Related papers: Polar decomposition and Brion's theorem
Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…
We give a simple proof of the uniqueness of extensions of good sections for formal Brieskorn lattices, which can be used in a paper of C. Li, S. Li, and K. Saito for the proof of convergence in the non-quasihomogeneous polynomial case. Our…
We discuss a few examples of structure functions for polarized, semi-inclusive scattering processes to show the richness of structure. Then we indicate how polarization and particle production can be used to study the quark and gluon…
Effective spin-orbit coupling can be created in cold atom systems using atom-light interaction. We study the BECs in an optical lattice using the Gross-Pitaevskii equation with spin-orbit coupling. Bloch states for the linear equation are…
We present a strategy for calculating the rare decay of a $\Sigma^+ (uus)$ baryon to a proton $(uud)$ and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point…
We systematically study the hadron longitudinal polarizations of the octet baryons at large $z$ from quark fragmentations in $e^+e^-$-annihilation, polarized charged lepton deep inelastic scattering (DIS) process, and neutrino…
Starting from an adapted Whitney decomposition of tube domains in $\C^n$ over irreducible symmetric cones of $\R^n,$ we prove an atomic decomposition theorem in mixed norm weighted Bergman spaces on these domains. We also characterize the…
We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…
Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the…
We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of $(R\cup\{-\infty\})^n$ can be written as the max-plus convex combination of at most $n+1$ of the extreme points of this…
We establish a Crapo complementation formula for the M\"obius function $\mu^X$ in a general decomposition space $X$ in terms of a convex subspace $K$ and its complement: $\mu^X \simeq \mu^{X\setminus K} + \mu^X*\zeta^K*\mu^X$. We work at…
This paper is about the combinatorics of finite point configurations in the tropical projective space or, dually, of arrangements of finitely many tropical hyperplanes. Moreover, arrangements of finitely many tropical halfspaces can be…
Production and decay rates, polarization and differential distributions of decay products are calculated for a heavy neutrino produced in charged pseudoscalar meson decay and decaying itself in charged pseudoscalar and lepton or a…
Using the helicity formalism of Jacob and Wick we derive spin density matrices of baryon antibaryon pairs produced in $e^+e^-$ annihilation. We consider the production of pairs with spins $1/2+\overline{1/2}$, $1/2+\overline{3/2}$ (+c.c.)…
In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral…
The production of various heavy-quark-containing baryons in electron-positron annihilation is considered. On the basis of exact formulas that we obtained previously within full perturbation theory, new numerical calculations of the…
Leptogenesis is a class of scenarios where the baryon asymmetry of the Universe is produced from a lepton asymmetry generated in the decays of a heavy sterile neutrino. We explain the motivation for leptogenesis. We review the basic…
We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions…
We give a soft geometric proof of the classical result due to Conn stating that a Poisson structure is linearizable around a singular point (zero) at which the isotropy Lie algebra is compact and semisimple.
We discuss how leptogenesis can explain the observed baryon asymmetry and summarize attempts of testing leptogenesis. We first perform estimates and discuss the main physics, and later outline the techniques that allow to perform precise…