Preface Sieve methods have had a long and fruitful history. The sieve of Eratosthenes (around 3rd century B.C.) was a device to generate prime numbers. Later Legendre used it in his studies of the prime number counting function π(x). Sieve methods bloomed and became a topic of intense investigation after the pioneering work of Viggo Brun (see [Bru16],[Bru19], [Bru22]). Using his formulation of ...

The large sieve has its origins in the work of Linnik and Rényi. It was developed to deal with sequences that avoid a positive proportion of residue classes. It was later simplified by Roth, Bombieri, Davenport, Halberstam, Montgomery, Gallagher and many others. For a survey see Montgomery [12] and Bombieri [1]. It is known that Montgomery’s large sieve [12] is a useful method when sifting sequ...

Sieve elements are one of the least understood cell types in plants. Translocation velocities and volume flow to supply sinks with photoassimilates greatly depend on the geometry of the microfluidic sieve tube system and especially on the anatomy of sieve plates and sieve plate pores. Several models for phloem translocation have been developed, but appropriate data on the geometry of pores, pla...

It is of interest in cryptographic applications to obtain practical performance improvements for the discrete logarithm problem over prime fields Fp with p of size ≤ 500 bits. The linear sieve and the cubic sieve methods described in Coppersmith, Odlyzko and Schroeppel’s paper [3] are two practical algorithms for computing discrete logarithms over prime fields. The cubic sieve algorithm is asym...

This review deals with aspects of the cellular and molecular biology of the sieve element/companion cell complex, the functional unit of sieve tubes in angiosperms. It includes the following issues: (a) evolution of the sieve elements; (b) the specific structural outfit of sieve elements and its functional significance; (c) modes of cellular and molecular interaction between sieve element and c...

A passive diffusion model has been developed which simultaneously accounts for the dependence of phloem mobility on permeability and acid dissociation. The model is consistent with the observation that the addition of an acid moiety to an otherwise phloem immobile compound may enhance that compound's ability to move in the phloem. However, acid trapping in the basic phloem is not the only enhan...

Macro-sieve electrodes were implanted in the sciatic nerve of five adult male Lewis rats following spinal cord injury to assess the ability of the macro-sieve electrode to interface regenerated peripheral nerve fibers post-spinal cord injury. Each spinal cord injury was performed via right lateral hemisection of the cord at the T9-10 site. Five months post-implantation, the ability of the macro...

According to an established concept, injury of the phloem triggers local sieve plate occlusion including callose-mediated constriction and, possibly, protein plugging of the sieve pores. Sieve plate occlusion can also be achieved by distant stimuli, depends on the passage of electropotential waves (EPWs), and is reversible in intact plants. The time-course of the wound response was studied in s...

We report the factorization of a 135-digit integer by the triple-large-prime variation of the multiple polynomial quadratic sieve. Previous workers [6][10] had suggested that using more than two large primes would be counterproductive, because of the greatly increased number of false reports from the sievers. We provide evidence that, for this number and our implementation, using three large pr...