Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Conditions for periodic vibrations in a symmetric n-string

100%

Gauthier C.

Open Mathematics

2008

tom 6

nr 2

287-300

A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.

On the periodicity of trigonometric functions generalized to quotient rings of R[x]

100%

Gauthier C.

Open Mathematics

2006

tom 4

nr 3

395-412

We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.

Ograniczanie wyników

2 Open Mathematics

2 Gauthier C.

1 2008

1 2006

Wyniki wyszukiwania

Conditions for periodic vibrations in a symmetric n-string

On the periodicity of trigonometric functions generalized to quotient rings of R[x]