An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities

A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281–296, 1998     

Thermal analysis characterization of isosorbide-containing thermosets

Sugar-based new monomers, polymers, and low molar mass additives have emerged as an exciting topic on green chemistry research, due to the worldwide focus on sustainable material. Isosorbide and its isomers, as ??Generally Recognized as Safe?? GRAS materials, possess unique stereochemistry and molecular geometry suitable for making cost-effective chemicals and polymers. With growing awareness of bisphenol A (BPA) as a xenoestrogen, isosorbide and its isomers holding the remarkable chemical properties and attractive price can be attached to glycidyl ether to make crosslinkable epoxy resin monomers with similar properties to BPA diglycidyl ether. By adding the hydrophobic functional group into the backbone of isosorbide epoxy or adjusting the amount and type of crosslinker, the mechanical properties and the water uptake ratios (from <1 to >50?wt%) of the isosorbide-derived epoxies could be optimized for different applications. The high water uptake epoxy with controllable biodegradation rate could be used as a drug delivery system or extracellular matrix for biomedical applications while the low water uptake epoxy with strong mechanical properties could be used for can coatings, bone cements, and other industrial additives and adhesives. The chemical structures and properties of the synthesized epoxy monomers and polymers were characterized by DSC, TG, and ¹H NMR.     

Low melting point agarose as a protection layer in photolithographic patterning of aligned binary proteins

A novel photolithography method to build aligned patterns of two different proteins is presented. Chessboard patterns of 125 microm x 125 microm squares are constructed on a silicon dioxide substrate, using standard photoresist chemistries in combination with low-temperature oxygen plasma etching. Low-melting-point agarose (LMPA) is used to protect underlying protein layers and, at the appropriate stage, the digestive enzyme GELase (EPICENTRE) is used to selectively remove the prophylactic LMPA layers. Two antibodies, mouse-IgG and human-IgG, were immobilized and patterned by this procedure. The patterned antibodies maintained the specificity of their antigen-antibody binding, as demonstrated by fluorescence microscopy. In addition, normalized fluorescence intensity profiles illustrate that the patterned proteins layers are uniform (standard deviations below 0.05). Finally, a trypsin activity test was conducted to probe the effect of the patterning protocol on immobilized enzymes; the results imply that this photolithographic process using LMPA as a protection layer preserves 70% of immobilized enzyme activity.     

Edge singularities and structure of the 3-D Williams expansion

The elastic solution in a vicinity of a re-entrant wedge can be described by a Williams like expansion in terms of powers of the distance to a point on the edge. This expansion has a particular structure due to the invariance of the problem by translation parallel to the edge. We show here that some terms, so-called primary solutions, derive directly from solutions to the 2-D corner problem posed in the orthogonal cross section of the domain. The others, baptized shadow functions, derive of the primary solutions by integration along the axis parallel to the edge. This 3-D Williams expansion is shown to be equivalent to the edge expansion proposed by Costabel et al. [M. Costabel, M. Dauge, Z. Yosibash, A quasidual function method for extracting edge stress intensity functions, SIAM J. Math. Anal. 35 (5) (2004) 1177–1202]. To cite this article: T. Apel et al., C. R. Mecanique 336 (2008).     

Functional polymers. XVI. Synthesis and polymerization of 2(2-hydroxy-5-isopropenylphenyl)-2H-benzotriazole and a new synthesis of 2(2-hydroxy-5-vinylphenyl)2H-benzotriazole

2(2-Hydroxy-5-isopropenylphenyl)2H-benzotriazole was synthesized in 40% overall yield starting from o-nitroaniline. Diazotization in aqueous hydrochloric acid gave o-nitrophenyl diazonium chloride which was condensed with p-hydroxyacetophenone; the azo compound was reduced to 2(2-hydroxy-5-acetylphenyl) 2H-benzotriazole with zinc powder in sodium hydroxide solution and the 2-hydroxy group of the compound was acetylated. Treatment of the acetyl compound with methyl Grignard reagent resulted in the methylation of the 5-acetyl group to 2[2-acetoxy-5(2-hydroxy-2-propyl)phenyl]2H-benzotriazole which was then dehydrated with potassium hydrogen sulfate to the desired 2(2-hydroxy-5-isopropenylphenyl)2H-benzotriazole. This monomer did not homopolymerize, but was copolymerized readily with styrene, methyl methacrylate, and n-butyl acrylate with azobisisobutyronitrile as the initiator. 2(2-Acetoxy-5-acetylphenyl)2H-benzotriazole was also reduced with sodium borohydride to form 2[2-acetoxy-5-(1-hydroxyethyl)phenyl]2H-benzotriazole which was dehydrated and hydrolyzed to the known 2(2-hydroxy-5-vinylphenyl)-2H-benzotriazole. This route provides a novel and simpler synthesis of 2(2-hydroxy-5-vinylphenyl)2H-benzotriazole.     

Triply Existentially Complete Triangle‐Free Graphs

A triangle‐free graph G is called k‐existentially complete if for every induced k‐vertex subgraph H of G, every extension of H to a ‐vertex triangle‐free graph can be realized by adding another vertex of G to H. Cherlin  11 , 12 asked whether k‐existentially complete triangle‐free graphs exist for every k. Here, we present known and new constructions of 3‐existentially complete triangle‐free graphs.     

Sequent Systems for Negative Modalities

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics.     

The writhe of permutations and random framed knots

We introduce and study the writhe of a permutation, a circular variant of the well‐known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non‐Gaussian limit distribution. This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model, studied with Hass, Linial, and Nowik (Discrete Comput Geom, 2016). The distribution of the framing in this model is equivalent to the writhe of random permutations. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 121–142, 2017