In the standard model ( SM ) of electroweak interactions, CP noninvariance arises from the nonzero phase in the CKM matrix. Its contribution to the quark electric dipole moment ( EDM ) vanishes surprisingly at two loop order. This makes the quark EDM extremely small in the SM. In this paper, we consider the two Higgs doublet extension of the SM and assume that CP noninvariance is still encoded ...

An example of homogeneous space which has no metric but has a connection with non–vanishing curvature suggests that " spacetime " should be not defined as a pair (M, g), a manifold plus a metric, but as a pair (M, Γ) — a differentiable manifold plus a connection. The general theory of homogeneous spaces ensures the existence of a certain well–defined connection independently of the existence of...

We show that for asymptotically vanishing Maxwell fields in Minkowski space with non-vanishing total charge, one can find a unique geometric structure, a null direction field, at null infinity.. From this structure a unique complex analytic world-line in complex Minkowski space that can be found and then identified as the complex center of charge. By ”sitting” in an imaginary sense, on this wor...

Let G be a bounded open subset of Euclidean space with real algebraic boundary Γ. Under the assumption that the degree d of Γ is given, and the power moments of the Lebesgue measure on G are known up to order 3d, we describe an algorithmic procedure for obtaining a polynomial vanishing on Γ. The particular case of semialgebraic sets defined by a single polynomial inequality raises an intriguing...

Let G be a bounded open subset of Euclidean space with real algebraic boundary Γ. Under the assumption that the degree d of Γ is given, and the power moments of the Lebesgue measure on G are known up to order 3d, we describe an algorithmic procedure for obtaining a polynomial vanishing on Γ. The particular case of semialgebraic sets defined by a single polynomial inequality raises an intriguing...

Reenable function vectors are usually given in the form of an innnite product of their reenement (matrix) masks in the frequency domain and approximated by a cascade algorithm in both time and frequency domains. We provide necessary and suu-cient conditions for the convergence of the cascade algorithm. We also give necessary and suucient conditions for the stability and orthonormality of reenab...

In this paper we show that any good toric contact manifold has well defined cylindrical contact homology and describe how it can be combinatorially computed from the associated moment cone. As an application we compute the cylindrical contact homology of a particularly nice family of examples that appear in the work of Gauntlett-Martelli-SparksWaldram on Sasaki-Einstein metrics. We show in part...

We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai, Probab. Theory Relat. Fields 103, 1995, on the Wiener ...

We study the large N limit in the presence of magnetic monopoles in the Yang-Mills/Higgs model in three dimensions. The physics in the limit depends strongly on the distribution of eigenvalues of the Higgs field in the vacuum, and we propose a particular, nondegenerate configuration. It minimizes the free energy at the moment of symmetry breaking. Given this, the magnetic monopoles show a wide ...

If A• is a bounded, constructible complex of sheaves on a complex analytic space X, and f : X → C and g : X → C are complex analytic functions, then the iterated vanishing cycles φg[−1](φf [−1]A •) are important for a number of reasons. We give a formula for the stalk cohomology H∗(φg[−1]φf [−1]A •)x in terms of relative polar curves, algebra, and the normal Morse data and micro-support of A•.