Dahlberg's theorem in higher co-dimension

In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension $n?1$ in ${\mathbb{R}}^n$, and later this result has been extended to more general non-tangentially accessible domains and beyond.In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph Γ of dimension d in ${\mathbb{R}}^n$, $d<n?1$, with a small Lipschitz constant. We construct a linear degenerate elliptic operator L such that the corresponding harmonic measure ${\omega }_L$ is absolutely continuous with respect to the Hausdorff measure on Γ. More generally, we provide sufficient conditions on the matrix of coefficients of L which guarantee the mutual absolute continuity of ${\omega }_L$ and the Hausdorff measure.     

The influence of radiation-induced vacancy on the formation of thin-film of compound layer during a reactive diffusion process

A theoretical approach is developed that describes the formation of a thin-film of AB-compound layer under the influence of radiation-induced vacancy. The AB-compound layer is formed as a result of a chemical reaction between the atomic species of A and B immiscible layers. The two layers are irradiated with a beam of energetic particles and this process leads to several vacant lattice sites creation in both layers due to the displacement of lattice atoms by irradiating particles. A- and B-atoms diffuse via these lattice sites by means of a vacancy mechanism in considerable amount to reaction interfaces A/AB and AB/B. The reaction interfaces increase in thickness as a result of chemical transformation between the diffusing species and surface atoms (near both layers). The compound layer formation occurs in two stages. The first stage begins as an interfacial reaction controlled process, and the second as a diffusion controlled process. The critical thickness and time are determined at a transition point between the two stages. The influence of radiation-induced vacancy on layer thickness, speed of growth, and reaction rate is investigated under irradiation within the framework of the model presented here. The result obtained shows that the layer thickness, speed of growth, and reaction rate increase strongly as the defect generation rate rises in the irradiated layers. It also shows the feasibility of producing a compound layer (especially in near-noble metal silicide considered in this study) at a temperature below their normal formation temperature under the influence of radiation.     

The Calculus of Moving Surfaces and Laplace Eigenvalues on an Ellipse with Low Eccentricity

Our goal is to demonstrate the utility of the calculus of moving surfaces (CMS) in boundary variation problems. We discuss the relative advantages of the CMS compared to the alternative approach of interior variations. We illustrate the technique by calculating the two leading terms of a power series for the Laplace eigenvalues on an ellipse with semi-axes 1 + a and 1 + b, where a and b are small. We compare the CMS estimates with those obtained by the conventional finite element method with Richardson extrapolation. The comparison confirms the cubic rate of convergence for the CMS estimates.     

Improving breakdown strength and energy storage efficiency of poly(vinylidene fluoride-co-chlorotrifluoroethylene) and polyurea blend films by double layer structure design

All-organic composites are widely used in energy storage application due to the high breakdown strength performance, but the improvement of energy storage was limited by the relatively low dielectric constant. Therefore, to satisfy the high demands of dielectric materials, energy storage properties of polymer composites should be further enhanced. In this article, poly(vinylidene fluoride-co-chlorotrifluoroethylene) (P(VDF-CTFE)) and polyurea (PUA), which are known as high dielectric ferroelectric material and linearly high energy storage efficiency material respectively, are composited through double layer (DL) casting method for the first time. The properties of DL structured composite film is contrasted with solution blending structure especially in energy storage efficiency, and the results demonstrate that DL structure design can make great use of advantages of two materials and also can avoid the influence of phase separation between P(VDF-CTFE) and PUA efficiently. Moreover, high breakdown strength (6180 kV/cm) and high energy storage efficiency (77%) of DL composites can be realized simultaneously by incorporating PUA as an insulating layer, and the mechanism is discussed in detail. This work provides an effective route to improve the energy storage properties of polymer dielectric materials and shows great application potential.     

A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in , the former being bounded, and the latter, its complement in . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L²‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.     

Densitometry and indirect normal‐phase HPTLC–ESI–MS for separation and quantitation of drugs and their glucuronide metabolites from plasma

The present work describes novel methods using densitometry and indirect or off‐line high performance thin‐layer chromatography–mass spectrometry (HPTLC–MS) for the simultaneous detection and quantification of asenapine, propranolol and telmisartan and their phase II glucuronide metabolites. After chromatographic separation of the drugs and their metabolites the analytes were scraped, extracted in methanol and concentrated prior to mass spectrometric analysis. Different combinations of toluene and methanol–ethanol–n‐butanol–iso‐propanol were tested for analyte separation and the best results were obtained using toluene–methanol–ammonia (6.9:3.0:0.1, v/v/v) as the elution solvent. All of the drug–metabolite pairs were separated with a homologous retardation factor difference of ≥22. The conventional densitometric approach was also studied and the method performances were compared. Both of the approaches were validated following the International Conference on Harmonization guidelines, and applied to spiked human plasma samples. The major advantage of the TLC–MS approach is that it can provide much lower limits of detection (1.98–5.83 pg/band) and limit of quantitation (5.97–17.63 pg/band) with good precision (?3.0% coefficient of variation) compared with TLC–densitometry. The proposed indirect HPTLC–MS method is simple yet effective and has tremendous potential in the separation and quantitation of drugs and their metabolites from biological samples, especially for clinical studies.     

Wound Healing Attributes of Polyelectrolyte Multilayers Prepared with Multi‐l‐arginyl‐poly‐l‐aspartate Pairing with Hyaluronic Acid and γ‐Polyglutamic Acid

Biodegradable multi‐l ‐arginyl‐poly‐l ‐aspartate (MAPA), more commonly cyanophycin, prepared with recombinant Escherichia coli contains a polyaspartate backbone with lysine and arginine as side chains. Two assemblies of polyelectrolyte multilayers (PEMs) are fabricated at three different concentration ratios of insoluble MAPA (iMAPA) with hyaluronic acid (iMAPA/HA) and with γ‐polyglutamic acid (iMAPA/γ‐PGA), respectively, utilizing a layer‐by‐layer approach. Both films with iMAPA and its counterpart, HA or γ‐PGA, as the terminal layer are prepared to assess the effect on film roughness, cell growth, and cell migration. iMAPA incorporation is higher for a higher concentration of the anionic polymer due to better charge interaction. The iMAPA/HA films when compared to iMAPA/γ‐PGA multilayers show least roughness. The growth rates of L929 fibroblast cells on the PEMs are similar to those on glass substrate, with no supplementary effect of the terminal layer. However, the migration rates of L929 cells increase for all PEMs. γ‐PGA incorporated films impart 50% enhancement to the cell migration after 12 h of culture as compared to the untreated glass, and the smooth films containing HA display a maximum 82% improvement. The results present the use of iMAPA to construct a new layer‐by‐layer system of polyelectrolyte biopolymers with a potential application in wound dressing.     

Nitrogen Doping and Carbon Coating Affects Substrate Selectivity of TiO2 Photocatalytic Organic Pollutant Degradation

A series of carbon-coated, nitrogen-doped titanium dioxide photocatalysts was produced and characterized. N-doped TiO₂ powder samples were prepared using a sol-gel method and subsequently used for making doped-TiO₂ thin films on glass substrates. Carbon layers were coated on the films by a thermal decomposition method using catechol. Diffuse reflectance spectra and Mott-Schottky analyses of the samples proved that nitrogen doping and carbon coating can slightly lower the band gap of TiO₂, broaden its absorption to visible light and enhance its n-type character. According to photocatalytic tests against model contaminants, carbon-coated nitrogen-doped TiO₂ films have better performance than simple TiO₂ on the degradation of Rhodamine B dye molecules, but are poorly effective for degrading 4-chlorophenol molecules. Several possible explanations are proposed for this result, supported by scavenging experiments. This reveals the importance of a broad substrate scope when assessing new photocatalytic materials for water treatment, something which is often overlooked in many literature studies.