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The Cauchy kernel for cones

Sławomir Michalik (2004)

Studia Mathematica

A new representation of the Cauchy kernel Γ for an arbitrary acute convex cone Γ in ℝⁿ is found. The domain of holomorphy of Γ is described. An estimation of the growth of Γ near the singularities is given.

The characteristic variety of a generic foliation

Jorge Vitório Pereira (2012)

Journal of the European Mathematical Society

We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

The Clifford bundle and the dynamics of the superparticle

Waldyr Rodrigues, Jayme Vaz, Matej Pavsic (1996)

Banach Center Publications

Using the Clifford bundle formalism we show that Frenet equations of classical differential geometry or its spinor version are the appropriate equations of motion for a classical spinning particle. We show that particular values of the curvatures appearing in Darboux bivector of the spinor form of Frenet equations produce a "classical" Dirac-Hestenes equation. Using the concept of multivector Lagrangians and Hamiltonians we provide a Lagrangian and Hamiltonian approach for our theory which then...

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