Related papers: A generalization of Pappus chain theorem

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…

In this paper, I generalize a previous one about hilbertian kernels and approximation theory

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.

We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.

We introduce a new generalization of Euler's $\varphi$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do…

Here we unify two results of Steinhaus and their corresponding category analogues by extending them in the settings of category bases. We further show that in any perfect translation base, every abundant Baire set contains a full subset for…

We survey the classical results of the Dirichlet Approximation Theorem.

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

The purpose of this paper is to derive the analogue of Lebesgue-Radon-Nikodym theorem with respect to $p$-adic $q$-invariant distribution on $\Bbb Z_p$ which is defined by author in [1].

We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.

We discuss some variants of cone theorem for movable curves in any codimensions.

In this paper we prove the theorem on freedom for relatively free groups with a single relation (analogous with the well-known result of Magnus) and a generalized Freiheitssatz for relatively free groups (analogous with the well-known…

The paper is devoted to an adaptation of author's approach to Leray theorems in bounded cohomology theory to infinite chains. The main results are a stronger and more general form of Gromov's Vanishing-finiteness theorem and a…

We give a modern account of the construction and structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.

We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.

We prove a generalized version of the no-broadcasting theorem, applicable to essentially \emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations.…

We prove a generalized Fej\'er's theorem for locally compact groups.

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…

I present a simple derivation of the de Gennes narrowing phenomenon.

We prove a general theorem that gives a linear recurrence for tuples of paths in every cylindrical network. This can be seen as a cylindrical analog of the Lindstr\"om-Gessel-Viennot theorem. We illustrate the result by applying it to Schur…