Related papers: A short proof of Isserlis' theorem
An technically interesting proof of a known theorem.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…
We prove several extensions of the Erdos-Fuchs theorem.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in the Lagrangian formalism dealing with second order vector…
An equivalent but useful version on the Homological Nerve Theorem is proved.
Analogues of invariant theory's well-known Roberts theorem are proved for ternary forms. We established that covariants, contravariants and mixed concomitants of a ternary form are uniquely determined by their lead coefficients.
We introduce the anisotropic tensor calculus, which is a way of handling with tensors that depend on the direction remaining always in the same class. This means that the derivative of an anisotropic tensor is a tensor of the same type. As…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
We prove that the symmetry group of an elasticity tensor is equal to the symmetry group of the corresponding Christoffel matrix.
It is proven an analogue of The Theorem of Moser according to an iterative normalization procedure depending on Generalized Fischer Decompositions.
This is a survey of the spectral theory of tensors.
We give a short proof of Ahlfors' theorem on covering surfaces.
We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and -- possibly coupled -- laws, including piezoelectricity…
Two tetrad spaces reproducing spherically symmetric spacetime are applied to the equations of motion of higher-order torsion theories. Assuming the existence of conformal Killing vector, two isotropic solutions are derived. We show that the…
In this note we briefly survey and propose some open problems related to isoparametric theory.