Weierstrasss Elliptic Functions Mathematics (3 results)

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The Weierstrass elliptic function can be defined in three closely related ways, each of which possesses certain advantages. One is as a function of a complex variable z and a lattice in the complex plane. Another is in terms of z and two complex numbers 1 and 2 defining a pair of generators, or periods, for the lattice. The third is in terms z and of a modulus in the upper half-plane. This is related to the previous definition by = 2 / 1, which by the conventional choice on the pair of periods is in the upper half-plane. Using this approach, for fixed z the Weierstrass functions become modular functions of .

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In mathematics and theoretical physics, quasiperiodic motion is in rough terms the type of motion executed by a dynamical system containing a finite number (two or more) of incommensurable frequencies. That is, if we imagine that the phase space is modelled by a torus T, the trajectory of the system is modelled by a curve on T that wraps around without ever exactly coming back on itself. A quasiperiodic function on the real line is the type of function (continuous, say) obtained from a function on T, by means of a curve R T, which is linear (when lifted from T to its covering Euclidean space), by composition. It is therefore oscillating, with a finite number of underlying frequencies. (NB the sense in which theta functions and the Weierstrass zeta function in complex analysis are said to have quasi-periods with respect to a period lattice is something distinct from this).

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space.