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Expansions of Theta Functions and Applications
A. Raouf Chouikha
We prove that the classical theta function may be expressed as $$ θ_4(v,τ) = θ_4(0,τ) \exp[- \sum_{p\geq 1} \sum_{k\geq 0} \frac {1}{p} \bigg(\frac {\sin πv}{(\sin (k+{1/2})π…
On the Existence of Certain Metrics with Non Parallel Ricci Tensor
A. Raouf Chouikha
A. Derdzinki [D] gave examples of Riemannian metrics with harmonic curvature and non parallel Ricci tensor on some compact manifolds . We examine their existence as well as…
Problems on polygons and Bonnesen-type inequalities
A. Raouf Chouikha
In this paper we are interested in some Bonnesen-type isoperimetric inequalities for plane n-gons in relation with the two conjectures proposed by P. Levy and X.M. Zhang.
Remark on Periodic Solutions of Non Linear Oscillators
A. Raouf Chouikha
We contribute to the method of trigonometric series for solving differential equations of certain non linear oscillators. Key Words: series power solution, trigonometric series.
The Period Function of Second Order Differential Equations
A. Raouf Chouikha
We interest in the behaviour of the period function for equations of the type and with a center at the origin 0. is a function of cla…
Non Parallelism of Ricci tensor of Pseudo-cylindric Metrics
A. Raouf Chouikha
We descrive examples of metrics in the conformal class on complete conformally flat Riemannian manifolds These metrics have a constant scalar curvature and an harmon…