منابع مشابه
Factorization in Quantum Planes
These results stem from a course on ring theory. Quantum planes are rings in two variables x and y such that yx = qxy where q is a nonzero constant. When q = 1 a quantum plane is simply a commutative polynomial ring in two variables. Otherwise a quantum plane is a noncommutative ring. Our main interest is in quadratic forms belonging to a quantum plane. We provide necessary and sufficient condi...
متن کاملQuantum Orthogonal Planes:
We construct differential calculi on multiparametric quantum orthogonal planes in any dimension N . These calculi are bicovariant under the action of the full inhomogeneous (multiparametric) quantum group ISOq,r(N), and do contain dilatations. If we require bicovariance only under the quantum orthogonal group SOq,r(N), the calculus on the q-plane can be expressed in terms of its coordinates x, ...
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We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quan-tization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation of the star-product and the operatorˆℓ Z , we show that the resulting representations exhausted all the irreducible representations of this g...
متن کاملClique Is Hard to Approximate within n1-o(1)
It was previously known that Max Clique cannot be approximated in polynomial time within n1− , for any constant > 0, unless NP = ZPP. In this paper, we extend the reductions used to prove this result and combine the extended reductions with a recent result of Samorodnitsky and Trevisan to show that unless NP ⊆ ZPTIME(2 n(log logn) 3/2)), clique cannot be approximated within n1−O(1/ √ log .
متن کاملTesting ±1-Weight Halfspaces
We consider the problem of testing whether a Boolean function f : {−1, 1} → {−1, 1} is a±1-weight halfspace, i.e. a function of the form f(x) = sgn(w1x1+w2x2+· · ·+wnxn) where the weightswi take values in {−1, 1}. We show that the complexity of this problem is markedly different from the problem of testing whether f is a general halfspace with arbitrary weights. While the latter can be done wit...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8093