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Register a new userLe module dendriforme sur le groupe cyclique
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Authors
Frederic Chapoton
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The structure of anticyclic operad on the Dendriform operad defines in particular a matrix of finite order acting on the vector space spanned by planar binary trees. We compute its characteristic polynomial and propose a (compatible) conjecture for the characteristic polynomial of the Coxeter transformation for the Tamari lattice, which is mostly a square root of this matrix.
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In this short note, I explain how the non-degeneracy condition of the KAM can be bypassed. The first version of the note has been submitted for publication back in 2010 and this version in 2012.
Let ${rm F}$ be a rank-2 semi-stable sheaf on the projective plane, with Chern classes $c_{1}=0,c_{2}=n$. The curve $beta_{rm F}$ of jumping lines of ${rm F}$, in the dual projective plane, has degree $n$. Let ${rm M}_{n}$ be the moduli space of equivalence classes of semi-stables sheaves of rank 2 and Chern classes $(0,n)$ on the projective plane and ${cal C}_{n}$ be the projective space of curves of degree $n$ in the dual projective plane. The Barth morphism $$beta: {rm M}_{n}longrightarrow{cal C}_{n}$$ associates the point $beta_{rm F}$ to the class of the sheaf ${rm F}$. We prove that this morphism is generically injective for $ngeq 4.$ The image of $beta$ is a closed subvariety of dimension $4n-3$ of ${cal C}_{n}$; as a consequence of our result, the degree of this image is given by the Donaldson number of index $4n-3$ of the projective plane.
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.
The algorithmic trading comes from digitalisation of the processing of trading assets on financial markets. Since 1980 the computerization of the stock market offers real time processing of financial information. This technological revolution has offered processes and mathematic methods to identify best return on transactions. Current research relates to autonomous transaction systems programmed in certain periods and some algorithms. This offers return opportunities where traders can not intervene. There are about thirty algorithms to assist the traders, the best known are the VWAP, the TWAP, TVOL. The algorithms offer the latest strategies and decision-making are the subject of much research. These advances in modeling decision-making autonomous agent can envisage a rich future for these technologies, the players already in use for more than 30% of their trading.
As a part of the Milky Way Imaging Scroll Painting (MWISP) survey, we performed a simultaneous 12CO(1-0), 13CO(1-0), C18O(1-0) mapping toward molecular clouds in a region encompassing 3.75 square degrees. We reveal three molecular clouds, the 15 km/s cloud, the 27 km/s cloud, and the 50 km/s cloud, in the surveyed region. The 50 km/s cloud is resolved with an angular resolution of around 1 for the first time. Investigating their morphology and velocity structures, we find that the 27 km/s cloud is likely affected by feedback from the stellar association Mon OB3 and the 50 km/s cloud is characterised by three large expanding molecular shells. The region is mapped in C18O (1-0) for the first time. We discover seven C18O clumps, which are likely to form massive stars, and 15 dust clumps based on the BGPS archival data. Using infrared color-color diagrams, we find 56 Class I and 107 Class II young stellar object (YSO) candidates. According to the distribution of YSO candidates, an overdensity is found around the HII region S287 and the intersection of two shells, indicative of triggering. The star formation efficiency and rate of the 27~km/s cloud are discussed. Comparing the observed values of the filament S287-main with the models of fragmentation, we suggest that turbulence controls the large scale of fragmentation in the filament while gravitational fragmentation plays an important role in the formation of YSOs on the small scale. We find that star-forming gas tends to have higher excitation temperature, higher 13CO opacity, and higher column density than non-star-forming gas, which is consistent with the point that star formation happens in denser gas and star-forming gas is heated by YSOs. Using the 1.1 mm dust emission to trace dense gas, we obtain a dense gas fraction of 2.7%-10.4% for the 27 km/s cloud.
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