Related papers: From Rolle's theorem to the Sturm-Hurwitz theorem

The Whitney-Graustein theorem states that regular closed curves in the 2-plane are classified, up to regular homotopy, by their rotation number. Here we give a simple proof based on contact geometry.

We provide a simple proof of Kamp's theorem.

New proofs of the duplication formulae for the gamma and the Barnes double gamma functions are derived using the Hurwitz zeta function. Concise derivations of Gauss's multiplication theorem for the gamma function and a corresponding one for…

We recover Reidemeister's theorem using smooth functions and transversality.

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

Stokes theorem holds for Lipschitz forms on a smooth manifold.

Given a II$_1$ factor M and a masa A of M, we prove a version of the Schur-Horn Theorem, together with a contractive version. These results are inspired on a recent conjecture of Arveson and Kadison (math.OA/0508482).

We attempt to generalize a congruence property of elliptic modular forms proved by Sturm to that of Haupttypus of Siegel modular forms of degree 2 with level. Namely, we give an explicit bound of Fourier coefficients required to determine…

We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.

We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l>2 be prime and A a finite abelian l-group. Then there…

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

A modified Version of the Hardy-Littlewood tauberian Theorem is used to prove under which conditions the moduli of the coefficients |a(n)/n| of schlicht functions tend uniformly to their Hayman Indexes as n tends to infinity.

In this work we present a novel proof of the Saalschutz formula by using the theory of discrete fractional calculus. The proofs of some results within this theory, namely, the fractional power rule and the fractional Leibniz rule are…

In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

In general, Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. In this paper, we initiate the study of…

I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

In the note, we give a proof, based on the Generalized Thom Conjecture, of Bennequin's Theorem on upper bound for the Euler number of a link which is considered as a closed braid. A lower bound for the Euler number of a link is also given.