Differentiability properties for a class of non-convex functions

Closed sets K ⊂ satisfying an external sphere condition with uniform radius (called ϕ-convexity or proximal smoothness) are considered. It is shown that for -a.e. x ∊ ∂K the proximal normal cone to K at x has dimension one. Moreover if K is the closure of an open set satisfying a (sharp) nondegeneracy condition, then the De Giorgi reduced boundary is equivalent to ∂ K and the unit proximal normal equals -a.e. the (De Giorgi) external normal. Then lower semicontinuous functions f : with ϕ-convex epigraph are shown, among other results, to be locally BV and twice -a.e. differentiable; furthermore, the lower dimensional rectifiability of the singular set where f is not differentiable is studied. Finally we show that for -a.e. x there exists δ (x) > 0 such that f is semiconvex on B(x,δ(x)). We remark that such functions are neither convex nor locally Lipschitz, in general. Methods of nonsmooth analysis and of geometric measure theory are used. Work partially supported by M.I.U.R., project “Viscosity, metric, and control theoretic methods for nonlinear partial differential equations.”     

A novel convenient synthesis of benzoquinazolines

[reaction: see text] A novel synthetic pathway to benzoquinazolines from naphthylamines is reported. Benzoquinazoline nucleus was cyclized in good yield from N-protected naphthylamines using hexamethylenetetramine in TFA and potassium ferricyanide in aqueous ethanolic KOH. This method is efficient and convenient with respect to previously reported synthetic pathways.     

Dynamic HPLC on chiral stationary phases: a powerful tool for the investigation of stereomutation processes

Dynamic HPLC on enantioselective stationary phases has become a well-established technique to investigate chiral molecules with internal motions that result in stereoinversion and occur on the time scale of the separation process. Kinetic parameters for the on-column interconversion phenomena can be extracted from experimental peak profiles by computer simulation or by direct calculation methods. The technique has been used in a wide range of temperatures and is complementary in scope to dynamic NMR spectroscopy.     

Torque detection using Brownian fluctuations

We report the statistical analysis of the movement of a submicron particle confined in a harmonic potential in the presence of a torque. The absolute value of the torque can be found from the auto- and cross-correlation functions of the particle's coordinates. We experimentally prove this analysis by detecting the torque produced onto an optically trapped particle by an optical beam with orbital angular momentum.     

Behavior of disordered boron carbide under stress

Gibbs free-energy calculations based on density functional theory have been used to determine the possible source of failure of boron carbide just above the Hugoniot elastic limit (HEL). A range of B4C polytypes is found to be stable at room pressure. The energetic barrier for shock amorphization of boron carbide is by far the lowest for the B12(CCC) polytype, requiring only 6 GPa approximately = P(HEL) for collapse under hydrostatic conditions. The results clearly demonstrate that the collapse of the B12(CCC) phase leads to segregation of B12 and amorphous carbon in the form of 2-3 nm bands along the (113) lattice direction, in excellent agreement with recent transmission electron microscopy results.     

Surface plasmon radiation forces

We report the first experimental observation of momentum transfer from a surface plasmon to a single dielectric sphere. Using a photonic force microscope, we measure the plasmon radiation forces on different polystyrene beads as a function of their distance from the metal surface. We show that the force magnitude at resonance is strongly enhanced compared to a nonresonant illumination. Measurements performed as a function of the probe particle size indicate that optical manipulation by plasmon fields has a strong potential for optical sorting.     

Solving Max-Cut to optimality by intersecting semidefinite and polyhedral relaxations

We present a method for finding exact solutions of Max-Cut, the problem of finding a cut of maximum weight in a weighted graph. We use a Branch-and-Bound setting that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly optimal” solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the Max-Cut problem, which has to be done several times during the bounding process. We review other solution approaches and compare the numerical results with our method. We also extend our experiments to instances of unconstrained quadratic 0–1 optimization and to instances of the graph equipartition problem. The experiments show that our method nearly always outperforms all other approaches. In particular, for dense graphs, where linear programming-based methods fail, our method performs very well. Exact solutions are obtained in a reasonable time for any instance of size up to n = 100, independent of the density. For some problems of special structure we can solve even larger problem classes. We could prove optimality for several problems of the literature where, to the best of our knowledge, no other method is able to do so. Supported in part by the EU project Algorithmic Discrete Optimization (ADONET), MRTN-CT-2003-504438.     

Global L p estimates for degenerate Ornstein–Uhlenbeck operators

We consider a class of degenerate Ornstein–Uhlenbeck operators in ${\mathbb{R}^{N}}We consider a class of degenerate Ornstein–Uhlenbeck operators in \mathbbR^N{\mathbb{R}^{N}} , of the kind

A o ?i, j=1p0aij?xixj2 + ?i, j=1Nbijxi?xj\mathcal{A}\equiv\sum_{i, j=1}^{p_{0}}a_{ij}\partial_{x_{i}x_{j}}^{2} + \sum_{i, j=1}^{N}b_{ij}x_{i}\partial_{x_{j}}      959. Risk Processes with Non-stationary Hawkes Claims Arrivals      Gabriele Stabile  Giovanni Luca Torrisi 《Methodology and Computing in Applied Probability》2010,12(3):415-429 We consider risk processes with non-stationary Hawkes claims arrivals, and we study the asymptotic behavior of infinite and finite horizon ruin probabilities under light-tailed conditions on the claims. Moreover, we provide asymptotically efficient simulation laws for ruin probabilities and we give numerical illustrations of the theoretical results.      960. Quantitative isoperimetric inequalities for a class of nonconvex sets      Giovanni Colombo  Khai T. Nguyen 《Calculus of Variations and Partial Differential Equations》2010,37(1-2):141-166 Quantitative versions (i.e., taking into account a suitable “distance” of a set from being a sphere) of the isoperimetric inequality are obtained, in the spirit of Fuglede (Trans Am Math Soc 314:619–638, 1989) and Fusco et al. (Ann Math 168:941–980, 2008) for a class of not necessarily convex sets called φ-convex sets. Our work is based on geometrical results on φ-convex sets, obtained using methods of both nonsmooth analysis and geometric measure theory.      [首页] « 上一页 [91] [92] [93] [94] [95] 96 [97] [98] [99] [100] 下一页 » 末  页»

Risk Processes with Non-stationary Hawkes Claims Arrivals

We consider risk processes with non-stationary Hawkes claims arrivals, and we study the asymptotic behavior of infinite and finite horizon ruin probabilities under light-tailed conditions on the claims. Moreover, we provide asymptotically efficient simulation laws for ruin probabilities and we give numerical illustrations of the theoretical results.     

Quantitative isoperimetric inequalities for a class of nonconvex sets

Quantitative versions (i.e., taking into account a suitable “distance” of a set from being a sphere) of the isoperimetric inequality are obtained, in the spirit of Fuglede (Trans Am Math Soc 314:619–638, 1989) and Fusco et al. (Ann Math 168:941–980, 2008) for a class of not necessarily convex sets called φ-convex sets. Our work is based on geometrical results on φ-convex sets, obtained using methods of both nonsmooth analysis and geometric measure theory.