Related papers: A generalization of Pappus chain theorem

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

An technically interesting proof of a known theorem.

We present here a simple and direct proof of the classic geometric version of Hahn-Banach Theorem from its analitic version, in the real case. The reciprocal implication, and the direct proofs of both versions, are already well kown, but…

We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We present infinite analogues of our splinter lemma from [Trees of tangles in abstract separation systems, arXiv:1909.09030]. From these we derive several tree-of-tangles-type theorems for infinite graphs and infinite abstract separation…

We derive a symplectic analogue of A-directed immersion theorem.

A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem.

In this note we give a detailed proof of a theorem of Aubin.

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 prove a theorem which implies a quantum (multiplicative) analogue of the Horn conjecture, and also of the saturation conjecture. We obtain transversality statements for quantum schubert calculus in any characteristic and also determine…

We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…

In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.

We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.

We give a sheaf-theoretic version of the universal coefficient theorem.

We study a type of object, called a pathway (generalizing pathways in the sense of P. E. Cohen [Proc. Amer. Math. Soc. 74, No. 2 (1979), 318--321]), which is useful for several set-theoretic constructions and whose existence, in a sense,…

Inspired by recent work of I. Baoulina, we give a simultaneous generalization of the theorems of Chevalley-Warning and Morlaye.

This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.