Related papers: Generalizations of Ceva's Theorem and Applications

In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is…

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

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

In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…

A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.

We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.

We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.

In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.

The Theorems of Pappus and Desargues are generalized by two special formulas that hold in the three-dimensional vector space over a field.

This paper generalizes the fundamental GAGA results of Serre cite{MR0082175} in three ways---to the non-separated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of…

We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.

We prove some new results related to Tanaka's formula.

A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…

We generalize Rado's extension theorem to complex spaces.

We generalize Stern's diatomic sequence in three ways.

We prove two conjectures posed in 2016 concerning a generalization of the Sawayama-Th\'ebault Theorem and the Sawayama Lemma. We show that this generalized statement can be viewed in Laguerre geometry, which provides a natural framework for…

New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.

Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…

In this article, we demonstrate the common fixed point theorems for three transformations on vector S-metric space by utilizing weakly compatible and point of coincidence. Moreover, some of our results generalize the existing results in the…