Search results
Results from the WOW.Com Content Network
Metal laboratory sieves An ami shakushi, a Japanese ladle or scoop that may be used to remove small drops of batter during the frying of tempura ancient sieve. A sieve, fine mesh strainer, or sift, is a tool used for separating wanted elements from unwanted material or for controlling the particle size distribution of a sample, using a screen such as a woven mesh or net or perforated sheet ...
The techniques of sieve theory can be quite powerful, but they seem to be limited by an obstacle known as the parity problem, which roughly speaking asserts that sieve theory methods have extreme difficulty distinguishing between numbers with an odd number of prime factors and numbers with an even number of prime factors. This parity problem is ...
In terms of sieve theory the Selberg sieve is of combinatorial type: that is, derives from a careful use of the inclusion–exclusion principle. Selberg replaced the values of the Möbius function which arise in this by a system of weights which are then optimised to fit the given problem.
The Legendre sieve has a problem with fractional parts of terms accumulating into a large error, which means the sieve only gives very weak bounds in most cases. For this reason it is almost never used in practice, having been superseded by other techniques such as the Brun sieve and Selberg sieve. However, since these more powerful sieves are ...
The Goldston–Pintz–Yıldırım sieve (also called GPY sieve or GPY method) is a sieve method and variant of the Selberg sieve with generalized, multidimensional sieve weights. The sieve led to a series of important breakthroughs in analytic number theory. It is named after the mathematicians Dan Goldston, János Pintz and Cem Yıldırım. [1]
The general number field sieve, on the other hand, manages to search for smooth numbers that are subexponential in the size of n. Since these numbers are smaller, they are more likely to be smooth than the numbers inspected in previous algorithms. This is the key to the efficiency of the number field sieve.
Sieve elements are specialized cells that are important for the function of phloem, which is a highly organized tissue that transports organic compounds made during photosynthesis. Sieve elements are the major conducting cells in phloem. Conducting cells aid in transport of molecules especially for long-distance signaling.
The quadratic sieve attempts to find pairs of integers x and y(x) (where y(x) is a function of x) satisfying a much weaker condition than x 2 ≡ y 2 (mod n). It selects a set of primes called the factor base, and attempts to find x such that the least absolute remainder of y(x) = x 2 mod n factorizes completely over the factor base.