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A stochastic differential equation model for foraging behavior of fish schools
We present a novel model of stochastic differential equations for foraging behavior of fish schools in space including obstacles. We then study the model numerically. Three configurations of space with different locations of foo ... Read More >
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Reeb components of leafwise complex foliations and their symmetries I
We review the standard Hopf construction of Reeb components with leafwise complex structure and almost determine the group of leafwise holomorphic smooth automorphisms for Reeb components of certain type in the case of complex l ... Read More >
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Fibré de Tango pondéré généralisé de rang $n-1$ sur l'espace $\mathbb{P}^{ ...
We study in this paper a new family of stable algebraic vector bundles of rank $ n-1 $ on the complex projective space $\mathbb{P}^{n}$ whose weighted Tango bundles of Cascini \cite{ca} belongs to. We show that these bundles are ... Read More >
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Méthode de Mahler: relations linéaires, transcendance et applications aux nomb ...
This paper is concerned with Mahler's method. We study in detail the structure of linear relations between values of Mahler functions at algebraic points. In particular, given a field ${\bf k}$, a Mahler function $f(z)\in{\bf k} ... Read More >
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The Ramsey number of mixed-parity cycles I
Denote by $R(G_1, G_2, G_3)$ the minimum integer $N$ such that any three-colouring of the edges of the complete graph on $N$ vertices contains a monochromatic copy of a graph $G_i$ coloured with colour $i$ for some $i\in{1,2,3}$ ... Read More >
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Schrödinger Operators With $A_\infty$ Potentials
We study the heat kernel $p(x,y,t)$ associated to the real Schr\"odinger operator $H = -\Delta + V$ on $L^2(\mathbb{R}^n)$, $n \geq 1$. Our main result is a pointwise upper bound on $p$ when the potential $V \in A_\infty$. In th ... Read More >
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On the pedant tree-connectivity of graphs
The concept of pedant tree-connectivity was introduced by Hager in 1985. For a graph $G=(V,E)$ and a set $S\subseteq V(G)$ of at least two vertices, \emph{an $S$-Steiner tree} or \emph{a Steiner tree connecting $S$} (or simply, ... Read More >
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Persistence exponent for random walk on directed versions of $Z^2$
We study the persistence exponent for random walks in random sceneries (RWRS) with integer values and for some special random walks in random environment in $\mathbb Z^2$ including random walks in $\mathbb Z^2$ with random orien ... Read More >
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A Viscosity Method in the Min-max Theory of Minimal Surfaces
We present the min-max construction of critical points of the area using penalization arguments. Precisely, for any immersion of a closed surface $\Sigma$ into a given closed manifold, we add to the area Lagrangian a term equal ... Read More >
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Bi-Cohen-Macaulay graphs
In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General bi-Cohen-Macaulay graphs are classified up to separation. The inseparable b ... Read More >