Relative Volume Comparison with Integral Curvature Bounds

In this paper we shall generalize the Bishop-Gromov relative volume comparison estimate to a situation where one only has an integral bound for the part of the Ricci curvature which lies below a given number. This will yield several compactness and pinching theorems. Submitted: August 1996, revised: July 1997     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

Classification of edges using compactly supported shearlets

We analyze the detection and classification of singularities of functions $f={\chi }_S$, where $S?{\mathbb{R}}^d$ and $d=2,3$. It will be shown how the set ?S can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ?S is a $d?1$ dimensional piecewise smooth manifold with $d=2$ or 3, we will classify smooth and non-smooth components of ?S. This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in 3 dimensions by compactly supported shearlets. Finally, geometric properties of ?S such as curvature are described in terms of the continuous shearlet transform of f.     

Test-time extension behind reflected shock waves using CO2–He and C3H8–He driver mixtures

To study combustion chemistry at low temperatures in a shock tube, it is of great importance to increase experimental test times, and this can be done by tailoring the interface between the driver and driven gases. Using unconventional driver-gas tailoring with the assistance of tailoring curves, shock-tube test times were increased from 1 to 15 ms for reflected-shock temperatures below 1,000 K. Provided in this paper is the introduction of tailoring curves, produced from a one-dimensional perfect gas model for a wide range of driver gases and the production and demonstration of successful driver mixtures containing helium combined with either propane or carbon dioxide. The He/CO₂ and He/C₃H₈ driver mixtures provide a unique way to produce a tailored interface and, hence, longer test times, when facility modification is not an option. The tailoring curves can be used to guide future applications of this technique to other configurations. Nonreacting validation experiments using driver mixtures identified from the tailoring curves were performed over a range of reflected-shock temperatures from approximately 800 to 1,400 K, and some examples of ignition-time experiments that could not have otherwise been erformed are presented.     

N-2-aryl-1,2,3-triazoles: a novel class of UV/blue-light-emitting fluorophores with tunable optical properties

The N-2-aryl-1,2,3-triazole derivatives (NATs) were developed as a new class of UV/blue-light-emitting fluorophores. Though both N-1-aryl-1,2,3-triazoles and N-2-aryl-1,2,3-triazoles gave strong photo absorption under excitation at 330 nm, only the N-2-analogous showed strong fluorescence emission in the UV/blue range with high efficiency in various solvents (quantum yield Φ around 0.3-0.5). Significant substituted group effects were observed, allowing tunable optical properties with emission (λ(max)) from 350-400 nm and Stokes shift from 38-93 nm. The computational studies along with X-ray crystal structures indicated the significance of the effective conjugation between triazole ring and aryl groups on the N-2 position. The planar intramolecular charge transfer (PICT) mechanism was proposed, which was supported by solvent effect studies. Simple derivatizations gave NAT-modified lysine and strong UV/blue emitting bis-NAT (Φ=0.76, λ(max)=390), which suggested the great potential of this new class of fluorophores in biological and material science research.     

Metal-free synthesis of aryl esters from carboxylic acids and diaryliodonium salts

An efficient arylation of carboxylic acids with diaryliodonium salts has been developed, giving aryl esters in high yields within short reaction times for both aromatic and aliphatic substrates. The transition-metal-free conditions are compatible with a range of functional groups, and good chemoselectivity is observed with unsymmetric diaryliodonium salts. Furthermore, steric hindrance in the ortho positions is well tolerated both in the carboxylic acid and in the diaryliodonium salt, yielding aryl esters that cannot be obtained via other esterification protocols.     

Bounding reflection length in an affine Coxeter group

In any Coxeter group, the conjugates of elements in the standard minimal generating set are called reflections, and the minimal number of reflections needed to factor a particular element is called its reflection length. In this article we prove that the reflection length function on an affine Coxeter group has a uniform upper bound. More precisely, we prove that the reflection length function on an affine Coxeter group that naturally acts faithfully and cocompactly on ℝ ⁿ is bounded above by 2n, and we also show that this bound is optimal. Conjecturally, spherical and affine Coxeter groups are the only Coxeter groups with a uniform bound on reflection length.     

Fulleropyrrolidine end-capped molecular wires for molecular electronics--synthesis, spectroscopic, electrochemical, and theoretical characterization

In continuation of previous studies showing promising metal-molecule contact properties a variety of C(60) end-capped "molecular wires" for molecular electronics were prepared by variants of the Prato 1,3-dipolar cycloaddition reaction. Either benzene or fluorene was chosen as the central wire, and synthetic protocols for derivatives terminated with one or two fullero[c]pyrrolidine "electrode anchoring" groups were developed. An aryl-substituted aziridine could in some cases be employed directly as the azomethine ylide precursor for the Prato reaction without the need of having an electron-withdrawing ester group present. The effect of extending the π-system of the central wire from 1,4-phenylenediamine to 2,7-fluorenediamine was investigated by absorption, fluorescence, and electrochemical methods. The central wire and the C(60) end-groups were found not to electronically communicate in the ground state. However, the fluorescence of C(60) was quenched by charge transfer from the wire to C(60). Quantum chemical calculations predict and explain the collapse of coherent electronic transmission through one of the fulleropyrrolidine-terminated molecular wires.     

Weak Limits of the Measures of Maximal Entropy for Orthogonal Polynomials

Potential Analysis - In this paper we study the sequence of orthonormal polynomials {Pn(μ;z)} defined by a Borel probability measure μ with non-polar compact support $S(\mu )\subset...