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After considerable negotiation, AECL assumed full responsibility for the reactor in a settlement. [10] The MAPLE facility was granted an extension on its operating license on 25 October 2007, which would permit operations until 31 October 2011. [11] This (final) submission envisioned that the MAPLE I reactor would be operational in late 2008. [12]
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The yellow polygons highlight the three types of polygons on the lattice, and the pink polygons highlight the two types of polygons on the dual lattice. The lattice has vertex types (1 ⁄ 2)(3 3,4 2) + (1 ⁄ 2)(3,4,6,4), while the dual lattice has vertex types (1 ⁄ 15)(4 6)+(6 ⁄ 15)(4 2,5 2)+(2 ⁄ 15)(5 3)+(6 ⁄ 15)(5 2,4). The critical ...
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
If the lattice is even, the form has level 1, and if the lattice is odd the form has Γ 0 (4) structure (i.e., it is a modular form of level 4). Due to the dimension bound on spaces of modular forms, the minimum norm of a nonzero vector of an even unimodular lattice is no greater than ⎣ n /24⎦ + 1.
Because the best-response functions are monotone, Tarski's fixed-point theorem can be used to prove the existence of a pure-strategy Nash equilibrium (PNE) in a supermodular game. Moreover, Topkis [13] showed that the set of PNE of a supermodular game is a complete lattice, so the game has a "smallest" PNE and a "largest" PNE.
Artificial lattice is a term encompassing every atomic-scale structures designed and controlled to confine electrons onto a chosen lattice. Research has been done on multiple geometries and one of the most notable being what is called molecular graphene (in order to mimic graphene structure).