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Let A be an abelian variety over a number field F and A_
its dual. B. Birch and
P. Swinnerton-Dyer, interested in defining the Tamagawa number (A) of A, were led to their
celebrated c...
A note on micro-instability for Hamiltonian systems close to integrable
micro-instability Hamiltonian systems close to integrable
2015/9/25
In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following resul...
Let M be a cg-connected manifold. Let L be a second-order
differential operator with real cg(R) coefficients on M and such that L1 0 (i.e., L
has no zero-order term). Assume that there exists a posi...
We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a ...
A NOTE ON STRONGLY SEPARABLE ALGEBRAS
Separable algebras invariants coinvariants coalgebras Hopf algebras
2015/8/14
Let A be an algebra over a field k. If M is an A–bimodule, we let
MA and MA denote respectively the k–spaces of invariants and coinvariants of
M, and 'M : MA
! MA be the natural map. In this note w...
It is shown that robust stability and robust performance questions for control systems with nonparametric uncertainties can be turned into those with a particularly simple parametric description. It i...
A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere
Gluing Dirac Type Operators Mirror Quantum Two-Sphere
2014/12/12
The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subjec...
Note on the Number of Steady States for a 2D Smoluchowski Equation
the Number Steady States 2D Smoluchowski Equation
2014/4/4
Dynamics of concentrated polymer solutions are modeled by a Smoluchowski equation. At high concentrations, such solutions form liquid crystalline polymers of nematic structure. We prove that at high i...
NOTE ON GLOBAL REGULARITY FOR 2D OLDROYD-B FLUIDS WITH DIFFUSIVE STRESS
Oldroyd-B, complex uids Fokker-Planck equations blow up global existence Euler equations Navier-Stokes equations kinetic equations
2014/4/3
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial di usion of the polymeric stresses.
A note on Freiman models in Heisenberg groups
Freiman models Heisenberg groups Number Theory
2012/7/11
Green and Ruzsa recently proved that for any $s\ge2$, any small squaring set $A$ in a (multiplicative) abelian group, i.e. $|A\cdot A|a Freiman $s$-model: it means that there exists a grou...
A note on modular forms and generalized anomaly cancellation formulas
Modular invariance Anomaly cancellation formulas
2018/4/19
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulasKe...
A Note on Coulhon type inequalities
Sobolev inequalities modulus of continuity symmetrization isoperimetric inequalities interpolation
2012/6/29
T. Coulhon introduced an interesting parametrization of Sobolev inequalities. We characterize Coulhon type inequalities in terms of rearrangement inequalities.
Given a homotopy equivalence f between two topological spaces we obtain an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.
A note on the unramified Brauer group of a homogeneous space
Unramified Brauer group homogeneous space linear algebraic group
2012/6/21
We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the un...
Let $v(n)$ be the minimum number of voters with transitive preferences which are needed to generate any strong preference pattern (ties not allowed) on $n$ candidates. Let $k=\lfloor \log_2 n\rfloor$....