High focal depth with fractional-power wave fronts

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.     

A programmable molecular diode driven by charge-induced conformational changes

The 3-nitro-2-(3'-nitro-2'-ethynylpyridine)-5-thiopyridine molecule shows charge-induced conformational switching and a rectifying behavior with a charge-induced controllable switching. This device can be used as a memory operated with an external field interacting with one of the rings local dipole. Alternatively, the molecule can be used as a nano-actuator controlling the rotation of the ring by charging the molecule with a bias voltage.     

Collision of a Solid with an Incompressible Fluid

We give a predictive theory of the collisions of a viscous incompressible fluid with solids. The theory is based on interior percussions which account for the very large stresses and contact forces resulting from the kinematic incompatibilities responsible for the collision. New equation of motion and constitutive laws result from the theory. Examples dealing with a fluid colliding with its container and with a diver impacting the water of a swimming pool are studied.     

When an algebraic frame is regular

It is shown that an algebraic frame L is regular if and only if its compact elements are complemented. More generally, it is shown that each pseudocomplemented element is regular if and only if each , with c compact, is complemented. With a mild assumption on L, each , with c compact, is regular precisely when for any two minimal primes p and q of L. These results are then interpreted in various frames of subobjects of lattice-ordered groups and f-rings.     

On the Behaviour of the First Eigenfunction of the p-Laplacian Near its Critical Points

In this paper, the behaviour of the positive eigenfunction of in u_| = 0, p > 1, isstudied near its critical points. Under some convexity and symmetryassumptions on , is seen to have a unique critical point atx = 0; also, the behaviour of both and is determined nearby.Positive solutions u to some general problems –_pu = f(u)in , u_| = 0, are also considered, with some convexity restrictionson u. 2000 Mathematics Subject Classification 35B05 (primary),35J65, 35J70 (secondary).     

Efficient Regular Polygon Dissections

We study the minimum number g(m,n) (respectively, p(m,n)) of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using glass-cuts (respectively, polygonal cuts). First we study regular polygon-square dissections and show that n/2 -2 g(4,n) (n/2) + o(n) and n/4 g(n,4) (n/2) + o(n) hold for sufficiently large n. We also consider polygonal cuts, i.e., the minimum number p(4,n) of pieces needed to dissect a square into a regular n-gon of the same area using polygonal cuts and show that n/4 p(4,n) (n/2) + o(n) holds for sufficiently large n. We also consider regular polygon-polygon dissections and obtain similar bounds for g(m,n) and p(m,n).     

Second Order Perturbations of a Schwarzschild Black Hole: Inclusion of Odd Parity Perturbations

We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the l = 2 axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge–Wheeler–Zerilli approach. This formulation is useful, for instance, for the treatment in the "close limit approximation" of the collision of counterrotating black holes.     

Gallavotti–Cohen Theorem,Chaotic Hypothesis and the Zero-Noise Limit

The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat—the Gallavotti–Cohen Theorem— relies on the ergodic properties of the system considered. We show that when perturbed by an energy-conserving random noise, the relation follows trivially for any system at finite noise amplitude. The time needed to achieve stationarity may stay finite as the noise tends to zero, or it may diverge. In the former case the Gallavotti–Cohen result is recovered, while in the latter case, the crossover time may be computed from the action of ‘instanton’ orbits that bridge attractors and repellors. We suggest that the ‘Chaotic Hypothesis’ of Gallavotti, Cohen and Ruelle can thus be reformulated as a matter of stochastic stability of the measure in trajectory space. In this form this hypothesis may be directly tested.     

Energetic and structural characterization of 2‐R‐3‐methylquinoxaline‐1,4‐dioxides (R = benzoyl or tert‐butoxycarbonyl): experimental and computational studies

The gaseous standard molar enthalpies of formation of two 2‐R‐3‐methylquinoxaline‐1,4‐dioxides (R = benzoyl or tert‐butoxycarbonyl), at T = 298.15 K, were derived using the values for the enthalpies of formation of the compounds in the condensed phase, measured by static bomb combustion calorimetry, and for the enthalpies of sublimation, measured by Knudsen effusion, using a quartz crystal oscillator. The three dimensional structure of 2‐tert‐butoxycarbonyl‐3‐methylquinoxaline‐1,4‐dioxide has been obtained by X‐ray crystallography showing that the two N? O bond lengths in this compound are identical. The experimentally determined geometry in the crystal is similar to that obtained in the gas‐phase after computations performed at the B3LYP/6‐311 + G(2d,2p) level of theory. The experimental and computational results reported allow to extend the discussion about the influence of the molecular structure on the dissociation enthalpy of the N? O bonds for quinoxaline 1,4‐dioxide derivatives. As found previously, similar N? O bond lengths in quinoxaline‐1,4‐dioxide compounds are not linked with N? O bonds having the same strength. Copyright © 2007 John Wiley & Sons, Ltd.     

Atomistic modeling of segregation and bulk ordering in Ag-Au alloys

The bulk and surface properties of Ag-Au alloys, for the whole range of concentration and as a function of temperature, is studied by means of a simple modeling scheme using the Bozzolo-Ferrante-Smith method for alloys. Evidence for short-range order is found and explained, as well as its relationship with the experimentally observed segregation behavior.