Abstract In this paper, we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The functionals double integrals, equivalent to semi-norms the Euclidean setting. extend analysis [14] concerning...

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this Letter, we initiate the elliptic integrals. Concretely, of twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain alphabet, contains 100 logarithms as well simple integrals, via Schubert-typ...

We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum stochastic product integrals, namely a necessary and su¢ cient condition for their unitarity, and the coboundary relatio...

The bis-bidentate bridging ligand L reacts with Ag(I) ions to form a conventional dinuclear [Ag(2)L(2)](2+) double helicate; individual double helicate units assemble via Ag···Ag interactions into infinite chains, three of which wrap around a central spine of anions to give a triple helical braid, which is therefore an infinite triple helix composed of molecular double helicate subunits.