PBW deformations of quadratic monomial algebras

A result of Braverman and Gaitsgory from 1996 gives necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of a Koszul algebra. The main theorem in this paper establishes conditions equivalent to the Braverman-Gaitsgory Theorem to efficiently determine PBW deformations of quadratic monomial algebras. In particular, a graphical interpretation is presented for this result, and we discuss circumstances under which some of the conditions of this theorem need not be checked. Several examples are also provided. Finally, with these tools, we show that each quadratic monomial algebra admits a nontrivial PBW deformation.     

Method development for the determination of wood preservatives in commercially treated wood using gas chromatography-mass spectrometry

Fungicides and insecticides are commonly used preservatives to protect wood products against microbiological degradations. Currently, there is a lack of analytical methods addressing the quantitative determination of a wide range of wood preserving species in wood matrices. In this study, a reliable method was developed for the determination of a mixture of wood preserving agents with differing chemical structures (i.e., properties), including tebuconazole (TAZ), propiconazole (PAZ), 3-iodo-2-propynyl butylcarbamate (IPBC), and permethrin (PER), in pine wood. The analyte recoveries obtained by Soxhlet and multiple-stage sonication extractions were compared. While both extraction methods yielded similar results (80–100%), Soxhlet extraction was found to be less labor-intensive and thus preferred providing also lower RSDs of 1–6%. In comparison to methanol, commonly used as an extraction solvent for triazoles, acetone yielded similar extraction efficiencies for all analytes while reducing the time of sample concentration. The solid phase extraction method for triazoles was adapted to allow for a separation of IPBC and PER from the wood matrix. As opposed to previous studies, three recovery standards were employed, which enabled the correction of individual analyte losses during the sample preparation. The matrix-affected limits of detection (LODs) using gas chromatography with mass spectrometric detection were nearly the same for triazoles 0.07 and 0.21 ng g⁻¹ for PAZ and TAZ in sapwood and 0.18 and 0.21 ng g⁻¹ in heartwood, respectively. Higher LODs were observed for IPBC and PER: 3.9 and 1.7 ng g⁻¹ in sapwood, and 2.0 and 6.0 ng g⁻¹ in heartwood, respectively. The recoveries in the wood submitted to commercial sample treatment showed gradient distribution of analytes depending on the penetration of the treatment.     

Laser Induced Marking of Polymer Chains with Radical Spin Traps

A pathway for marking of polymer chains with radical spin traps during pulsed laser polymerization in free radical polymerization is presented. By introducing a so‐called marker that forms a non‐propagating radical at (or shortly after) the incidence of a laser pulse, a polymer subdistribution is generated by specifically terminating propagating radicals via combination with such a marker radical. The generated polymer subdistribution can subsequently be imaged by modern soft‐ionization mass spectrometry. Herein, the general methodology of the method in which such marker is generated via reaction of an initiating radical with a nitrone is demonstrated on the examples of BA and VAc.

     

Extended three-dimensional impedance map methods for identifying ultrasonic scattering sites

The frequency-dependent ultrasound backscatter from tissues contains information about the microstructure that can be quantified. In many cases, the anatomic microstructure details responsible for ultrasonic scattering remain unidentified. However, their identification would lead to potentially improved methodologies for characterizing tissue and diagnosing disease from ultrasonic backscatter measurements. Recently, three-dimensional (3D) acoustic models of tissue microstructure, termed 3D impedance maps (3DZMs), were introduced to help to identify scattering sources [J. Mamou, M. L. Oelze, W. D. O'Brien, Jr., and J. F. Zachary, "Identifying ultrasonic scattering sites from 3D impedance maps," J. Acoust. Soc. Am. 117, 413-423 (2005)]. In the current study, new 3DZM methodologies are used to model and identify scattering structures. New processing procedures (e.g., registration, interpolations) are presented that allow more accurate 3DZMs to be constructed from histology. New strategies are proposed to construct scattering models [i.e., form factor (FF)] from 3DZMs. These new methods are tested on simulated 3DZMs, and then used to evaluate 3DZMs from three different rodent tumor models. Simulation results demonstrate the ability of the extended strategies to accurately predict FFs and estimate scatterer properties. Using the 3DZM methods, distinct FFs and scatterer properties were obtained for each tumor examined.     

The Paradox of Time in Dynamic Causal Systems

Recent work has shown that people use temporal information including order, delay, and variability to infer causality between events. In this study, we build on this work by investigating the role of time in dynamic systems, where causes take continuous values and also continually influence their effects. Recent studies of learning in these systems explored short interactions in a setting with rapidly evolving dynamics and modeled people as relying on simpler, resource-limited strategies to grapple with the stream of information. A natural question that arises from such an account is whether interacting with systems that unfold more slowly might reduce the systematic errors that result from these strategies. Paradoxically, we find that slowing the task indeed reduced the frequency of one type of error, albeit at the cost of increasing the overall error rate. To explain these results we posit that human learners analyze continuous dynamics into discrete events and use the observed relationships between events to draw conclusions about causal structure. We formalize this intuition in terms of a novel Causal Event Abstraction model and show that this model indeed captures the observed pattern of errors. We comment on the implications these results have for causal cognition.     

A height bound for abelian schemes with real $$\times \mathbb {Q}^{2}$$ multiplication

Archiv der Mathematik - In this paper, we prove a height bound for points on the base of a family of abelian varieties at which the fibre possesses additional endomorphisms. This complements a...     

Practical and General Alcohol Deoxygenation Protocol

Herein, we describe a practical protocol for the removal of alcohol functional groups through reductive cleavage of their benzoate ester analogs. This transformation requires a strong single electron transfer (SET) reductant and a means to accelerate slow fragmentation following substrate reduction. To accomplish this, we developed a photocatalytic system that generates a potent reductant from formate salts alongside Brønsted or Lewis acids that promote fragmentation of the reduced intermediate. This deoxygenation procedure is effective across structurally and electronically diverse alcohols and enables a variety of difficult net transformations. This protocol requires no precautions to exclude air or moisture and remains efficient on multigram scale. Finally, the system can be adapted to a one-pot benzoylation-deoxygenation sequence to enable direct alcohol deletion. Mechanistic studies validate that the role of acidic additives is to promote the key C(sp³)−O bond fragmentation step.     

Materials for polymer electronics applications – semiconducting polymer thin films and nanoparticles

The paper presents two different approaches to nanostructured semiconducting polymer materials: (i) the generation of aqueous semiconducting polymer dispersions (semiconducting polymer nanospheres SPNs) and their processing into dense films and layers, and (ii) the synthesis of novel semiconducting polyfluorene-block-polyaniline (PF-b-PANI) block copolymers composed of conjugated blocks of different redox potentials which form nanosized morphologies in the solid state.