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Let k be an algebraically closed field of characteristic 2. We prove that the restricted nilpotent commuting variety C, that is the set of pairs of (n x n)-matrices (A, B) such that A(2) = B-2 = [A, B] = 0, is equidimensional. C can be identified with the ...
Higher Green functions are real-valued functions of two variables on the upper half-plane, which are bi-invariant under the action of a congruence subgroup, have a logarithmic singularity along the diagonal, and satisfy the equation f = k(1−k) f ; here i ...
From several decades, non-adjacent form (NAF) representations for integers have been extensively studied as an alternative to the usual binary number system where digits are in {0,1}. In cryptography, the non-adjacent digit set (NADS) {-1,0,1} is used for ...
In this paper we exhibit the full prime factorization of the ninth Fermat number F9 = 2(512) + 1. It is the product of three prime factors that have 7, 49, and 99 decimal digits. We found the two largest prime factors by means of the number field sieve, wh ...
Modern programming languages have adopted the floating point type as a way to describe computations with real numbers. Thanks to the hardware support, such computations are efficient on modern architectures. However, rigorous reasoning about the resulting ...
Hard-wired carry chains in FPGAs are designed to improve efficiency of important arithmetic primitives. Although they are proven to be effective for arithmetic-rich functions, there are very few studies on the optimization opportunities of carry chains for ...
Silicon NanoWire (SiNW) based Field Effect Tran- sistors (FETs) are promising candidates to extend Moore’s law in the coming years. Recently, Double-Gate (DG) SiNWFETs have been demonstrated to allow on-line configurability of n -type and p -type device po ...
Despite the progress of the last decades in electronic design automation, arithmetic circuits have always received way less attention than other classes of digital circuits. Logic synthesisers, which play a fundamental role in design today, play a minor ro ...
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