Edge Singular Behavior for the Heat Equation on Polyhedral Cylinders in \boldsymbol{\mathbb{R}}^{\bf 3}

We study the Heat equation in the polyhedral cylinder with a non-convex edge. We construct the singularity functions depending on the time and edge axis, and the coefficient of the singularity, called the stress intensity distributions, and show regularity results for the solution and the coefficient. The regularity is achieved in the (not weighted) Sobolev space in the L² and L ^q spaces, respectively. An application to the finite polyhedral cylinder is described.     

Characterization of Oil-Wax Gel with Higher Velocity Gradient

The properties of solid surface on oil-wax gel are one of the most important factors which decide the quality of products such as cosmetics. The thixotropic property of solid surface depends on the velocity gradient and it is increased with higher velocity gradient as controlling the morphology on solid surface of oil-wax gel. The morphological change of oil-wax gel in compliance with surface properties of wax matrix can cause different rheological behaviors. Rheological behavior of oil-wax gel regarding the surface transition range in accordance with shear strain was observed to characterize surface properties. In an earlier article, the morphological mechanism of causing surface transition range and the factors of influencing surface transition range were examined by studying the rheological behaviors of a solid-state emulsion. Here, we investigated, in the lattice structure terms, the morphological change of oil-wax gel by measuring surface transition range depending on velocity gradient, which could influence the hardness and sweating phenomenon. We confirmed that the morphological change of oil-wax gel was accompanied by crystal size, crystal conformation, the degree of crystallinity. Surface transition range depending on velocity gradient was shown in large and regular lattice structure of oil-wax gel better than small and irregular one.     

Synthesis and Properties of Thermosensitive Poly(N-Isopropylacrylamide)/Waterborne Polyurethane Graded Concentration Hybrid Films

Temperature-sensitive hybrid films were synthesized with a concentration gradient by casting and UV curing of N-isopropylacrylamide (NIPAAm) monomers (0%–70%) on the free surface of waterborne polyurethane (WPU) films on a Teflon substrate. The surface hardness and contact angle of the free surface with a water drop increased asymptotically with the addition of NIPAAm, whereas those on the substrate side were virtually unchanged. The diffusion coefficient (D), rates of swelling at 20°C (below the lower critical solution temperature (LCST) of poly(N-isopropylacrylamide) (PNIPAM)) and deswelling at 50°C (above the LCST) increased with increasing NIPAM content, showing favorable thermosensitivity. In addition, the glassy state modulus and glass transition temperature (Tg) of the film increased with increasing NIPAM content, whereas the rubbery modulus decreased due to the increased molecular weight between the crosslinks. In addition, as the NIPAM content increased, the film showed a positive yield with an increased yield and fracture stress and decreased ductility. Above 50% NIPAM, the film became brittle, showing a linear stress–strain relationship.     

Visible-Light-Induced C4-Selective Functionalization of Pyridinium Salts with Cyclopropanols

The site-selective C?H functionalization of heteroarenes is of considerable importance for streamlining the rapid modification of bioactive molecules. Herein, we report a general strategy for visible-light-induced β-carbonyl alkylation at the C4 position of pyridines with high site selectivity using various cyclopropanols and N-amidopyridinium salts. In this process, hydrogen-atom transfer between the generated sulfonamidyl radicals and O?H bonds of cyclopropanols generates β-carbonyl radicals, providing efficient access to synthetically valuable β-pyridylated (aryl)ketones, aldehydes, and esters with broad functional-group tolerance. In addition, the mild method serves as an effective tool for the site-selective late-stage functionalization of complex and medicinally relevant molecules.     

The antipode of a quasitriangular quasi-Turaev group coalgebra is bijective

In order to construct a class of new Turaev-braided group category with nontrivial associativity, the concept of a quasitriangular quasi-Turaev group coalgebras was recently introduced. Inside the definition, the conditions of invertibility of the R-matrix R and bijectivity of the antipode S are required. In this article, we prove that the antipode of a quasitriangular quasi-Turaev group coalgebra without the assumptions about invertibility of the antipode and R-matrix is inner, and a fortiori, bijective. As an application, we prove that for a quasitriangular quasi-Turaev group coalgebra, two conditions mentioned above are unnecessary.     

Noncovalent Intermolecular Interaction in Cofacially Stacked 24π Antiaromatic Hexaphyrin Dimer

π–π Stacking is omnipresent not only in nature but in a wide variety of practical fields applied to our lives. Because of its importance in a performance of natural and artificial systems, such as light harvesting system and working layer in device, many researchers have put intensive effort into identifying its underlying nature. However, for the case of π–π stacked systems composed of antiaromatic units, the understanding of the fundamental mechanisms is still unclear. Herein, we synthesized a new type of planar β,β’-phenylene-bridged hexaphyrin (1.0.1.0.1.0), referred as naphthorosarin which possesses the 24π-electron conjugated pathway. Especially, the corresponding antiaromatic porphyrinoid shows the unique property to form dimeric species adopting the face-to-face geometry which is unprecedented in cases of known annulated naphthorosarins. In order to elucidate the intriguing properties derived from the stacked dimer, the current study focuses on the experimental support to rationalize the observed π–π interactions between the two subunits.     

Simultaneous determination of 75 abuse drugs including amphetamines,benzodiazepines, cocaine,opioids, piperazines,zolpidem and metabolites in human hair samples using liquid chromatography–tandem mass spectrometry

A liquid chromatography–tandem mass spectrometric method for the simultaneous determination of 75 abuse drugs and metabolites, including 19 benzodiazepines, 19 amphetamines, two opiates, eight opioids, cocaine, lysergic acid diethylamide, zolpidem, three piperazines and 21 metabolites in human hair samples, was developed and validated. Ten‐milligram hair samples were decontaminated, pulverized using a ball mill, extracted with 1 mL of methanol spiked with 28 deuterated internal standards in an ultrasonic bath for 60 min at 50°C, and purified with Q‐sep dispersive solid‐phase extraction tubes. The purified extracts were evaporated to dryness and the residue was dissolved in 0.1 mL of 10% methanol. The 75 analytes were analyzed on an Acquity HSS T3 column using gradient elution of methanol and 0.1% formic acid and quantified in multiple reaction monitoring mode with positive electrospray ionization. Calibration curves were linear (r ≥ 0.9951) from the lower limit of quantitation (2–200 pg/mg depending on the drug) to 2000 pg/mg. The coefficients of variation and accuracy for intra‐ and inter‐assay analysis at three QC levels were 4.3–12.9% and 89.2–109.1%, respectively. The overall mean recovery ranged from 87.1 to 105.3%. This method was successfully applied to the analysis of 11 forensic hair samples obtained from drug abusers.