Related papers: On the polar decomposition of circular variables
We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.
We establish two equivalent characterizations of $\mathrm{VMO}$ in terms of vanishing Carleson measures. First, we show that any $\mathrm{VMO}$ function admits a decomposition into a continuous boundary term and an integral operator…
The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.
We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as…
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
In his talk "Integral Apollonian disk Packings" Peter Sarnak asked if there is a "proof from the Book" of the Descartes theorem on circles. A candidate for such a proof is presented in this note
We give down-to-earth proofs of the structure theorems for persistence modules.
We show that the existence of disintegration for cylindrical measures follows from a general disintegration theorem for countably additive measures.
Deformations in piezoelectric materials lead to conduction effects, which are due to two contributions: the relative displacements of the ionic cores, and the so-called orbital polarization. This work is devoted to the rigorous derivation…
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We generalize the logarithmic decomposition theorem of Deligne-Illusie to a filtered version. There are two applications. The easier one provides a mod $p$ proof for a vanishing theorem in characteristic zero. The deeper one gives rise to a…
We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.
It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 viscosity grad log P, where the P's are explicitly known…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
We determine a strong form of the decomposition theorem for proper toric maps over finite fields.
In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an…
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
The result of this paper is proved in arXiv:1112.1163
Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions…
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.