An interior estimate for a nonlinear parabolic equation

In this paper the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^∞-norm of the initial condition are estimated.     

Canonical connections with an algebraic curvature tensor field on naturally reductive spaces

We study Ambrose-Singer connections with an algebraic curvature tensor on simply connected manifolds carrying a homogeneous Riemannian structure of class ₃ in the classification given by F. Tricerri and L. Vanhecke.This work was partially supported by MURST.     

Polygon triangulation inO(n log logn) time with simple data structures

We give a newO(n log logn)-time deterministic algorithm for triangulating simplen-vertex polygons, which avoids the use of complicated data structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run inO(n log*n) time. The major new techniques employed are the efficient location of horizontal visibility edges that partition the interior of the polygon into regions of approximately equal size, and a linear-time algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibility partition of the entire chain. The latter technique has other interesting applications, including a linear-time algorithm to convert a Steiner triangulation of a polygon into a true triangulation.This research was partially supported by the following grants: NSERC 583584, NSERC 580485, ONR-N00014-87-0467, and by DIMACS, an NSF Science and Technology Center (NSF-STC88-09648).     

Elliptic Equations with Degenerate Coercivity： Gradient Regularity

In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is where for example, a(x,u)=(1+|u|)^−θ with θ ∈ (0,1). We study the same problem for minima of functionals closely related to the previous equation.     

Asymptotic behavior of solutions of variational equations

In questo articolo si considerano equazioni differenziali ordinarie del secondo ordine della forma $$\{ A(u')u'\} ' + \delta (r)A(u')u' + f(r,u) = 0,$$ dove cioè la nonlinearità è presente sia nella variabile soluzioneu che nella sua derivata. Si forniscono proprietà di monotonia, oscillazione e un accurato studio del comportamento asintotico all’ infinito delle soluzioni, quandoA, δ,f hanno crescite asintotiche di tipo algebrico.     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

Heteronuclear decoupling under fast MAS by a rotor-synchronized Hahn-echo pulse train

A new heteronuclear decoupling mechanism under fast magic-angle spinning MAS is introduced. It is based on refocusing the coherences responsible for the dephase of low-gamma nuclei ((13)C, (15)N) transverse spin-polarization in the presence of strongly dipolar-coupled protons, and has the advantage that can be implemented by pulsed techniques, with all the benefits resulting from a reduced duty cycle compared with conventional decoupling by continuous rf irradiation. The decoupling efficiency of a simple rotor-synchronized Hahn-echo pulse train is analyzed both theoretically and experimentally. It was found that a substantial improvement in sensitivity and resolution can be achieved in compounds with small (1)H chemical shielding parameters even at moderate sample spinning, and some interesting applications are shown. It is also shown that much faster spinning frequencies, or alternative refocusing sequences, are needed for applications on rigid organic solids, i.e., in systems with larger (1)H chemical shifts.