Weak invariance principles for sums of dependent random functions

Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.     

Well adjusted: Using expediting and cancelation to manage store replenishment inventory for a seasonal good

We consider an inventory problem that can be translated into a two-period newsvendor setting where the day prior to sales, the newsvendor places an initial preliminary order—a semi-binding forecast—with the publisher. At the beginning of the actual day of sales, the newsvendor has a better forecast for the day’s demand: based on knowing the actual content of the paper, he knows whether it will be a high-demand day due to breaking news or a low-demand day due to slow news. He then can revise the preliminary order quantity by expediting additional papers or canceling all or part of the order, but each of these activities has an associated cost.     

Utility of 2-Diphenylphosphoryloxy-1,3-Dienes in Multicomponent Hetero-Diels–Alder Reactions to Construct Functionalized Six-Membered Nitrogen Heterocycles

The utility of 2-diphenylphosphoryloxy-1,3-dienes for the construction of substituted six-membered nitrogen heterocycles is presented. These dienes undergo boron trifluoride-promoted aza-Diels–Alder reactions when reacted with imines or related species formed in situ using aldehydes and amine derivatives. The stability of the dienes allows this three-component reaction to be carried out with no special precautions to eliminate water or air. Thirty-one examples of this process are presented. The usefulness of the enol phosphate functional group is highlighted in further reactions after the cycloaddition step to generate functionalized piperidenes or pyridines.     

Chemists around the World,Take Your Part in the Circular Economy!

Based on recent examples and initiatives reported in the literature, this concept article discusses how chemistry can contribute to the circular economy approach in order to improve our current and future economical, societal, and environmental system. Through five proposed levels of contribution, chemists can take a significant part in this global approach via the consideration of green chemistry principles, the simplification of syntheses, the limitation of complex products preparation, the efficient utilization of resources but also the novel ways of waste valorization. A more systematic and generalized environmental and economic assessment from the lab-scale is also recommended. At last, chemists have to work even more collaboratively and in a multidisciplinary way, within chemistry and beyond.     

Investigation of two‐ and three‐bond carbon–hydrogen coupling constants in cinnamic acid based compounds

Two‐ and three‐bond coupling constants (²J_HC and ³J_HC) were determined for a series of 12 substituted cinnamic acids using a selective 2D inphase/antiphase (IPAP)‐single quantum multiple bond correlation (HSQMBC) and 1D proton coupled ¹³C NMR experiments. The coupling constants from two methods were compared and found to give very similar values. The results showed coupling constant values ranging from 1.7 to 9.7 Hz and 1.0 to 9.6 Hz for the IPAP‐HSQMBC and the direct ¹³C NMR experiments, respectively. The experimental values of the coupling constants were compared with discrete density functional theory (DFT) calculated values and were found to be in good agreement for the ³J_HC. However, the DFT method under estimated the ²J_HC coupling constants. Knowing the limitations of the measurement and calculation of these multibond coupling constants will add confidence to the assignment of conformation or stereochemical aspects of complex molecules like natural products. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of digestion,chemical separation,and deposition on Po-210 quantitative analysis

The purpose of this work was to determine polonium losses from a variety of sample types (soil, cotton fiber, and air filter) due to digestion technique, chemical separation, and deposition method for alpha energy analysis. Results demonstrated that yields from a perchloric acid wet-ash (87 ± 5 %) were similar to that from a microwave digestion (100 ± 7 %), but both were greater than the dry-ash procedure (38 ± 5 %). The polonium was separated from an SRM soil using an AG1X8 ion exchange column and deposited on a Ag disk with a recovery of 83 ± 7 % of polonium-209 (Po-209). Deposition yields without chemical separation averaged 90 ± 5 % of Po-209. The polonium-210 content was successfully measured in the three matrix types and quantitated using alpha spectroscopy.     

The Synthesis and Characterization of the Tri-rhenium(VI) Capped Wells–Dawson Polyoxometalate, [{(C4H9)4N)5(C2H5)3NH}{Re3P2W15O62}]

The tri-rhenium(VI) capped Wells–Dawson polyoxometalate, [Re₃P₂W₁₅O₆₂]^6– with quaternary ammonium cations was synthesized by reacting the trivacant lacunary species, [P₂W₁₅O₅₆]^12– with [ReOCl₃(PPh₃)₂] in an organic solvent. Elemental analysis by thermogravimetry and inductively coupled plasma mass spectroctrometry confirmed the substitution of three rhenium atoms, single-crystal X-ray diffraction as well as infra red spectroscopy showed the complete Wells–Dawson structure. The presence of all three rhenium atoms in one cap is indicated by ³¹P nuclear magnetic resonance spectroscopy and the electron spin resonance spectrum shows that the tri-rhenium(V) species with three unpaired electrons is low spin, S = ½.