Related papers: On the Erdos-Fuchs theorem

We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.

Continuing from part (I), we develop properties of real intersection theory that turns out to be an extension of the well-established theory in algebraic geometry.

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…

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

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We present a relative form of the Toponogov comparison theorem.

In this paper we prove an extension of the Blaschke-Lebesgue theorem for a family of convex domains called disk-polygons. Also, this provides yet another new proof of the Blaschke-Lebesgue theorem.

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…

An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.

A short and almost elementary proof of the Boros-F\"uredi-B\'ar\'any-Pach-Gromov theorem on the multiplicity of covering by simplices in $\mathbb R^d$ is given.

Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.

We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the $q$-Fibonacci polynomials appearing in Schur's work. The proofs of most of…

We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.

We derive the Gallai-Edmonds Structure Theorem from Hall's Theorem.

In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…

We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.

A proof of Sendov's conjecture is given.

This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.