Related papers: Bykovskii's theorem and generalized Larcher's theo…

One of the most fruitful results from Minkowski's geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume of an o-symmetric convex body whose only interior lattice…

In this article we prove an existence theorem for coincidence points of mappings in Banach spaces. This theorem generalizes the Kantorovich fixed point theorem.

Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a "master equation" possessing a bicomplex formulation.

We give a new proof of Lucas' Theorem in elementary number theory.

In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke's point, Kariya's point, and to other remarkable points from the triangle geometry.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

This note is an (exact) copy of the report of Jaak Peetre, "Generalizing Ovchinnikov's Theorem". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…

We present a natural reverse Minkowski-type inequality for lattices, which gives upper bounds on the number of lattice points in a Euclidean ball in terms of sublattice determinants, and conjecture its optimal form. The conjecture exhibits…

In this paper, we successfully set up a generalized sphere theorem for compact Riemannian manifolds with radial Ricci curvature bounded.

We study lattice-theoretical extensions of the celebrated Sauer-Shelah-Perles Lemma. We conjecture that a general Sauer-Shelah-Perlem Lemma holds for a lattice $L$ if and only if $L$ is relatively complemented, and prove partial results…

We give an algorithmic proof of Pick's theorem which calculates the area of a lattice-polygon in terms of the lattice-points.

We comment on the set of visible points of a lattice and its Fourier transform, thus continuing and generalizing previous work by Schroeder and Mosseri. A closed formula in terms of Dirichlet series is obtained for the Bragg part of the…

Some occurrences of $n$ can be replaced by $n-1$ in a special case of the Shapley-Folkman lemma.

We prove a sharp upper bound on the number of boundary lattice points of a rational polygon in terms of its denominator and the number of interior lattice points, generalizing Scott's inequality. We then give sharp lower and upper bounds on…

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

A short proof of a theorem of M.H. Albert, and its application to lattices.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.