosthenes-Legendre: We introduced the general sieve problem and derived the most basic estimate in the subject, the Sieve of Eratosthenes-Legendre, from the fundamental property of the Möbius function.
		Sieve Methods: Lecture 1 Handout: Introduction to sieves, discussion of notation and preliminaries, and statement/proof of the Sieve of Eratosthenes-Legendre.
		Sieve Methods: Lectures 2, 3 Handout: Develops Brun's simple pure sieve and uses it to establish that the series of reciprocals of the twin primes is either a convergent infinite series or a finite sum.
	www.princeton.edu /~ppollack/notes/course.htm (1115 words)

	[No title]
		The difficulty with proof by sieve methods is known as the "parity problem".
		With respect to Chen's result, the parity problem means that after conducting the sieve you are left with one prime plus a number which has either one or two prime factors and you can't tell which because of uncertainty/error in the sieve.
		This is known as the fundamental lemma of the sieve.
	www.math.niu.edu /~rusin/known-math/00_incoming/sieves (1088 words)

	Atlas: Sieve Methods in Combinatorics by Ram Murty (Site not responding. Last check: 2007-09-17)
		We will present a combinatorial analogue of a sieve method originating in a 1934 paper of Paul Turan which we call the Turan sieve.
		The advantage of the Turan sieve is that it is "Mobius function free".
		Thus, in a combinatorial setting, this sieve method has wider applications and we explore some of these, such as getting good estimates for the number of proper colorings of the vertices of a graph.
	atlas-conferences.com /cgi-bin/abstract/caok-42 (105 words)

	[How] - XYYXF - factorizations of x^y+y^x
		The main idea of integer factorization is to extract small factors by ECM until cofactor became prime or factorable enough quickly with sieve methods.
		Usually, when running ECM on many composites at the same time, some smaller ones should be taken out and factored with sieve methods as soon as the average period of extracting ECM factors become twice less than sieve running time for those small composites.
		Some papers about methods of integer factorization and their applications are listed in the Links section.
	xyyxf.at.tut.by /how.html (654 words)

	Visualizing Categorical Data
		Some methods (sieve diagrams, mosaic displays) are well-suited for detecting and patterns of association in the process of model building; others are useful in model diagnosis, or as graphical summaries for presentation of results.
		For quantitative data, graphical methods are commonplace adjuncts to all aspects of statistical analysis, from the basic display of data in a scatterplot, to diagnostic methods for assessing assumptions and finding transformations, to the final presentation of results.
		Second, it may be argued that graphical methods for quantitative data are easily generalized; for example, the scatterplot for two variables provides the basis for visualizing any number of variables in a scatterplot matrix; available graphical methods for categorical data tend to be more specialized.
	www.math.yorku.ca /SCS/Papers/casm/casm.html (7349 words)

	[No title]
		Choosing p prime simplifies the sieve, the primality of > p is not used elsewhere.
		Choosing p prime simplifies the sieve, the primality of > > p is not used elsewhere.
		Hooley's book _Applications of sieve methods to the theory of numbers_ is good although out of print.
	www.math.niu.edu /~rusin/known-math/99/selfridge (2619 words)

	Sieve Methods Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-09-17)
		Looking For sieve methods - Find sieve methods and more at Lycos Search.
		Find sieve methods - Your relevant result is a click away!
		Look for sieve methods - Find sieve methods at one of the best sites the Internet has to offer!
	www.karr.net /search/encyclopedia/Sieve_methods (755 words)

	A Survey on the Number Field Sieve (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		The Number Field Sieve is expected to be the fastest among the recent major factoring methods.
		Keywords: Factoring Method, Sieving Method, NFS, SNFS, GNFS, DLP Recent developments of computational number theory have been very much infuenced by cryptography.
		In this note, a survey on the Number Field Sieve, or NFS, will be given as one of the most important of these methods.
	citeseer.ist.psu.edu /312752.html (546 words)

	Thirty Years of Integer Factorization
		A lot of different methods exist to factor a number, starting from the linear sieve up to the algebraic sieve, including methods based on elliptic curves.
		The method of combination of congruences is an extension of Kraitchik's method.
		One of the first sieves concerning primality and factorization is the Erastothene sieve.
	pauillac.inria.fr /algo/seminars/sem00-01/morain.html (1633 words)

	C285-88(2005) Standard Test Methods for Sieve Analysis of Wet-Milled and Dry-Milled Porcelain Enamel (Site not responding. Last check: 2007-09-17)
		1.3 Method A is intended for use where a referee method of higher accuracy is required, while Method B is intended to meet the needs of normal enamel plant production control operations where a rapid, simplified method of sieve testing is required.
		The accuracy of the simplified method has proved to be entirely adequate for this use.
		It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
	www.astm.org /DATABASE.CART/JUNK/C285.htm (204 words)

	Sieve Methods (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		The first chapter is a discussion of the basic sieve...
		26 Sieve Methods (context) - Halberstam, Richert - 1974
		1 Beitrage zur Viggo Brunschen Methode in der Zahlentheorie (context) - Hans - 1924
	citeseer.ist.psu.edu /462462.html (664 words)

	ipedia.com: Inclusion-exclusion principle Article (Site not responding. Last check: 2007-09-17)
		In many cases where the principle could give an exact formula (in particular, counting prime numbers using the sieve of Eratosthenes), the formula arising doesn't offer useful content because the number of terms in it is excessive.
		After a slow start, his ideas were taken up by others, and a large variety of sieve methods developed.
		These for example may try to find upper bounds for the "sieved" sets, rather than an exact formula.
	www.ipedia.com /inclusion_exclusion_principle_1.html (451 words)

	C92-95(1999) Standard Test Methods for Sieve Analysis and Water Content of Refractory Materials
		This method is recommended for use with materials that require water addition, and that slake in normal industrial use.
		It is recommended (1) for clays, when the slaking action of water is undesirable, (2) when the material is in the form of coarsely ground grog and calcine, and (3) when the clay is to be used in such a way that the ultimate particle size is of secondary importance.
		Included is a method for obtaining the water content of other refractory materials, such as plastic refractories and wet mixes.
	www.astm.org /DATABASE.CART/REF_PAGES/C92.htm (351 words)

	Sieve
		Manufactures molecular sieve (zeolite) adsorbents and catalysts, as well as silica gel for chromatography and desiccant applications.
		Manufactures test sieve separators and wire cloth particle size measurement devices, as well as providing equipment calibration services.
		The Liver Sieve research group has an interest in the fine vessels of the liver.These pages describe some of the background, findings and publications arising from this work.
	www.omniknow.com /common/wiki.php?in=en&term=Sieve (1162 words)

	Amazon.de: English Books: Sieve Methods, Exponential Sums, and Their Applications in Number Theory (London Mathematical ... (Site not responding. Last check: 2007-09-17)
		Sieve Methods, Exponential Sums, and Their Applications in Number Theory (London Mathematical Society Lecture Note)
		In particular, many of the papers reflect the interaction among the different fields of sieve theory, Dirichlet series (including the Riemann Zeta-function), and exponential sums, while displaying the subtle interplay between the additive and multiplicative aspects of the subjects.
		The fundamental problems discussed include recent work on Waring's problem, primes in arithmetical progressions, Goldbach numbers in short intervals, the ABC conjecture, and the moments of the Riemann Zeta-function.
	www.amazon.de /exec/obidos/ASIN/0521589576/ww2afvportalinpa (302 words)

Try your search on: Qwika (all wikis)