Výsledky vyhledávání - "Ebanks Bruce"

Akademický článek

Autor: Ebanks Bruce

Publikováno v: Annales Mathematicae Silesianae, Vol 38, Iss 1, Pp 18-28 (2024)

This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G genera

Externí odkaz: https://doaj.org/article/f59d1cba21744d7cacf72e0ae8c226a8

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Akademický článek

Sine Subtraction Laws on Semigroups

Autor: Ebanks Bruce

Publikováno v: Annales Mathematicae Silesianae, Vol 37, Iss 1, Pp 49-66 (2023)

We consider two variants of the sine subtraction law on a semi-group S. The main objective is to solve f(xy∗ ) = f(x)g(y) − g(x)f(y) for unknown functions f, g : S → ℂ, where x ↦ x* is an anti-homomorphic involution. Until now this equation

Externí odkaz: https://doaj.org/article/d21f94e5e5bb4f058c9387624242f65a

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Akademický článek

A Levi–Civita Equation on Monoids, Two Ways

Autor: Ebanks Bruce

Publikováno v: Annales Mathematicae Silesianae, Vol 36, Iss 2, Pp 151-166 (2022)

We consider the Levi–Civita equation f(xy)=g1(x)h1(y)+g2(x)h2(y)f\left( {xy} \right) = {g_1}\left( x \right){h_1}\left( y \right) + {g_2}\left( x \right){h_2}\left( y \right) for unknown functions f, g1, g2, h1, h2 : S → ℂ, where S is a monoid.

Externí odkaz: https://doaj.org/article/78349633eed748e5bdb8fd45eb36d8c1

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Akademický článek

The Cosine-Sine Functional Equation on Semigroups

Autor: Ebanks Bruce

Publikováno v: Annales Mathematicae Silesianae, Vol 36, Iss 1, Pp 30-52 (2022)

The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup. The name refers to the fact that it contains both the sine and cosine addit

Externí odkaz: https://doaj.org/article/dd463b5a817d44d9908c86bdf18b25b0

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