The Spectral Density Function for the Laplacian on High Tensor Powers of a Line Bundle

For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin–Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density function. We give an explicit computation of the spectral density function, by constructing certain quasimodes on the associated principle bundle.     

Two negative minima of the first normal stress difference in a cellulose‐based cholesteric liquid crystal: Helix uncoiling

The shear rate dependence of material functions such as shear viscosity (η) and the first normal stress difference (N₁) were given and interpreted earlier by Kiss and Porter. Their widely accepted work revealed the possibility of having a negative minimum of N₁ for polymeric liquid crystals. In this work, we disclose for the first time the evidence of two negative N₁ minima on a sheared cellulosic lyotropic system. The lower shear rate minimum is ascribed to the uncoiling of the cholesteric helix, as theoretically predicted earlier. Our findings contribute also to the understanding of the other minimum already reported in the literature and attributed to the nematic director tumbling mode. Moreover, the elastic change that the LC‐HPC sample undergoes during the helix unwinding of the cholesteric structure is also by means of oscillatory measurements. This study is a contribution for the understanding of the structure‐properties relationship linked with the complex rheological behavior of chiral nematic cellulose‐based systems and may help to improve their further processing. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 821–830     

Rebuttal of “Existence of attractor and control of a 3D differential system” by Z. Wang

A paper, ??Existence of attractor and control of a 3D differential system,?? was published in the journal Nonlinear Dynamics. The author tries to prove the existence of horseshoe chaos by means of the Shilnikov criterion. To do that, he uses the undetermined coefficient method to analytically demonstrate the existence of heteroclinic orbits in a Lorenz-like system. Unfortunately, his proof is not correct for two reasons. Firstly, he considers an odd function to represent the heteroclinic orbit whereas such an orbit joining two saddle-focus equilibria can never have that symmetry. Secondly, he looks for a structurally unstable Shilnikov heteroclinic orbit by means of uniformly convergent series expansions: This would imply that the dynamical object found is structurally stable.     

Simple Characterization of Green-Synthesized Silver Nanoparticles by Capillary Electrophoresis

The development of methodologies for the characterization of silver nanoparticles (AgNPs) synthesized using natural products has received increasing attention, especially to monitoring its stability and size for further application. In this paper, a capillary electrophoretic (CE) method is presented for characterization of AgNPs synthesized using honey or glucose as reducing agents. A simple electrolyte solution composed of 20 mM sodium borate and 20 mM sodium dodecylsulfate (SDS) at pH 8.5 was used for separation of AgNPs within a short analysis time (<12 min). The obtained results were compared with the traditional characterization techniques, such as transmission electron microscopy (TEM) and dynamic light scattering (DLS), showing satisfactory correlation in terms of size distribution. In addition, valuable information about electrophoretic mobility and zeta potential values of AgNPs was obtained by applying the CE-UV/Vis method. Thus, the proposed methodology represents a straightforward tool for the fast and cost-effective characterization of AgNPs within a single analysis, employing minimal amounts of reagents and samples.     

Ultrafast gas chromatography coupled to electronic nose to identify volatile biomarkers in exhaled breath from chronic obstructive pulmonary disease patients: A pilot study

An analytical method to identify volatile organic compounds (VOCs) in the exhaled breath from patients with a diagnosis of chronic obstructive pulmonary disease (COPD) using a ultrafast gas chromatography system equipped with an electronic nose detector (FGC eNose) has been developed. A prospective study was performed in 23 COPD patients and 33 healthy volunteers; exhalation breathing tests were performed with Tedlar bags. Each sample was analyzed by FCG eNose and the identification of VOCs was based on the Kovats index. Raw data were reduced by principal component analysis (PCA) and canonical discriminant analysis [canonical analysis of principal coordinates (CAP)]. The FCG eNose technology was able to identify 17 VOCs that distinguish COPD patients from healthy volunteers. At all stages of PCA and CAP the discrimination between groups was obvious. Chemical prints were correctly classified up to 82.2%, and were matched with 78.9% of the VOCs detected in the exhaled breath samples. Receiver operating characteristic curve analysis indicated the sensitivity and specificity to be 96% and 91%, respectively. This pilot study demonstrates that FGC eNose is a useful tool to identify VOCs as biomarkers in exhaled breath from COPD patients. Further studies should be performed to enhance the clinical relevance of this quick and ease methodology for COPD diagnosis.     

Aminomethyl Transfer (Mannich) Reactions Between an O-Triethylsilylated Hemiaminal and Anilines,RnC6H5−nNH2 Leading to New Diamines,Triamines, Imines,or 1,3,5-Triazines Dependent upon Substituent R

The reactions of the Mannich reagent Et₃SiOCH₂NMe₂ ( 1 ) with a variety of anilines (mono-substituted RC₆H₄NH₂, R=H, 4-CN, 4-NO₂, 4-Ph, 4-Me, 4-MeO, 4-Me₂N; di-substituted R₂C₆H₃NH₂, R₂=3,5-(CH₃)₂, 3,5-(CF₃)₂; tri-substituted R₃C₆H₂NH₂, R₃=3,5-Me₂-4-Br and a “super bulky” aniline (Ar*NH₂) [Ar*=2,6-bis(diphenylmethyl)-4-tert-butylphenyl]) led to the formation of a range of products dependent upon the substituent. With electron-withdrawing substituents, previously unknown diamines, RC₆H₄NH(CH₂NMe₂) [R=CN ( 2 a ), NO₂ ( 2 b )] and R₂C₆H₃NH(CH₂NMe₂) [R₂=3,5-(CF₃)₂ ( 2 c) ] were formed. Further reaction of 2 a , b , c with 1 yielded the corresponding triamines RC₆H₄N(CH₂NMe₂)₂ (R=CN ( 3 a ), NO₂ ( 3 b ) and R₂C₆H₃N(CH₂NMe₂)₂, R₂=3,5-(CF₃)₂ ( 3 c ). The new polyamines were characterized by NMR spectroscopy, and for 2 a , 2 c _, and 3 c , by single crystal XRD. In the case of electron-donating groups, R=4-OMe, 4-NMe₂, 4-Me, 3,5-Me₂, 3,5-Me₂-4-Br, and for R=4-Ph, the reactions with 1 immediately led to the formation of the related 1,3,5-triazines, R=4-MeO ( 5 a ), 4-Me₂N ( 5 b ), 4-Me ( 5 c ), 3,5-Me₂ ( 5 d ), 3,5-Me₂-4-Br ( 5 e ), 4-Ph ( 5 f ), 4-Cl ( 5 g ). The “super bulky” aniline rapidly produced a single product, namely the corresponding imine Ar*N=CH₂ ( 4 ) which was also characterized by single crystal XRD. Imine 4 is both thermally and oxidatively stable. All reactions are very fast, thus based upon the presence of Si we are tempted to denote the reactions of 1 as examples of “Silick” chemistry.     

Improving accuracy by subpixel smoothing in the finite-difference time domain

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.     

Synthesis of quinine and quinidine using sulfur ylide-mediated asymmetric epoxidation as a key step

The epoxidation of meroquinene aldehyde with a chiral sulfur ylide as the key step in the synthesis of quinine and quinidine is described. The epoxidation reactions proceed under reagent control with high selectivity and good yield. The effect of sulfide and ylide substituents on the stereochemical outcome of the reaction is discussed.     

Mechanical model for fiber-laden membranes

An integrated mechanical model for fiber-laden membranes is presented and representative predictions of relevance to cellulose ordering and orientation in the plant cell wall are presented. The model describes nematic liquid crystalline self-assembly of rigid fibers on an arbitrarily curved fluid membrane. The mechanics of the fluid membrane is described by the Helfrich bending-torsion model, the fiber self-assembly is described by the 2D Landau-de Gennes quadrupolar Q-tensor order parameter model, and the fiber-membrane interactions (inspired by an extension of the 2D Maier-Saupe model to curved surfaces) include competing curvo-philic (curvature-seeking) and curvo-phobic (curvature-avoiding) effects. Analysis of the free energy reveals three fiber orientation regimes: (a) along the major curvature, (b) along the minor curvature, (c) away from the principal curvatures, according to the competing curvo-philic and curvo-phobic interactions. The derived shape equation (normal stress balance) now includes curvature-nematic ordering contributions, with both bending and torsion renormalizations. Integration of the shape and nematic order equations gives a complete model whose solution describes the coupled membrane shape/fiber order state. Applications to cylindrical membranes, relevant to the plant cell wall, shows how growth decreases the fiber order parameter and moves the fibers’ director from the axial direction towards the azimuthal orientation, eventually leading to a state of stress predicted by pure membranes. The ubiquitous 54.7° cellulose fibril orientation with respect to the long axis in a cylindrical plant cell wall is shown to be predicted by the preset model when the ratio of curvo-phobic and curvo-philic interactions is in the range of the cylinder radius.