Quantum Ergodicity for Quantum Graphs without Back-Scattering

We give an estimate of the quantum variance for d-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum ergodicity for these families of graphs. Our proof is based on a uniform control of an associated random walk on the bonds of the graph. We show that recent constructions of Ramanujan graphs, and asymptotically almost surely, random d-regular graphs, satisfy the necessary conditions to conclude that quantum ergodicity holds.     

New figuring model based on surface slope profile for grazing‐incidence reflective optics

Surface slope profile is widely used in the metrology of grazing‐incidence reflective optics instead of surface height profile. Nevertheless, the theoretical and experimental model currently used in deterministic optical figuring processes is based on surface height, not on surface slope. This means that the raw slope profile data from metrology need to be converted to height profile to perform the current height‐based figuring processes. The inevitable measurement noise in the raw slope data will introduce significant cumulative error in the resultant height profiles. As a consequence, this conversion will degrade the determinism of the figuring processes, and will have an impact on the ultimate surface figuring results. To overcome this problem, an innovative figuring model is proposed, which directly uses the raw slope profile data instead of the usual height data as input for the deterministic process. In this paper, first the influence of the measurement noise on the resultant height profile is analyzed, and then a new model is presented; finally a demonstration experiment is carried out using a one‐dimensional ion beam figuring process to demonstrate the validity of our approach.     

Reverse mathematics,well-quasi-orders,and Noetherian spaces

A quasi-order Q induces two natural quasi-orders on \({\mathcal{P}(Q)}\), but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on \({\mathcal{P}(Q)}\) preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on \({\mathcal{P}(Q)}\) are Noetherian, which means that they contain no infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) \({\mathcal{P}(Q)}\) is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA₀ over RCA₀. To state these theorems in RCA₀ we introduce a new framework for dealing with second-countable topological spaces.     

Versatile Catalytic Hydrogenation Using A Simple Tin(IV) Lewis Acid

Despite the rapid development of frustrated Lewis pair (FLP) chemistry over the last ten years, its application in catalytic hydrogenations remains dependent on a narrow family of structurally similar early main‐group Lewis acids (LAs), inevitably placing limitations on reactivity, sensitivity and substrate scope. Herein we describe the FLP‐mediated H₂ activation and catalytic hydrogenation activity of the alternative LA iPr₃SnOTf, which acts as a surrogate for the trialkylstannylium ion iPr₃Sn⁺, and is rapidly and easily prepared from simple, inexpensive starting materials. This highly thermally robust LA is found to be competent in the hydrogenation of a number of different unsaturated functional groups (which is unique to date for main‐group FLP LAs not based on boron), and also displays a remarkable tolerance to moisture.     

Stable carbon and nitrogen isotope discrimination and turnover in a small-bodied insectivorous lizard

Laboratory experiments are useful for estimating the carbon and nitrogen isotope discrimination factors and turnover rates that are critical for drawing field-based inferences on consumer diets using stable isotopes. Although the utility of these discrimination factors is widely recognized, work in terrestrial systems has largely been limited to studies involving mammals and birds. In contrast, scant attention has been paid to the application of isotopic techniques to reptiles, despite their broad diversity in terms of numbers of species as well as their trophic roles. Here we estimate carbon and nitrogen isotope discrimination factors and turnover for the tree lizard (Urosaurus ornatus) using a diet-switch experiment. Lizards were collected from a C₄-dominated grassland and then switched to C₃-based diet (crickets) in the laboratory. We estimated discrimination by lizard claw tissue as Δ¹³C?=?1.2?±?0.1?‰ for carbon and Δ¹⁵N?=?0.7?±?0.1?‰ (mean?±?1 SE) for nitrogen, with 95?% turnover occurring after ～15.5 days. These estimates should be appropriate for use in trophic studies of U. ornatus, and possibly other related small-bodied insectivorous lizards.     

Simultaneous LC-MS/MS quantitation of a highly hydrophobic pharmaceutical compound and its metabolite in urine using online monolithic phase-based extraction

This article describes the use of monolithic material as extraction support in simultaneous LC-MS/MS quantitation of a highly hydrophobic pharmaceutical compound and its hydroxylated metabolite in urinary matrix. DMSO was added to urine samples to aid the solubilization of analytes during storage and transfer. Samples were then diluted and injected onto an online extraction system for high-throughput analysis in an automated fashion. A linear range of 1.03-103 ng/mL was validated for the parent compound and 7.02-1400 ng/mL for the metabolite. The accuracy (%bias) at the lower LOQ (LLOQ) for the parent compound was -2.9% and the precision (%CV) at the LLOQ was 5.4%, while the accuracy at LLOQ for the metabolite was 6.3% and the precision at LLOQ was 5.5%. The results show that quantitative LC-MS/MS analysis by online extraction using the monolithic support is reproducible, sensitive, and accurate enough to satisfy bioanalytical testing requirements in a good laboratory practice (GLP) regulated environment. Monolithic phase based online extraction provided efficient sample cleanup, which was evidenced in matrix effect testing against multiple lots of urinary matrix. The method described within can be a generic approach for quantitative analysis of analytes with poor solubility in aqueous matrix.