Higher dimensional Ginzburg–Landau equations under weak anchoring boundary conditions

For $n\ge 3$ and $0<?\le 1$, let $\mathrm{\Omega }?{\mathbb{R}}^n$ be a bounded, simply connected, smooth domain, and $u_{?}:\mathrm{\Omega }?{\mathbb{R}}^n\to {\mathbb{R}}^2$ solve the Ginzburg–Landau equation under the weak anchoring boundary condition:

$\{\begin{array}{cc}?\mathrm{\Delta }{u}_{?}=\frac{1}{{?}^2}(1?|u_{?}{|}^2)u_{?}\hfill & \mathrm{in}\mathrm{\Omega },\hfill \\ \frac{?u_{?}}{?\nu }+{\lambda }_{?}(u_{?}?g_{?})=0\hfill & \mathrm{on}?\mathrm{\Omega },\hfill \end{array}$

where the anchoring strength parameter ${\lambda }_{?}=K{?}^{?\alpha }$ for some $K>0$ and $\alpha \in [0,1)$, and $g_{?}\in C^2(?\mathrm{\Omega },{\mathbb{S}}^1)$. Motivated by the connection with the Landau–De Gennes model of nematic liquid crystals under weak anchoring conditions, we study the asymptotic behavior of $u_{?}$ as ? goes to zero under the condition that the total modified Ginzburg–Landau energy satisfies $F_{?}(u_{?},\mathrm{\Omega })\le M|\log ??|$ for some $M>0$.     

Combined Photoredox and Carbene Catalysis for the Synthesis of Ketones from Carboxylic Acids**

As a key element in the construction of complex organic scaffolds, the formation of C−C bonds remains a challenge in the field of synthetic organic chemistry. Recent advancements in single-electron chemistry have enabled new methods for the formation of various C−C bonds. Disclosed herein is the development of a novel single-electron reduction of acyl azoliums for the formation of ketones from carboxylic acids. Facile construction of the acyl azolium in situ followed by a radical–radical coupling was made possible merging N-heterocyclic carbene (NHC) and photoredox catalysis. The utility of this protocol in synthesis was showcased in the late-stage functionalization of a variety of pharmaceutical compounds. Preliminary investigations using chiral NHCs demonstrate that enantioselectivity can be achieved, showcasing the advantages of this protocol over alternative methodologies.     

‘Praying Mantis’ diffuse reflectance accessory for UV-Vis-NIR spectroscopy

Conclusion The characteristics of the PM accessory allow reflecting measurements on a new variety of samples such as fruits, vegetables, tissue cultures, fermentation broths or reagent-impregnated dip sticks currently being developed for clinical laboratories.     

On weighted heights of random trees

Consider the family treeT of a branching process starting from a single progenitor and conditioned to havev=v(T) edges (total progeny). To each edge <e> we associate a weightW(e). The weights are i.i.d. random variables and independent ofT. The weighted height of a self-avoiding path inT starting at the root is the sum of the weights associated with the path. We are interested in the asymptotic distribution of the maximum weighted path height in the limit asv=n. Depending on the tail of the weight distribution, we obtain the limit in three cases. In particular ify ² P(W(e)> y)0, then the limit distribution depends strongly on the tree and, in fact, is the distribution of the maximum of a Brownian excursion. If the tail of the weight distribution is regularly varying with exponent 0<2, then the weight swamps the tree and the answer is the asymptotic distribution of the maximum edge weight in the tree. There is a borderline case, namely,P(W(e)> y)cy ^–2 asy, in which the limit distribution exists but involves both the tree and the weights in a more complicated way.     

Synthesis of Filamentary Carbon Material on a Self-Organizing Ni–Pt Catalyst in the Course of 1,2-Dichloroethane Decomposition

A series of model microdisperse Ni_1–xPt _x alloys (x =0–0.05) was synthesized by a coprecipitation method with the subsequent sintering of the precipitate in an atmosphere of H₂ at 800°C. Their chemical and phase compositions were determined (by AAS and XRD analysis, respectively), and it was found that the synthesis method proposed afforded Ni–Pt solid solutions based on the face-centered nickel lattice. The kinetic features of the carbon erosion of Ni_1–xPt _x alloys in their contact with 1,2-dichloroethane vapor in a temperature range of 550–700°C were studied. It was found that the presence of Pt in the alloy increased the rate of accumulation of carbon product by a factor of ~1.5 regardless of the concentration of Pt. The catalyst did not undergo deactivation for 5 h of reaction to ensure a high yield of carbon material (103 g/g_Cat). With the use of electron microscopy (SEM and TEM techniques), it was found that the carbon product consisted of carbon fibers with a segmented structure. An increase in the concentration of Pt in the alloy to 4.3 wt % sharply changed the disintegration of the alloy to cause the formation of carbon product with a bimodal fiber diameter distribution (d_av = 0.4 and 1.2 μm).     

Database diversity assessment: New ideas, concepts, and tools

We present some new ideas for characterizing and comparing largechemical databases. The comparison of the contents of large databases is nottrivial since it implies pairwise comparison of hundreds of thousands ofcompounds. We have developed methods for categorizing compounds into groupsor series based on their ring-system content, using precalculatedstructure-based hashcodes. Two large databases can then be compared bysimply comparing their hashcode tables. Furthermore, the number of distinctring-system combinations can be used as an indicator of database diversity.We also present an indepen- dent technique for diversity assessment calledthe saturation diversity approach. This method is based on picking as manymutually dissimilar compounds as possible from a database or a subsetthereof. We show that both methods yield similar results. Since the twomethods measure very different properties, this probably says more about theproperties of the databases studied than about the methods.     

The Application of Scientific Methodology to a Contemporary Sports Journal

Often neglected as a foundation for scientific inquiry are contemporary sports journals and the articles contained within them. It is common to encounter authoritative assertions by various authors that are in truth ordinary suppositions infrequently based on tenable scientific data. This article outlines a model for transforming an ordinary factual statement, taken from a recent sporting journal, into an educational experience that includes experimental design, supporting documentation, methods of experimental verification, and the scientific method as a whole.     

Pretreatment of corn fiber by pressure cooking in water

The pretreatment of corn fiber using liquid water at temperatures between 220 and 260°C enhances enzymatic hydrolysis. This paper describes the laboratory reactor system currently in use for cooking of corn fiber at temperatures ranging from 200 to 260°C. The corn fiber at approx 4.4% solid/liquid slurry was treated in a 2-L, 304 SS, Parr reactor with three turbine propeller agitators and a Proportional-Integral-Derivative (PID), controller that controlled temperature within ±1°C. Heat-up times to the final temperatures of 220, 240, or 260°C were achieved in 50 to 60 min. Hold time at the final temperature was less than 10 s. A serpentine cooling coil, through which tap water was circulated at the completion of the run, cooled the reactor’s contents to 180°C within 2 min after the maximum temperature was attained. Ports in the reactor’s head plate facilitated sampling of the slurry and monitoring the pH. A continuous pH monitoring system was developed to help observe trends in pH during pretreatment and to assist in the development of a base (2.0M KOH) addition profile to help keep the pH within the range of 5.0 to 7.0. Enzymatic hydrolysis gave 33 to 84% conversion of cellulose in the pretreated fiber to glucose compared to 17% for untreated fiber.     

Enantioselective partial reduction of 2,5-disubstituted pyrroles via a chiral protonation approach

[reaction: see text] The partial reduction of 2,5-pyrrole diester 1 followed by enantioselective protonation in situ to furnish synthetically useful building blocks is described. An enantiomeric excess of up to 74% was achieved using (-)-ephedrine and related analogues as chiral proton sources. The pyrroline product obtained could be recrystallized to give enantiomerically pure material.