Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition

We discuss local solvability of operators of the form where theV _j are left-invariant vector fields on the Heisenberg group such that [V _j ,V _j+n ]=U for 1≤j≤n andA=(a _jk )=A ₁+iA ₂ is a complex symmetric matrix satisfying the “cone condition” |A ₂|≤CA ₁. The authors acknowledge the support for this work by the European Commission through the European HCM-program “Fourier Analysis” and the TMR network “Harmonic Analysis”.     

Maximal functions with polynomial densities in lacunary directions

Given a real polynomial in one variable such that , we consider the maximal operator in ,

0\,,\,i,j\in \mathbb{Z}}\frac{1... ...t f\big (x_{1}-2^{i}p(t),x_{2}-2^{j}p(t)\big )\big \vert\,dt . \end{displaymath}">

We prove that is bounded on for 1$"> with bounds that only depend on the degree of .

     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

Γ-Limit of Periodic Obstacles

We compute the -limit of a sequence obstacle functionals in the case of periodic obstacles.     

Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

Convex curves, Radon transforms and convolution operators defined by singular measures

Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents.     

Discrete γ-rays in the reactions of 143 MeV32S with58Ni

The reactions induced by 143 MeV³²S on⁵⁸Ni have been studied detecting discrete γ-rays in coincidence with projectile-like fragments (PLF). Information on PLF excitation probability and sequential decay of target-like fragments (TLF) has been obtained. For the²⁸Si+⁶²Zn outgoing channel at small energy loss (¦Q¦<20 MeV), both PLF and TLF data indicate that thermal equilibrium is not attained. The hypothesis of an equal excitation energy partition between the two reaction fragments does not describe properly experimental TLF data. A dependence of PLF excitation probability on the outgoing channel is found for the two final channels³²S+⁵⁸Ni and²⁸Si+⁶²Zn. The values of the spin alignment parameterP _zz, derived for PLF and TLF from measurements ofγ-rays anisotropy, are in disagreement with the expectations of the transport theory for dissipative collisions.     

Ligand–macromolecule complexes: affinity index determination by selective nuclear relaxation analysis

Proton NMR selective and non-selective spin–lattice relaxation rate measurements were used to monitor the strength of the overall complexation behaviour of a ligand (carbamazepine) toward a macromolecular receptor (albumin). The ‘affinity index,’ a quantitative parameter related to the strength of the ligand–macromolecule interaction, was determined from the experimental contribution of the bound ligand molar fraction to the observed selective spin–lattice relaxation rate. The effect of a second ligand (lamotrigine) on the carbamazepine–albumin interaction was also investigated and was found to have a modulation effect on the carbamazepine–albumin interaction. Copyright © 2001 John Wiley & Sons, Ltd.