Related papers: A generalization of Pappus chain theorem

We generalize the property that Riemann sums of a continuous function corresponding to equidistant subdivision of an interval converge to the integral of that function, and we give some applications of this generalization.

In this paper we generalize the DP framework to a relative DP framework, where a so called split is possible.

In this work a quantum analogue of Bayesian inference is considered. Based on the notion of instrument, we propose a quantum analogue of Bayes' rule, which elaborates how a prior normal state updates under observations. Besides, we…

Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.

We describe recent advances in the study of random analogues of combinatorial theorems.

We present type $\theta$ Stokes' theorem for type $\theta$ $k$-chains which extends the fundamental theorem of calculus in higher dimensions.

A very simple but useful almost sure convergence theorem of probability is given.

We introduce a class of association schemes that generalizes the Hamming scheme. We derive generating functions for their eigenvalues, and use these to obtain a version of MacWilliams theorem.

The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.

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

We prove tight closure analogues of results of Watanabe about chains and families of integrally closed ideals.

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

In this paper, we obtained some global approximation results for general Gamma type operators.

We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

We prove a uniformization theorem in complex algebraic geometry.

We prove a Chevalley restriction theorem and its double analogue for the cyclic quiver.