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In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the non-isochronism of oscillations. These phenomena are all the more important as we move away from the oscillations at small angles, which represent the domain of validity of the harmonic approximation. The measurement is apprehended by means of the acquisition box SYSAM-SP5 coupled with the Latis pro software and the Eurosmart pendulum. We show that only a detailed analysis by fitting the recorded curve can provide sufficient accuracy to describe the quadratic evolution of the period as a function of the amplitude of the oscillations. We we can detect the additional harmonics in the oscillations when the amplitude becomes very high.
In the geometric situation of some simple unitary Shimura varieties studied by Harris and Taylor, I have built two filtrations of the perverse sheaf of vanishing cycles. The graduate of the first are the $p$-intermediate extension of some local Harri
Let G be a Coxeter group of type A_n, B_n, D_n or I_2(N), or a complex reflection group of type G(de,e,n). Let V be its standard representation and let k be an integer greater than 2. Then G acts on S(V)^{otimes k}. We show that the algebra of invari
Bitmap indexes are frequently used to index multidimensional data. They rely mostly on sequential input/output. Bitmaps can be compressed to reduce input/output costs and minimize CPU usage. The most efficient compression techniques are based on run-
On the rank of Jacobians over function fields.} Let $f:mathcal{X}to C$ be a projective surface fibered over a curve and defined over a number field $k$. We give an interpretation of the rank of the Mordell-Weil group over $k(C)$ of the jacobian of th
In this article we show that all results proved for a large class of holomorphic germs $f : (mathbb{C}^{n+1}, 0) to (mathbb{C}, 0)$ with a 1-dimension singularity in [B.II] are valid for an arbitrary such germ.