By Ams-asl Joint Special Session on Interac, Alexandre Borovik
Because the pioneering works of Novikov and Maltsev, staff concept has been a trying out flooring for mathematical good judgment in its many manifestations, from the idea of algorithms to version conception. The interplay among good judgment and team conception ended in many admired effects which enriched either disciplines. This quantity displays the main subject matters of the yankee Mathematical Society/Association for Symbolic good judgment Joint exact consultation (Baltimore, MD), Interactions among common sense, team concept and laptop technological know-how. integrated are papers dedicated to the improvement of recommendations used for the interplay of workforce idea and common sense. it really is appropriate for graduate scholars and researchers attracted to algorithmic and combinatorial workforce concept. A supplement to this paintings is quantity 349 within the ""AMS"" sequence, ""Contemporary arithmetic, Computational and Experimental workforce Theory"", which arose from an identical assembly and concentrates at the interplay of workforce concept and desktop technology
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Extra info for Groups, Languages, Algorithms: Ams-asl Joint Special Session On Interactions Between Logic, Group Theory, And Computer Science, January 16-19, 2003, Baltimore, Maryland
40 43 56 64 65 67 40 Jean-Louis Verger-Gaugry 1 Introduction The mathematics of uniformly discrete point sets and Delone sets developed recently has at least four different origins: (i) the experimental evidence of nonperiodic states of matter in condensed matter physics, so-called aperiodic crystals, like quasicrystals , , , ,  incommensurate modulated crystals phases ,  and their geometric modelization (cf. Appendix), (ii) works of Delone , , ,  on geometric crystallography (comparatively, see , , ,  for a classical mathematical approach of periodic crystals), (iii) works of Meyer on now called cut-and-project sets and Meyer sets , , ,  (for a modern language of Meyer sets in locally compact abelian groups: ), (iv) the theory of self-similar tilings , ,  and the use of ergodic theory to understand diffractivity , , .
One considers the prime number decomposition d = ri=1 piei , takes its ˜ + 1 MUBs from the tensorial product smallest factor m ˜ = mini (piei ), and gets m (k) r (k) ˜ B = ⊗i=1 Bi , (k = 0, . . , m). At this point it is instructive to enlighten the above-described construction of MUBs by confining ourselves to the Galois ring in d = 6. Let us take the latter as the quotient GR(62 ) = Z6 [x]/(x 2 + 3x + 1) of polynomials over Z6 by a polynomial irreducible over both Z2 and Z3 . GR(62 ) has 36 elements.
Problems pertinent to quantum information theory are touching more and more branches of pure mathematics, such as number theory, abstract algebra and projective geometry. This paper focuses on one of the most prominent issues in this respect, namely the construction of sets of mutually unbiased bases (MUBs) in a Hilbert space of finite dimension. An updated list of open problems related to the development of quantum technologies can be, for example, found in . To begin with, one recalls that two different orthonormal bases A and B of a dd dimensional Hilbert space √H with metrics .