Related papers: Harder-Narasimhan theory

The goal of this note is to give a variant of the generic fibration theorem for Waldhausen K-theory without assuming the factorization axiom.

The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…

The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.

In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic analysis in the last 90 years, reviewing, on the one hand, the…

This paper has been withdrawn by the authors due to an error.

In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.

A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.

This is a survey on Sarnak's Conjecture

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

The issue and proof of Gurzadyan theorem are presented concisely, avoiding tedious and unnecessary calculations that would mask what is essential. The goal is to provide a good mathematical and physical understanding of the theorem, making…

We present a simple inductive proof of the Lagrange Inversion Formula.

We shall here consider extended theories of gravitation in the metric-affine formalism with matter coupled directly to the connection. A sufficiently general procedure will be exhibited to solve the resulting field equation associated to…

In this paper, we investigate the relationships between Harder-Narasimhan filtrations and derived Hall algebras. We extend several results from abelian categories to triangulated categories, including Reineke inversions, wall-crossing…

These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…

A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3--for--2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and…

Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.

We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor. Our approach allows a unified treatment of various subcases and an easy identification of the degrees of freedom of the…

We define torsion pairs for quasi-abelian categories and give several characterisations. We show that many of the torsion theoretic concepts translate from abelian categories to quasi-abelian categories. As an application, we generalise the…