We provide a uniform vanishing result for the graded components of finite length Koszul module associated to subspace K⊆∧2V as well sharp upper bound its Hilbert function. This purely algebraic statement has interesting applications study number invariants finitely generated groups, such Alexander invariants, Chen ranks, and degree growth virtual nilpotency class. For instance, we explicitly af...

Stochastic fluctuations of coherent and incoherent components of the resonance fluorescence intensity induced by Wiener-Levy laser phase noise are investigated. Statistical properties of the atomic dipole moment and stochastic Mollow spectra of atomic dipole fluctuations for different values of the laser linewidth and Rabi frequency are calculated. It is shown that these spectra exhibit a tripl...

This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the cone and its dual nonnegative polynomials. By technique homogenization, give a convergent hierarchy Moment-SOS relaxations for approximating these cones. With them, method solving Finitely atomic representing measures, or certificates their nonexistence, can be obtained by p...

Let us say that space is discrete if and only if every finite extended region of space is composed of finitely many atomic regions of space. I assume here that regions of space are individuals rather than sets of points, and have mereological structure; their parts are all and only their subregions. A region of space is an atomic region if and only if it has no proper parts, i.e., if and only i...

interpretation. Current work is devoted to defining an abstract contextual process, which finitely represents the possibly infinite set of possibly infinite concrete structures which can be obtained for a given abstract "query mode." Notice that, while the CC schedule analysis can be performed both on eventual and on atomic CC programs (and the corresponding semantic structures), the analysis n...

We study Banach spaces with a weak stable unit ball, that is, where every convex combination of relatively weakly open subsets in its ball is again subset ball. It proved the class L1 preduals agree those which are purely atomic, ℓ1(Γ) for some set Γ, getting this way complete geometrical characterization atomic L1, answers setting problem. As consequence, we prove equivalence different propert...

Denote by μn = ∫ x n1 1 . . . x nd d dμ(x) the n’th moment of a Borel probability measure μ on the unit cube I = [0, 1] in R. Generalizing results of Hausdorff, Hildebrandt and Schoenberg, we give a sufficient condition in terms of moments, that μ is absolutely continuous with respect to a second Borel measure ν on I. We also review a constructive approximation of measures by atomic measures us...

The presence of infinite dimensional chiral symmetries is central to the study of two dimensional conformal field theories. These symmetries, called chiral algebras, are formed by the purely holomorphic and purely anti-holomorphic fields, respectively. How the field content of a conformal field theory (CFT) is organised into representations of the chiral algebras is encoded in the fusion ring. ...

This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter γ2 beyond the transition phase (i.e. γ2 > 2d) and check the duality relation with sub-critical Gaussian multiplicative chaos. On the other hand, we give a sim...

A generalization of the the flat extension theorems of Curto and Fialkow and Laurent and Mourrain is obtained by seeing the problem as one of ideal projection. Some other results on ideal projection are generalized, and it is seen that a linear functional on the k-variate polynomials over C is finitely atomic if and only if its moment matrix has finite rank, a fact previously known for positive...