The security of the RSA cryptosystem depends on the difficulty of factoring large integers. The best current factoring algorithm is the Number Field Sieve (NFS), and its most difficult part is the sieving step. In 1999 a large distributed computation involving hundreds of workstations working for many months managed to factor a 512-bit RSA key, but 1024-bit keys were believed to be safe for the...

With the on growing use of RNA based sequencing techniques in molecular ecology, new concerns regarding the effects of different soil homogenization methods on the interpretation of results were raised, since soil bacteria transcriptional regulation is highly sensitive and indicative towards environmental changes. We present the first study addressing the effects of sieving to the structure of ...

These are notes on a preliminary follow-up to a question of Jim Propp, about cyclic sieving of cyclic codes. We show that two of the Mahonian polynomials are cyclic sieving polynomials for certain Dual Hamming Codes: X and X inv for q = 2, 3 and q = 2, respectively.

The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the stabilizers group actions on finite sets using q-analogue polynomials. Eu Fu demonstrated a generalized cluster complexes every type q-Catalan numbers. In this paper, we exhibit dihedral phenomenon, introduced for odd n by Rao Suk, clusters type. A case, show that Raney numbers count both reflection-symmetric k-angula...

aggregate stability is an important soil property because it dictates how strongly a soil can resist water erosion. the objectives in this study were: (1) to compare the stability of six soil aggregate size fractions, primarily to determine if aggregate stability varies with aggregate size, and (2) to determine with which aggregate size fraction the stability of most soils would be different fr...