Related papers: Generalizations of Ceva's Theorem and Applications

In this paper, we present a novel generalization of the classical Ceva theorem to arbitrarily dimensional simplexes. Our approach allows cevians to have any dimension (smaller than the dimension of the base simplex). Consequently, our…

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

We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.

The paper contains an interesting generalization of the classical Taylor expansion formula and four applications

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

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

Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.

In this paper we introduce new generalizations of the zeta function, the Tricomi functions; their main properties are studied. This opens the way to a deeper, better application of these functions both in the theory of special functions,…

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a three-parameter family of inequalities which we call Ceva's triangle inequalities. Our…

In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.

The connection between Lefschetz formulae and zeta function is explained. As a particular example the theory of the generalized Selberg zeta function is presented. Applications are given to the theory of Anosov flows and prime geodesic…

We generalize the classical Ceva's and Menelaus's theorems to curvilinear triangles bounded by circular arcs. We introduce trilinear coordinates associated with such triangles and develop several geometric constructions. In particular, for…

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

We discuss five ways of proving Chernoff's bound and show how they lead to different extensions of the basic bound.

The present thesis represents developments in two main directions related to the simple Lie algebras. The first one is devoted to the representation theory of the simple Lie algebras. Specifically, we present recent results, which include…

In the present note a generalization of Borel-Cantelli Lemma is proposed.

A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…

We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.