On Lipschitz continuity of solutions of hyperbolic Poisson’s equation

In this paper, we investigate solutions of the hyperbolic Poisson equation \(\Delta _{h}u(x)=\psi (x)\), where \(\psi \in L^{\infty }(\mathbb {B}^{n}, {\mathbb R}^n)\) and

$$\begin{aligned} \Delta _{h}u(x)= (1-|x|^2)^2\Delta u(x)+2(n-2)\left( 1-|x|^2\right) \sum _{i=1}^{n} x_{i} \frac{\partial u}{\partial x_{i}}(x) \end{aligned}$$

is the hyperbolic Laplace operator in the n-dimensional space \(\mathbb {R}^n\) for \(n\ge 2\). We show that if \(n\ge 3\) and \(u\in C^{2}(\mathbb {B}^{n},{\mathbb R}^n) \cap C(\overline{\mathbb {B}^{n}},{\mathbb R}^n )\) is a solution to the hyperbolic Poisson equation, then it has the representation \(u=P_{h}[\phi ]-G_{ h}[\psi ]\) provided that \(u\mid _{\mathbb {S}^{n-1}}=\phi \) and \(\int _{\mathbb {B}^{n}}(1-|x|^{2})^{n-1} |\psi (x)|\,d\tau (x)<\infty \). Here \(P_{h}\) and \(G_{h}\) denote Poisson and Green integrals with respect to \(\Delta _{h}\), respectively. Furthermore, we prove that functions of the form \(u=P_{h}[\phi ]-G_{h}[\psi ]\) are Lipschitz continuous.

     

Preparation of indole-phosphine oxazoline (IndPHOX) ligands and their application in allylic alkylation

Two classes of indole-phosphine oxazoline ligands have been prepared from readily available starting materials in good overall yields. These modular ligands include an indole skeleton with either a phosphine moiety or an oxazoline ring at the 2- or 3-position, respectively. The utility of these ligands was demonstrated in a catalytic asymmetric reaction: the palladium-catalyzed allylic alkylation of 1,3-diphenyl-2-propenyl acetate with dimethyl malonate was performed with enantioselectivities as high as 98%.     

Effect of microfibrillated cellulose and fines on the drainage of kraft pulp suspension and paper strength

Different types of microfibrillated cellulose (MFC) and fines suspensions were produced, characterized, and then added to a papermaking pulp suspension. High and medium molar mass cationic polyelectrolytes were used as fixatives. The drainage behavior of the pulp suspensions with additives were evaluated against the strength properties of hand sheets made thereof. The effects of salt concentration, pH, fixative type, dosage and type of fibrillar material on drainage were examined. All the MFC and fines samples produced had clearly different properties due to their dissimilar production methods, and they also introduced specific responses on the measured drainage and paper strength. Generally, the addition of MFC decreased the drainage rate of pulp suspension and increased the strength of paper. However, it was shown that by optimum selection of materials and process conditions an enhancement of the strength properties could be achieved without simultaneously deteriorating the drainage.     

Poly(glyceryl glycerol): A multi‐functional hydrophilic polymer for labeling with boronic acids

The synthesis of poly(glyceryl glycerol) (PGG), a polymer featuring a polyethylene oxide backbone and 1,2‐diol groups in every repeating unit, is presented. PGG was prepared by monomer‐activated ring‐opening polymerization of (dl ?1,2‐isopropylidene glyceryl) glycidyl ether, introducing a functional azido‐ or bromo‐head group to each chain. The 1,2‐diol groups, which were released by acidic deprotection, readily reacted with boronic acid derivatives, enabling the attachment of functional moieties under mild aqueous conditions. PGG was conjugated to poly(l ‐lactide) (PLLA) via azide‐alkyne cycloaddition and the resulting copolymer assembled into nanoparticles of 70 nm diameter in aqueous solution. Labeling of the PGG–PLLA particles was achieved by simple mixing with a boronic acid‐functional fluorophore. The labeling efficiency was determined by fluorescence spectroscopy to be 85.5% for boronic acid‐functional rhodamine B compared with 0.2% for plain rhodamine B. The strong interaction of PGG with boronic acids is ascribed to its polyol structure. This study demonstrates the usefulness and versatility of PGG as a hydrophilic polymer for possible biomedical applications. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 1822–1830     

Comparing the quality and predictiveness between 3D QSAR models obtained from manual and automated alignment

A set of 113 flexible cyclic urea inhibitors of human immunodeficiency virus protease (HIV-1 PR) was used to compare the quality and predictive power of CoMFA and CoMSIA models for manually or automatically aligned inhibitor set. Inhibitors that were aligned automatically with molecular docking were in agreement with information obtained from existing X-ray structures. Both alignment methods produced statistically significant CoMFA and CoMSIA models, with the best q(2) value being 0.649 and the best predictive r(2) being 0.754. The manual alignment gave statistically higher values, whereas the automated alignment gave more robust models for predicting the activities of an external inhibitor set. Both models utilized similar amino acids in the HIV-1 PR active site, supporting the idea that hydrogen bonds form between an inhibitor and the backbone carbonyl oxygens of Gly48 and Gly48' and also the backbone NH group of Asp30, Gly48, Asp29', and Gly48' of the enzyme. These results suggest that an automated inhibitor alignment can yield predictive 3D QSAR models that are well comparable to manual methods. Thus, an automated alignment method in creating 3D QSAR models is encouragable when a well-characterized structure of the target protein is available.     

Using chemometrics for navigating in the large data sets of genomics, proteomics, and metabonomics (gpm)

This article describes the applicability of multivariate projection techniques, such as principal-component analysis (PCA) and partial least-squares (PLS) projections to latent structures, to the large-volume high-density data structures obtained within genomics, proteomics, and metabonomics. PCA and PLS, and their extensions, derive their usefulness from their ability to analyze data with many, noisy, collinear, and even incomplete variables in both X and Y. Three examples are used as illustrations: the first example is a genomics data set and involves modeling of microarray data of cell cycle-regulated genes in the microorganism Saccharomyces cerevisiae. The second example contains NMR-metabonomics data, measured on urine samples of male rats treated with either of the drugs chloroquine or amiodarone. The third and last data set describes sequence-function classification studies in a set of G-protein-coupled receptors using hierarchical PCA.     

Electron impact mass spectra of 2-(2-pyridyl)methylene-1,3-dicarbonyl compounds: Unusual abundance of the [M + 1]+ ion and the effect of stereochemistry

Electron impact mass spectra of 2-(2-pyridyl)methylene-1,3-dicarbonyl compounds and related heteroaryl species have been investigated. In 3-(2-pyridyl)methylene-2,4-pentanedione, its 6′-methyl and 6′-methoxycarbonyl derivatives and in E- and Z-ethyl 3-oxo-2-(2-pyridyl)methylenebutanoates the base peak arises from the loss of methyl radical from the molecular ion to produce a 3-oxo-3H-indolizinium ion. A marked difference is observed in the behaviour of the geometric isomers of the keto esters. The diketones and E-keto ester carrying a 2-pyridyl substituent and ketone functionality on the same side of the carbon-carbon double bond exhibit an unusually high [M + 1]⁺/[M]^+˙ ratio (about 2.5) under normal ionization conditions (pressure 10–100 μPa). This abnormality is a function of pressure only and independent of temperature. In the case of the Z-keto ester, the corresponding malonate, 3- and 4-(2-pyridyl)methylene-2,4-pentanediones, and 2-furyl, 2-thienyl and phenyl diketone analogues, the ratio does not differ much from that due to the natural isotope abundance. Results for 1,1,1,5,5,5-hexadeuterio-2-(2-pyridyl)-methylene-2,4-pentanedione (strong M + 2 peak) suggest one mass unit transfer as an intermolecular proton shift from a methyl group to give a 3-hydroxy-3-methyl-3H-indolizinium ion. This real mass spectrometric phenomenon is a unique example of low pressure self-chemical ionization.     

Conical upper density theorems and porosity of measures

We study how measures with finite lower density are distributed around (n−m)-planes in small balls in Rn. We also discuss relations between conical upper density theorems and porosity. Our results may be applied to a large collection of Hausdorff and packing type measures.     

Fast and accurate single-island charge pump: implementation of a cooper pair pump

We introduce a Cooper pair "sluice" for the implementation of a frequency-locked current source. The device consists of two mesoscopic SQUIDs and of a single superconducting island with a gate. We demonstrate theoretically that it is possible to obtain a current as high as 0.1 nA at better than ppm accuracy via periodically modulating both the gate charge and the effective Josephson coupling. We find that the device is tolerant against background charge noise and operates well even in a dissipative environment. The effect of the imperfect suppression of the Josephson coupling and the finite operating frequency are also investigated.     

Non-Gaussianity from preheating

We consider a two-field model for inflation where the second order metric perturbations can be amplified by a parametric resonance during preheating. We demonstrate that there can arise a considerable enhancement of non-Gaussianity sourced by the local terms generated through the coupled perturbations. We argue that the non-Gaussianity parameter could be as large as f(NL) approximately 50. Our results may provide a useful test of preheating in future cosmic microwave background experiments.