Synthesis of Bridged Benzazocines and Benzoxocines by a Titanium‐Catalyzed Double‐Reductive Umpolung Strategy

A sequence of two titanium(III)‐catalyzed reductive umpolung reactions is reported that allows the rapid construction of benzazo‐ and benzoxozine building blocks. The first step is a reductive cross‐coupling of quinolones or chromones with Michael acceptors. This reaction proceeds with complete syn‐selectivity for the quinolone functionalization while the anti‐diastereomers are obtained as the major products from chromones. With different reaction conditions, the stereochemical outcome can be altered to afford the syn‐chromanone products as well. A subsequent reductive ketyl radical cyclization forges the tricyclic title compounds in good yields. A stereochemical model explaining the observed stereoselectivities is provided and the product configurations were unambiguously verified by X‐ray analyses and 2D NMR spectroscopic experiments.     

Discrete orthogonal polynomials and difference equations of several variables

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.     

Predictive modeling of electrocatalyst structure based on structure-to-property correlations of x-ray photoelectron spectroscopic and electrochemical measurements

Chemical structure and catalytic activity of nonplatinum porphyrin-based electrocatalyst for oxygen reduction is characterized by combination of X-ray photoelectron spectroscopy (XPS) and rotating disk electrode. The goal of the study is to show how modifications in the molecular structure affect catalytic characteristics and how to use these structural modifications in a purposeful manner to increase catalytic activity. Initial correlation of structure to electrochemical performance is achieved through the application of principal component analysis (PCA) to curve-fits of high-resolution XPS spectra combined with results of electrochemical measurements. Furthermore, a predictive model that describes this correlation is build using the combination of genetic algorithm (GA) and multiple linear regression (MLR). Based on structure-to-property correlations, two types of active sites responsible for the catalytic activity, i.e., Co associated with pyropolymer and Co particles covered by oxide layer, are determined, and a dual-site for oxygen reduction on cobalt porphyrins is hypothesized, allowing for designing a catalyst structure with optimal performance characteristics.     

The Geodesic Ray Transform on Riemannian Surfaces with Conjugate Points

We study the geodesic X-ray transform X on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and, therefore, this transform is always unstable (ill-posed). We describe the microlocal kernel of X and relate it to the conjugate locus. We present numerical examples illustrating the cancellation of singularities. We also show that the attenuated X-ray transform is well posed if the attenuation is positive and there are no more than two conjugate points along each geodesic; but it is still ill-posed if there are three or more conjugate points. Those results follow from our analysis of the weighted X-ray transform.     

Comparative Study on Microencapsulation of Lavender (Lavandula angustifolia Mill.) and Peppermint (Mentha piperita L.) Essential Oils via Spray-Drying Technique

Essential oils have been studied for various applications, including for therapeutic purposes. There is extensive literature regarding their properties; however, their low stability limits their application. Generally, the microencapsulation of essential oils allows enhanced stability and enables the potential incorporation in solid dosage forms. Lavender and peppermint oils were encapsulated in microparticles using a spray-drying technique under optimized conditions: 170 °C temperature, 35 m³/h aspiration volume flow, and 7.5 mL/min feed flow. Arabic gum and maltodextrin were used as coating polymers individually in varying concentrations from 5 to 20% (w/v) and in combination. The microparticles were studied for morphology, particle size, oil content, and flowability. The formulated powder particles showed a high yield of 71 to 84%, mean diameter 2.41 to 5.99 µm, and total oil content of up to 10.80%. The results showed that both the wall material type and concentration, as well as the type of essential oil, significantly affected the encapsulation process and the final particle characteristics. Our study has demonstrated that the encapsulation of lavender and peppermint oils in Arabic gum/maltodextrin microparticles by spray-drying represents a feasible approach for the conversion of liquids into solids regarding their further use in powder technology.     

On ℤp-graded identities and cocharacters of the Grassmann algebra

Let p be an odd prime number, F a field of characteristic zero, and let Ebe the unitary Grassmann algebra generated by the infinite-dimensionalF-vector space L. We determine the bases of the ?_p-graded identities.Moreover we compute the ?_p-graded codimension and cocharacter sequences for the algebra E endowed with any ?_p-grading such that L is a homogeneous subspace.     

Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials

We consider the Hill operator