Related papers: Comparison theorems and some of their applications

This note is based on Professor Vitali Kapovitch's comparison geometry course at the University of Toronto. It delves into various comparison theorems, including those by Rauch and Toponogov, focusing on their applications, such as…

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over…

A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.

In this paper we present theorems and applications of Wallis theorem related to trigonometric integrals.

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

In this short paper we review and extract some features of the Fredholm Alternative problem .

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.

We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on…

We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.

We give some Korovkin-type theorems on convergence and estimates of rates of approximations of nets of functions, satisfying suitable axioms, whose particular cases are filter/ideal convergence, almost convergence and triangular…

In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

This is a survey of the author's recent results on the Kadison and Halmos similarity problems and the closely connected notion of ``length'' of an operator algebra.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

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

In this paper, we propose non-commutative analogues of infimum and supremum with the help of algebraic orthogonality.