Related papers: A relative Toponogov comparison theorem

An technically interesting proof of a known theorem.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

A generalization of the law of total covariance is presented and proved.

An equivalent but useful version on the Homological Nerve Theorem is proved.

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

We introduce relative homological and weakly homological categories, where ``relative'' refers to a distinguished class of normal epimorphisms. It is a generalization of homological categories, but also protomodular categories can be…

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

We propose the notion of semi-infinite homology for algebras over operads using the relative homology theory for operadic algebras.

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.

We study topological properties of the graph topology.

We prove an analogue of the prime number theorem for finite fields.

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.

We derive a relative version of the slicing Bennequin inequalities for cobordant Legendrian knots, and review a few proofs of the result.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

A Short Course on Frame Theory.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.