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Register a new userEtude des effets non lineaires observes sur les oscillations dun pendule simple
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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.
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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 Harris-Taylors local systems, while for the second, obtained by duality, they are the $p+$-intermediate extensions. In this work, we describe the difference between these $p$ and $p+$ intermediate extension. Precisely, we show, in the case where the local system is associated to an irreducible cuspidal representation whose reduction modulo $l$ is supercuspidal, that the two intermediate extensions are the same. Otherwise, if the reduction modulo $l$ is just cuspidal, we describe the $l$-torsion of their difference.
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 invariants (S(V)^{otimes k})^G is a free (S(V)^G)^{otimes k}-module of rank |G|^{k-1}, and that S(V)^{otimes k} is not a free (S(V)^{otimes k})^G-module.
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-length encoding (RLE), such as Word-Aligned Hybrid (WAH) compression. This type of compression accelerates logical operations (AND, OR) over the bitmaps. However, run-length encoding is sensitive to the order of the facts. Thus, we propose to sort the fact tables. We review lexicographic, Gray-code, and block-wise sorting. We found that a lexicographic sort improves compression--sometimes generating indexes twice as small--and make indexes several times faster. While sorting takes time, this is partially offset by the fact that it is faster to index a sorted table. Column order is significant: it is generally preferable to put the columns having more distinct values at the beginning. A block-wise sort is much less efficient than a full sort. Moreover, we found that Gray-code sorting is not better than lexicographic sorting when using word-aligned compression.
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 the generic fibre (modulo the constant part) in terms of average of the traces of Frobenius on the fibers of $f$. The results also give a reinterpretation of the Tate conjecture for the surface $mathcal{X}$ and generalizes results of Nagao, Rosen-Silverman and Wazir.
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.
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