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We give an asymptotic expression for the tail of the maximum of Brownian motion minus a parabola. This confirms a conjecture about the exponential term in the tail behavior, due to Svante Janson.
On the distribution of exponential functionals for Levy processes with jumps of rational transform
exponential functionals Levy processes rational transform
2010/11/22
We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou o...
Optimal Design of Minimum-Power Stimuli for Spiking Neurons
Optimal Design Minimum-Power Stimuli Spiking Neurons
2010/11/22
In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to targeted spiking ti...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
2010/11/22
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...
Existence and concentration of solutions for a class of biharmonic equations
Existence and concentration of solutions biharmonic equations
2010/11/22
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existe...
This article gives explicit solutions to the Yang-Mills equations. The solutions have positive energy that can be made arbitrarily small by selection of a parameter showing that Yang-Mills field theor...
Definability of the variety generated by a commutative monoid in the lattice of commutative semigroup varieties
commutative monoid lattice commutative semigroup varieties
2010/11/11
Let M be a commutative monoid. We provide an explicit first-order formular that defines the variety generated by M in the lattice of commutative semigroup varieties.
On the stability of weight spaces of enveloping algebra in prime characteristic
enveloping algebra prime characteristic
2010/11/15
By the result of Dixmier, any weight space of enveloping algebra of Lie algebra L over a field of characteristic 0 is adL stable. In this paper we will show that this result need not be true, if F is...
An analogue of the Harer-Zagier formula for unicellular maps on general surfaces
the Harer-Zagier formula unicellular maps on general surfaces
2010/11/15
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is simply connected. In a famous article, Harer and Zagier established a formula fo...
Localized bases for finite dimensional homogenization approximations with non-separated scales and high-contrast
finite dimensional homogenization non-separated scales and high-contrast
2010/11/9
We construct finite-dimensional approximations of solution spaces of divergence form operators with $L^\infty$-coefficients. Our method does not rely on concepts of ergodicity or scale-separation, but...
The Hadamard Type Inequalities for M-Convex Functions
The Hadamard Type Inequalities M-Convex Functions
2010/11/11
In this paper we obtained some new Hadamard-Type inequalities for functions whose derivatives absolute values m-convex. Some applications to special means of real numbers are given.
Multivariate Rogers-Szegö polynomials and flags in finite vector spaces
Multivariate Rogers-Szegö polynomials flags in finite vector spaces
2010/11/9
We give a recursion for the multivariate Rogers-Szeg\"o polynomials, along with another recursive functional equation, and apply them to compute special values. We also consider the sum of all $q$-mu...
A posteriori error estimator based on gradient recovery by averaging for convection-diffusion-reaction problems approximated by discontinuous Galerkin methods
averaging convection-diffusion-reaction problems discontinuous Galerkin methods
2010/11/9
We consider some (anisotropic and piecewise constant) convection-diffusion-reaction problems in domains of R2, approximated by a discontinuous Galerkin method with polynomials of any degree. We propos...
A counterexample for Improved Sobolev Inequalities over the 2-adic group
Sobolev Inequalities the 2-adic group
2010/11/9
On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first s...
In this article, a class of second order differential equations on [0,1], driven by a general H\"older continuous function and with multiplicative noise, is considered. We first show how to solve thi...