Related papers: A new and elementary proof of Newton's "favorite" …

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…

This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.

When Newton's method, or Halley's method is used to approximate the $p${th} root of $1-z$, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case,…

This note is intended to explain the proof of two facts about quadrature domains: first, they are essentially unique if they exist; and second, they do exist for a large class of weight functions. The proofs roughly follow Sakai's…

Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.

We prove some new results related to Tanaka's formula.

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.

In this paper, we find a new recurrence formula fo the Euler zeta functions.

The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases:…

We give a new proof of a formula for the fusion rules for type $A_2$ due to B\'egin, Mathieu, and Walton. Our approach is to symbolically evaluate the Kac-Walton algorithm.

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.

In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.

We give a new proof of Chen-Lin result with Li-Zhang method.

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.

For the class of polynomial quadrature rules we show that conveniently chosen bases allow to compute both the weights and the theoretical error expression of a $n$-point rule via the undetermined coefficients method. As an illustration, the…

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.