Largest bounding box,smallest diameter,and related problems on imprecise points

Imprecision of input data is one of the main obstacles that prevent geometric algorithms from being used in practice. We model an imprecise point by a region in which the point must lie. Given a set of imprecise points, we study computing the largest and smallest possible values of various basic geometric measures on point sets, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding box. We give efficient algorithms for most of these problems, and identify the hardness of others.     

Wave propagation with tunneling in a highly discontinuous layered medium

An impulsive plane wave traverses a stratified medium consisting of a large number N of homogeneous isotropic perfectly elastic layers. The directly transmitted wave is greatly reduced by the cumulative effect of scattering loss at each of the many interfaces. However, close to the arrival of the direct wave is a broad pulse, arising from multiple scattering; this pulse does not decay as rapidly as the direct wave and ultimately appears to diffuse about a moving center. The latter process, which is determined by the medium statistics, leads to time delays, effective anisotropy, and apparent attenuation.

The present work may be regarded as an extension of that described by Burridge, White and Papanicolaou (1988) and Burridge and Chang (1989) to allow for tunneling P waves for S-wave incidence beyond the critical angle.

When the reflection coefficients at the interfaces are scaled as 1/√N while N → ∞, and when time is measured in units of vertical travel time across an average layer, numerical solutions of the exact problem show that the shape of the broad transmitted pulse approaches the limiting form given as the solution of a certain integrodifferential equation in accordance with our asymptotic theory.     

Six‐Coordinate Group 13 Complexes: The Role of d Orbitals and Electron‐Rich Multi‐Center Bonding

Bonding in six‐coordinate complexes based on Group 13 elements (B, Al, Ga, In, Tl) is usually considered to be identical to that in transition‐metal analogues. We herein demonstrate through sophisticated electronic‐structure analyses that the bonding in these Group 13 element complexes is fundamentally different and better characterized as electron‐rich hypervalent bonding with essentially no role for the d orbitals. This characteristic is carried through to the molecular properties of the complex.     

High‐Resolution Single‐Molecule Fluorescence Imaging of Zeolite Aggregates within Real‐Life Fluid Catalytic Cracking Particles

Fluid catalytic cracking (FCC) is a major process in oil refineries to produce gasoline and base chemicals from crude oil fractions. The spatial distribution and acidity of zeolite aggregates embedded within the 50–150 μm‐sized FCC spheres heavily influence their catalytic performance. Single‐molecule fluorescence‐based imaging methods, namely nanometer accuracy by stochastic chemical reactions (NASCA) and super‐resolution optical fluctuation imaging (SOFI) were used to study the catalytic activity of sub‐micrometer zeolite ZSM‐5 domains within real‐life FCC catalyst particles. The formation of fluorescent product molecules taking place at Brønsted acid sites was monitored with single turnover sensitivity and high spatiotemporal resolution, providing detailed insight in dispersion and catalytic activity of zeolite ZSM‐5 aggregates. The results point towards substantial differences in turnover frequencies between the zeolite aggregates, revealing significant intraparticle heterogeneities in Brønsted reactivity.     

Improved Spectral Coverage and Fluorescence Quenching in Donor–acceptor Systems Involving Indolo[3‐2‐b]carbazole and Boron‐dipyrromethene or Diketopyrrolopyrrole

A novel π‐conjugated triad and a polymer incorporating indolo[3,2‐b]‐carbazole (ICZ) and 4,4‐difluoro‐4‐bora‐3a,4a‐diaza‐s‐indacene (BODIPY) were synthesized via a Sonogashira coupling. Compared to the parent BODIPY the absorption and fluorescence spectrum were for both compounds broader and redshifted. The redshift of the fluorescence and the decrease of the fluorescence quantum yield and decay time upon increasing solvent polarity were attributed to the formation of a partial charge‐transfer state. Upon excitation in the ICZ absorption band the ICZ fluorescence was quenched in both compounds mainly due to energy transfer to the BODIPY moiety. In a similar ICZ–π–DPP polymer (where DPP is diketopyrrolopyrrole), a smaller redshift of the absorption and fluorescence spectra compared to the parent DPP was observed. A less efficient quenching of the ICZ fluorescence in the ICZ–π–DPP polymer could be related to the unfavorable orientation of the transition dipoles of ICZ and DPP. The rate constant for energy transfer was for all compounds an order of magnitude smaller than predicted by Förster theory. While in a solid film of the triad a further redshift of the absorption maximum of nearly 100 nm was observed, no such shift was observed for the ICZ–π–BODIPY polymer.