Related papers: A Counting Proof of the Graham Pollak Theorem
We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We prove Burkholder inequality using Bregman divergence.
In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.
We prove an analogue of the prime number theorem for finite fields.
We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.
We present an elementary proof of a reduced version of Gleason's theorem and the Kochen-Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of…
In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…
We will present a new proof of the Gromoll-Grove diameter rigidity theorem.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.
We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
We prove a distribution-theoretic conjecture of Robert Coleman, thereby also obtaining an explicit description of the complete set of Euler systems for the multiplicative group over Q.
We show that the existence of disintegration for cylindrical measures follows from a general disintegration theorem for countably additive measures.
We present a relative form of the Toponogov comparison theorem.