We introduce a new micro-macro decomposition of collisional kinetic equations in the specific case of the diffusion limit, which naturally incorporates the incoming boundary conditions. The idea is to write the distribution function f in all its domain as the sum of an equilibrium adapted to the boundary (which is not the usual equilibrium associated with f) and a remaining kinetic part. This e...

We investigate the unpolarized virtual photon structure functions F 2 x;Q2; P2 and F L x;Q2; P2 in perturbative QCD for the kinematical region 2 P2 Q2, where Q2 ( P2) is the mass squared of the probe (target) photon and is the QCD scale parameter. Using the framework of the operator product expansion supplemented by the renormalization group method, we derive the definite predictions for the mo...

We investigate the unpolarized virtual photon structure functions F γ 2 (x,Q 2, P 2) and F γ L(x,Q 2, P 2) in perturbative QCD for the kinematical region Λ2 ≪ P 2 ≪ Q2, where −Q2(−P 2) is the mass squared of the probe (target) photon and Λ is the QCD scale parameter. Using the framework of the operator product expansion supplemented by the renormalization group method, we derive the definite pr...

3D rotation invariants based on orthogonal Gaussian–Hermite moments are proposed in this paper. We present an elegant and easy theoretical derivation of them. At the same time we prove by experiments that the Gaussian–Hermite invariants have better numerical stability than the traditional invariants composed of geometric moments. © 2014 Elsevier B.V. All rights reserved. d a w s i i d r [ t m i...

We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to expanding moments of Satake parameters of holomorphic cuspidal newforms in terms of the moments of the corresponding Fourier coefficients, which has applications i...

We perform a complete “Michel parameter” analysis of all possible helicity structures which can appear in the process B → Xc l ν̄l. We take into account the full set of operators parametrizing the effective Hamiltonian and include the complete one-loop QCD corrections as well as the non-perturbative contributions. The moments of the leptonic energy as well as the combined moments of the hadronic...

We compute the leading order (in α s) perturbative QCD and power (1/m 2 b) corrections to the hadronic invariant mass and hadron energy spectra in the decay B → X s ℓ + ℓ − in standard model using the heavy quark expansion technique (HQET). Results for the first two hadronic moments S n H and E n H , n = 1, 2, are presented here working out their sensitivity on the HQET parameters λ 1 and ¯ Λ. ...

A simple scheme is presented for modifying geometric moments to use geodesic distances. This provides a set of global shape descriptors that are invariant to bending as well as rotation, translation and scale.

Abstract. This paper considers the timeand space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the (angular) cut-off case, mild L1-solutions are constructed as limits of the iterate functions and boundedness of higher velocity moments are discussed in the case of inverse power collisions forces. Then the problem of...