Search results for "FOS: Mathematics"
showing 10 items of 1448 documents
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
The F-pure threshold of quasi-homogeneous polynomials
2018
Abstract Inspired by the work of Bhatt and Singh [3] we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x , y , z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi–Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n + 1 variables x 0 , … , x n of degree equal to the degree of x 0 ⋯ x n .
Irregular Time Dependent Obstacles
2010
Abstract We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and does not have regularity in the time variable. Two quite different procedures yield the same solution.
Computational approach to compact Riemann surfaces
2017
International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…
Building Anosov flows on $3$–manifolds
2014
We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting both of a transitive Anosov vector field and a non-transitive Anosov vector field; 2. for any n, we build a 3-manifold M supporting at least n pairwise different Anosov vector fields; 3. we build transitive attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive attractors; 4. we build a transitive Anosov vector field admitting infinitely many pairwise non-isotopic trans- verse tori.
Bifurcations in the elementary Desboves family
2017
International audience; We give an example of a family of endomorphisms of $\mathbb{P}^2(\mathbb{C})$ whose Julia set depends continuously on the parameter and whose bifurcation locus has non-empty interior.
Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules
2017
We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.
The dual and the double of a Hopf algebroid are Hopf algebroids
2017
Let $H$ be a $\times$-bialgebra in the sense of Takeuchi. We show that if $H$ is $\times$-Hopf, and if $H$ fulfills the finiteness condition necessary to define its skew dual $H^\vee$, then the coopposite of the latter is $\times$-Hopf as well. If in addition the coopposite $\times$-bialgebra of $H$ is $\times$-Hopf, then the coopposite of the Drinfeld double of $H$ is $\times$-Hopf, as is the Drinfeld double itself, under an additional finiteness condition.
Categorical action of the extended braid group of affine type $A$
2017
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.