E. Bombieri [12] has written at length concerning applications of the large sieve to number theory. Our intent here is to complement his exposition by devoting our attention to the analytic principle of the large sieve; we describe only briefly how applications to number theory are made. The large sieve was studied intensively during the decade 1965-1975, with the result that the subject has lo...

To overcome the large memory requirement of classical lattice sieving algorithms for solving hard lattice problems, Bai–Laarhoven–Stehlé [ANTS 2016] studied tuple lattice sieving, where tuples instead of pairs of lattice vectors are combined to form shorter vectors. Herold–Kirshanova [PKC 2017] recently improved upon their results for arbitrary tuple sizes, for example showing that a triple sie...

A method was designed for in vivo observation of sieve element/companion complexes by using confocal laser scanning microscopy. A leaf attached to an intact fava bean plant was mounted upside down on the stage of a confocal microscope. Two shallow paradermal cortical cuts were made in the major vein. The basal cortical window allowed us to observe the phloem intact. The apical window at 3 cm fr...

Carbon molecular sieve membranes (CMSMs) are an important alternative for gas separation because of their ease of manufacture, high selectivity due to molecular sieve separation, and high permeance. The integration of separation by membranes and reaction in only one unit lead to a high degree of process integration/intensification, with associated benefits of increased energy, production effici...

The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number, discrete logarithm computations) is a variant of the quadratic sieve factoring algorithm. Paradoxical as it sounds, the principles of the number field sieve, in a strict sense, could not be applied to number field computations, yet. In this article we give an in...

The number field sieve is a relatively new method to factor large integers. Its most notable success is the factorization of the ninth Fermat number. It is significantly faster than all known existing integer factoring algorithms. We examine the theoretical underpinnings of the sieve; after understanding how it works, we state the algorithm. We look mostly to the algebraic number theory aspects...

In the present research work, a low-ash coal, from Ghouzlou deposit in Iran, with an average ash content of 12% was subjected to some beneficiation experiments such as heavy media separation and flotation. Sieve analysis showed that 62.3% of the coal sample with the size of +2 mm had around 7.3% ash contents. Also, heavy media tests carried out on five size fractions revealed that by setting th...

Nowadays distillation is recognized as one of the economical and the most trustable separation methods in chemical, petroleum, gas and petrochemical industries. It is almost used as a first and the most applicable choice in separation methods. In this article the effect of inlet downcomer on the hydrodynamics of industrial sieve tray has been elaborated. The study was carried out by using a 3-D...