Characterizations of Lipschitz-type,Bloch-type and Dirichlet-type spaces

Monatshefte für Mathematik - In this paper, we will give new characterizations of Lipschitz-type spaces, and establish related growth theorems for Bloch-type spaces. Then we will present...     

On global and local mesh refinements by a generalized conforming bisection algorithm

We examine a generalized conforming bisection (GCB-)algorithm which allows both global and local nested refinements of the triangulations without generating hanging nodes. It is based on the notion of a mesh density function which prescribes where and how much to refine the mesh. Some regularity properties of generated sequences of refined triangulations are proved. Several numerical tests demonstrate the efficiency of the proposed bisection algorithm. It is also shown how to modify the GCB-algorithm in order to generate anisotropic meshes with high aspect ratios.     

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.