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A sieve analysis (or gradation test) is a practice or procedure used in geology, civil engineering, [1] and chemical engineering [2] to assess the particle size distribution (also called gradation) of a granular material by allowing the material to pass through a series of sieves of progressively smaller mesh size and weighing the amount of material that is stopped by each sieve as a fraction ...
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. The prototypical example of a sifted set is the set of prime numbers up to some prescribed limit X .
Sieve analysis apparatus Sieve analysis is often used because of its simplicity, cheapness, and ease of interpretation. Methods may be simple shaking of the sample in sieves until the amount retained becomes more or less constant.
It is easy to see from the definition that the union or intersection of any family of sieves on c is a sieve on c, so Sieve(c) is a complete lattice. A Grothendieck topology is a collection of sieves subject to certain properties. These sieves are called covering sieves. The set of all covering sieves on an object c is a subset J(c) of Sieve(c).
In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular problems. Halberstam & Richert [ 1 ] : 92–93 write:
Pages in category "Sieve theory" The following 15 pages are in this category, out of 15 total. This list may not reflect recent changes. ...
Terence Tao gave this "rough" statement of the problem: [1]. Parity problem.If A is a set whose elements are all products of an odd number of primes (or are all products of an even number of primes), then (without injecting additional ingredients), sieve theory is unable to provide non-trivial lower bounds on the size of A.
Size-exclusion chromatography, also known as molecular sieve chromatography, [1] is a chromatographic method in which molecules in solution are separated by their shape, and in some cases size. [2] It is usually applied to large molecules or macromolecular complexes such as proteins and industrial polymers . [ 3 ]