Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

Diffusion of non-volatile phenolic compounds in zeolite beta and silicalite in liquid phase

The present study aims to systematically investigate the adsorption kinetics of “non-volatile” phenolic compounds with different critical diameters (p-coumaric acid, ferulic acid, sinapinic acid, p-hydroxybenzoic acid, vanillic acid, syringic acid, and vanillin) onto zeolite beta and silicalite in several solvents. In the aqueous phase, the corrected diffusivity of non-volatile phenolic compounds is 2–5 orders of magnitude smaller than that of volatile aromatic compounds with the same critical diameter. On the other hand, the corrected diffusivity in zeolite beta is on the same order of magnitude among non-volatile phenolic compounds, despite the significant difference in critical diameter of the adsorbate. This suggests that the intracrystalline diffusivity of the non-volatile adsorbate is strongly affected by its original molecular immobility, rather than by the size (narrowness) of the adsorbate and micropore aperture. Non-volatility is considered to remarkably lower the molecular mobility of adsorbate on the surface of zeolite, even in the liquid phase. In addition, the intracrystalline diffusivity of non-volatile adsorbate is strongly affected by the type of solvent, and a close correlation was found between intracrystalline diffusivity and adsorption affinity. Revelations as to the kinetic behavior of non-volatile adsorbate in zeolite are expected to supply more information on the kinetic separation of compounds in the liquid phase. The significant difference in diffusivity among non-volatile and volatile adsorbates in zeolite leads to the possibility of kinetic separation among these adsorbates.     

DNA Origami Scaffolds as Templates for Functional Tetrameric Kir3 K+ Channels

In native systems, scaffolding proteins play important roles in assembling proteins into complexes to transduce signals. This concept is yet to be applied to the assembly of functional transmembrane protein complexes in artificial systems. To address this issue, DNA origami has the potential to serve as scaffolds that arrange proteins at specific positions in complexes. Herein, we report that Kir3 K⁺ channel proteins are assembled through zinc‐finger protein (ZFP)‐adaptors at specific locations on DNA origami scaffolds. Specific binding of the ZFP‐fused Kir3 channels and ZFP‐based adaptors on DNA origami were confirmed by atomic force microscopy and gel electrophoresis. Furthermore, the DNA origami with ZFP binding sites nearly tripled the K⁺ channel current activity elicited by heterotetrameric Kir3 channels in HEK293T cells. Thus, our method provides a useful template to control the oligomerization states of membrane protein complexes in vitro and in living cells.     

Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada–Watanabe theorem (Yamada and Watanabe, 1971, [31,32]) and the Feller test for explosions (Feller, 1951, 1954), there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $\mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called free energy function on the density function space, we prove that the density functions, which are solutions of the Fokker–Planck equation, converge to the stationary density function exponentially under the Kullback–Leibler divergence, thus also in the total variation norm. The results show that there is a relation between the Bakry–Émery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher–Lamperti transformation. Several applications are discussed, including the Cox–Ingersoll–Ross model and the Ait-Sahalia model in finance and the Wright–Fisher model in population genetics.     

Effect of carbon nanotubes on the crystallization and properties of polypropylene

The effect of different concentrations of single‐walled carbon nanotubes (SWNTs) on the nonisothermal crystallization kinetics, morphology, and mechanical properties of polypropylene (PP) matrix composites obtained by melt compounding was investigated by means of X‐ray diffraction, differential scanning calorimetry, optical and scanning electron microscopy, and dynamic mechanical thermal analysis. Microscopy showed well‐dispersed nanotube ropes together with small and large aggregates. The modulus was found to increase by about 75% at a level of 0.5 wt % nanotubes. The SWNTs displayed a clear nucleating effect on the PP crystallization, favoring the α crystalline form rather than the β form. The crystallization kinetics analysis showed a significant increase in activation energy on incorporating nanotubes. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2445–2453, 2005     

Electrodeposited Amorphous Tungsten‐doped Cobalt Oxide as an Efficient Catalyst for the Oxygen Evolution Reaction

Thin film of amorphous tungsten‐doped cobalt oxide (W:CoO) was successfully grown on a conducting electrode via an electrochemical oxidation process employing a [Co(WS₄)₂]^2? deposition bath. The W:CoO catalyst displays an attractive performance for the oxygen evolution reaction in an alkaline solution. In an NaOH solution of pH 13, W:CoO operates with a moderate onset overpotential of 230 mV and requires 320 mV overpotential to generate a catalytic current density of 10 mA cm^?2. A low Tafel slope of 45 mV decade^?1 was determined, indicating a rapid O₂‐evolving kinetics. The as‐prepared W:CoO belongs to the best cobalt oxide‐based catalysts ever reported for the oxygen evolution (OER) reaction.     

A genetic design of linguistic terms for fuzzy rule based classifiers

The determination of fuzzy information granules including the estimation of their membership functions play a significant role in fuzzy system design as well as in the design of fuzzy rule based classifiers (FRBCSs). However, although linguistic terms are fundamental elements in the process of elucidating expert’s knowledge, the problem of linguistic term design along with their fuzzy-set-based semantics has not been fully addressed, since term-sets of attributes have not been interpreted as a formalized structure. Thus, the essential relationship between linguistic terms, as syntax, and the constructed fuzzy sets, as their quantitative semantics, or in other words, the problem of the natural semantics of terms behind the linguistic literal has not been addressed. In this paper, we introduce the problem of the design of optimal linguistic terms and propose a method of the design of FRBCSs which may incorporate with the design of linguistic terms to ensure that the presence of linguistic literals are supported not only by data but also by their natural semantics. It is shown that this problem plays a primordial role in enhancing the performance and the interpretability of the designed FRBCSs and helps striking a better balance between the generality and the specificity of the desired fuzzy rule bases for fuzzy classification problems. A series of experiments concerning 17 Machine Learning datasets is reported.     

Extraction and isolation of catechins from tea

Tea is a major source of catechins, which have become well known for their antioxidant potential. Numerous human, animal, and in vitro studies have linked tea catechins with prevention of certain types of cancers, reduction of the risks for obesity, diabetes, and cardiovascular disease, and improvement of the immune system. Tea catechins are widely used in various neutraceuticals, pharmaceuticals, and cosmetics for either enhancing product shelf-life or for enhancing human health. Thus, the demand for catechins has increased considerably. Catechins have been extracted and isolated from tea leaves by numerous methods through several steps including: treatment of the tea leaves, extraction of catechins from teas into solvents, isolation of catechins from other extracted components, and drying the preparations to obtain catechin extracts in a powder form. This paper outlines the physical and chemical properties of the tea catechins and reviews the extraction steps of the various extraction methods, as a basis to improve and further develop the extraction and isolation of the tea catechins.     

Interaction of diatomic germanium with lithium atoms: electronic structure and stability

Quantum chemical calculations were applied to investigate the electronic structure of mono-, di-, and trilithiated digermanium (Ge2Lin) and their cations (n=0-3). Computations using a multiconfigurational quasidegenerate perturbation approach based on complete active space self-consistent-field wave functions, and density functional theory reveal that Ge2Li has a 2B1 ground state with a doublet-quartet energy gap of 33 kcal/mol. Ge2Li2 has a singlet ground state with a 3Au-1A1 gap of 29 kcal/mol, and Ge2Li3 a doublet ground state with a 4B2-2A2 separation of 22 kcal/mol. The cation Ge2Li+ has a 3B1 ground state, being 13 kcal/mol below the open-shell 1B1 state. The computed electron affinities for diatomic germanium are EA(1)=1.9 eV, EA(2)=-2.5 eV, and EA(3)=-6.0 eV, for Ge2-, Ge2 (2-), and Ge2 (3-), respectively, indicating that only the monoanion is stable with respect to electron detachment, in such a way that Ge2Li is composed by Ge2-Li+ ions. An "atoms-in-molecules" analysis shows the absence of a ring critical point in Ge(2)Li. An electron localization function analysis on Ge2Li supports the view that the Ge-Li bond is predominantly ionic; however, a small covalent character could be anticipated from the analysis of the Laplacian at the Ge-Li bond critical point. The ionic picture of the Ge-Li bond is further supported by a natural-bond-order analysis and the Laplacian of the electron density. The calculated Li affinity value for Ge2 is 2.08 eV, while the Li+ cation affinity value for Ge2- is 5.7 eV. The larger Li+ cation affinity value of Ge2- suggests a Ge2-Li+ interaction and thus supports the ionic nature of Ge-Li bond. In GeLi4 and Ge2Li, the presence of trisynaptic basins indicates a three-center bond connecting the germanium and lithium atoms.