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Crystals of hexamethylenetetramine (HMT) with aliphatic dicarboxylic acids in 1:1 molar ratio exhibit different behaviour depending on the number n of carbons in the aliphatic chain. For n=8 and 10, incommensurate phases have been observed, while for n=9, ...
The single-crystal investigation of the self-hosting sigma-structure of beta-tantalum (beta-Ta) at 120 K (low-temperature, LT, structure) and at 293 K (RT-I before cooling and RT-II after cooling and rewarming; RT represents room temperature) shows that th ...
Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization. ...
D.J. Bernstein has proposed a circuit-based implementation of the matrix step of the number field sieve factorization algorithm (see "Circuits for integer factorization: a proposal", http://cr.yp.to/papers.html#nfscircuit, 2001). These circuits offer an as ...
We investigate a general approach for the numerical approximation of incompressible Navier-Stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve. The splitting is obtained through an algebraic appro ...
We describe an enhanced version of the TWINKLE factoring device and analyse to what extent it can be expected to speed up the sieving step of the quadratic Sieve and number field Sieve factoring algorithms. The bottom line of our analysis is that the TWINK ...
Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to twelve million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger codes (Shokrollahi (1996)). ...
This paper reports on the factorization of the 512 bit number RSA-155 by the number field Sieve factoring method (NFS) and discusses the implications for RSA ...
We have measured the magnetization of a two-dimensional electron system that has been laterally patterned to an array of mesoscopic dots. In our experimental data we observe sawtooth-like de Haas–van Alphen (dHvA) oscillations of the equilibrium magnetizat ...
The generation of prime numbers underlies the use of most public-key schemes, essentially as a major primitive needed for the creation of key pairs or as a computation stage appearing during various cryptographic setups. Surprisingly, despite decades of in ...
