Hasil untuk "math.HO"

Shaun Cooper

This note discusses elliptic functions in Ramanujan's work.

Bela Bajnok

We present the problems and solutions to the 50th Annual USA Mathematical Olympiad.

Davoud Mirzaei

Welcome to a beautiful subject in scientific computing: numerical solution of ordinary differential equations (ODEs) with initial conditions.

Selman Akbulut

Remarks relating the various notions of corks.

Alain Lasjaunias, Jean-Paul Tran

This short note is a comment on a historical aspect of a famous formula dating from the 18th century.

Ho Park

Abstract The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σ r ♯ ( n ; N / 4 , N ) {\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible, where N / 4 N\hspace{-0.08em}\text{/}\hspace{-0.08em}4 is an arbitrary odd positive integer. This generalizes previous result in combination with Cho and Kim, which is about the case N = 4 N=4 . While obtaining our main theorem, we derive some generalizations of other identities to the case that we are dealing with.

Andrei Okounkov

This is a popular article about the work of James Maynard, 2022 Fields medalist.

Cristobal Arratia

For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.

Franz Lemmermeyer

We give a short proof of the quadratic reciprocity law using Gauss's Lemma and Hermite's identity.

Veselin Jungic

The purpose of this note is to honour memory of Ubiratan D'Ambrosio, a Brazilian mathematics educator, who passed away on May 12, 2021.

Soichiro Fujii

The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.

Alexander Aycock

We show that an apparently overlooked result of Euler from \cite{E421} is essentially equivalent to the general multiplication formula for the $Γ$-function that was proven by Gauss in \cite{Ga28}.

Irina Shevtsova

Convergence rate estimates in limit theorems for sums of independent random variables are considered.

Franz Hofbauer

The theorem of Feuerbach states that the nine-point circle of a nonequilateral triangle is tangent to both its incircle and its three excircles. We give a simple proof of this theorem.

S. N. Gladkovskii

The autor propose the elementary derivation of the continued fraction expansion for function sec(x) + tan(x).

Math Dicker

A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism.

Chris Preston

These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.

V. Pizzigoni

This study use some philological and historical means in order to understand Fermat's way of thinking.

S. Kutateladze

This is a brief overview of some turning points in the history of infinitesimals.

Diem Ho