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Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
Classical quantum behavior integrated density of states randomly perturbed lattice
2010/12/31
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single...
Algebra in superextensions of semilattices
semilattice band commutative semigroup the space of upfamilies
2010/12/31
Given a semilattice X we study the algebraic properties of the semigroup (X) of upfamilies on
X. The semigroup (X) contains the Stone-ˇCech extension (X), the superextension (X), and the space of...
Stabilizers of Subspaces under Similitudes of the Klein Quadric, and Automorphisms of Heisenberg Algebras
Klein quadric Grassmann space automorphism orbit nilpotent Lie algebra Heisenberg algebra
2010/12/31
We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of
class 2 and small dimension, over arbitrary fields (including the characteristic 2 case).
Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
2010/12/31
We produce three vast classes of exact periodic and solitonic solutions to the one-dimensional
Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL),induced...
Bounds for coefficients of cusp forms and extremal lattices
coefficients of cusp forms extremal lattices
2010/12/31
A cusp form f(z) of weight k for SL2(Z) is determined uniquely by its first ℓ := dim Sk Fourier coefficients. We derive an explicit bound on the nth coefficient of f in terms of its first ℓ...
Stable lattice Boltzmann scheme for a moving Burgers shock wave
Hyperbolic conservation laws entropy convex hull
2010/12/9
We follow the mathematical framework proposed by Bouchut [3] in order to derive equilibrium functions for D1Q3 lattice Boltzmann simulations of the Burgers equation. When a particular convexity proper...
Holomorphic quantization of linear field theory in the general boundary formulation
Holomorphic quantization of linear field theory general boundary formulation
2010/9/28
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the Kähle...
Classification of non-symplectic automorphisms on $K3$ surfaces which act trivially on the Néron-Severi lattice
K3 surface non-symplectic automorphism
2010/9/24
We treat non-symplectic automorphisms on K3 surfaces which act trivially on the N´eron-Severi lattice. In this paper,we classify non-symplectic automorphisms of prime-power order,especially 2-po...
An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance
Optimal Lower Bound Communication Complexity Gap-Hamming-Distance
2010/9/20
We prove an optimal W(n) lower bound on the randomized communication complexity of the much-studied GAP-HAMMING-DISTANCE problem. As a consequence, we obtain essentially optimal multi-pass space lower...
Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers
Boundary quotients Toeplitz algebra affine semigroup natural numbers
2010/9/20
We study the Toeplitz algebra T (N ⋊ N×) and three quotients of this algebra: the C-algebra QN recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative bound...
Computer Generated Images for Quadratic Rational Maps with a Periodic Critical Point
rational map complex dynamics plane curve singularities geometric
2010/9/17
We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperboli...
An improved upper bound on the Entropy Production for the Kac Master equation
Entropy Production Villani’s Conjecture
2010/9/17
In this paper we take an idea presented in recent paper by Carlen, Carvalho,Le Roux, Loss, and Villani ([3]) and push it one step forward to find an exact estimation on the entropy production. The new...
Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
strong solidity lattices
2010/9/14
We show that the group factors L, where is an ICC lattice in either SO(n, 1)or SU(n, 1), n ≥ 2, are strongly solid in the sense of Ozawa and Popa [13]. This strengthens a result o...
Brolin-Lyubich measure R of a rational endomorphism R : ˆC !ˆC with deg R 2 is the unique invariant measure of maximal entropy hR =htop(R) = log d.
Infinite generation of non-cocompact lattices on right-angled buildings
Infinite generation non-cocompact lattices right-angled buildings
2010/9/1
Let be a non-cocompact lattice on a locally finite regular right-angled building X. We prove that if has a strict fundamental domain then is not finitely generated. We...