相关论文: Polar decomposition and Brion's theorem
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non-degenerate linear operators in $R^2$.
The lepton polarization asymmetry in the B\to\ell^{+}\ell^{-} decay, when one of the leptons is polarized, is investigated using the most general form of the effective Hamiltonian. The sensitivity of the asymmetry to the new Wilson…
We consider the integer point transform $\sigma _P (\mathbf{x}) = \sum _{\mathbf{m} \in P\cap \mathbb{Z}^n} \mathbf{x}^\mathbf{m} \in \mathbb C [x_1^{\pm 1},\ldots, x_n^{\pm 1}]$ of a polytope $P\subset \mathbb{R}^n$. We show that if $P$ is…
We derive the relativistic kinetic equation for Compton scattering of polarized radiation in strong magnetic field using the Bogolyubov method. The induced scattering and the Pauli exclusion principle are taken into account. The electron…
A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a generalization of the reconstruction theorem of Kontsevich and…
We extend chiral perturbation theory to include linear dependence on the lattice spacing $a$ for the Wilson action. The perturbation theory is written as a double expansion in the small quark mass $m_q$ and lattice spacing $a$. We present…
Highlights from recent computations in lattice QCD involving baryons are presented. Calculations of the proton mass and spin decompositions are discussed, a percent level determination of the nucleon axial coupling is described, and…
A polar hypersurface P of a complex analytic hypersurface germ, f=0, can be investigated by analyzing the invariance of certain Newton polyhedra associated to the image of P, with respect to suitable coordinates, by certain morphisms…
The Voronoi conjecture on parallelohedra claims that for every convex polytope $P$ that tiles Euclidean $d$-dimensional space with translations there exists a $d$-dimensional lattice such that $P$ and the Voronoi polytope of this lattice…
We propose a framework of baryogenesis and leptogenesis that relies on a supercooled confining phase transition (PT) in the early universe. The baryon or lepton asymmetry is sourced by decays of hadrons of the strong dynamics after the PT,…
Starting from Ritt's classical theorems, we give a survey of results in functional decomposition of polynomials and of applications in Diophantine equations. This includes sufficient conditions for the indecomposability of polynomials, the…
We introduce a natural weighted enumeration of lattice points in a polytope, and give a Brion-type formula for the corresponding generating function. The weighting has combinatorial significance, and its generating function may be viewed as…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
We state the formula for the critical number of vertices of a convex lattice polygon that guarantees that the polygon contains at least one point of a given sublattice and give a partial proof of the formula. We show that the proof can be…
Polar ring galaxies are flattened stellar systems with an extended ring of gas and stars rotating in a plane almost perpendicular to the central galaxy. We show that their formation can occur naturally in a hierarchical universe where most…
In this paper, we introduce the super telescoping formula, a natural generalization of well-known telescoping formula. We explore various aspects of the formula including its origin and the telescoping cancellations emerging from symmetric…
We review the experimental evidence for a net baryon density in cosmology, and the theoretical mechanism for producing it, called leptogenesis, which relies on the creation of a lepton asymmetry at an intermediate step. The naturality of…
Inspired by the works of Adiprasito, Babson, Nevo, and Murai on the $g$-conjecture, we consider different classes of PL-spheres and the relations between them. We focus on a certain class of spheres that is in the intersection of…
We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…
Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular…