In this paper, we show that the property of tight affine frame decomposition of functions in L can be extended in a stable way to functions in Sobolev spaces when the generators of the tight affine frames satisfy certain mild regularity and vanishing moment conditions. Applying the affine frame operators Qj on j-th levels to any function f in a Sobolev space reveals the detailed information Qjf...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the [Formula: see text] cross section, generalizing previous studies on [Formula: see text] decays and [Formula: see text] scattering, and verify our result by comparing to [Formula: see text] data. We perform the analytic continuation to the ...

Low-energy results from measurements of leptonic dipole moments are used to derive constraints on the CP–violating phases of the dimensionful parameters of the minimal supersymmetric extension of the standard model (MSSM). We use these (known) bounds to investigate the impact of these phases on CP–even cross sections at high–energy e+e− and e−e− colliders. To that end we define two measures of ...

We provide a real algebraic symbolic-numeric algorithm for computing the real variety VR(I) of an ideal I ⊆ R[x], assuming VR(I) is finite (while VC(I) could be infinite). Our approach uses sets of linear functionals on R[x], vanishing on a given set of polynomials generating I and their prolongations up to a given degree, as well as on polynomials of the real radical ideal R √ I obtained from ...

We analyze the status of the exotic solutions to the solar neutrino problem, i.e., those solutions based on new phenomena which are not the usual neutrino oscillations induced by masses and mixing. These solutions are based on di erent assumptions: a) resonant spinavor precession induced by non-vanishing neutrino magnetic moment, b) the existence of non-standard avor-changing and non-universal ...

Polarized photon structure can be studied in the future polarized e+e− colliding-beam experiments. We investigate the spin-dependent structure function of the virtual photon g 1 (x,Q , P ), in perturbative QCD for Λ P 2 Q, where −Q2 (−P ) is the mass squared of the probe (target) photon. The analysis is performed to next-to-leading order in QCD. We particularly emphasize the renormalization sch...

We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the des...