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Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
2010/12/28
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
2011/3/1
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...
Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
strong solidity lattices
2010/12/3
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...
Infinite generation of non-cocompact lattices on right-angled buildings
Infinite generation non-cocompact lattices right-angled buildings
2010/12/9
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...
Modular and lower-modular elements of lattices of semigroup varieties
Semigroup variety lattice of varieties commutative variety
2010/12/3
The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the varie...