On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains

The purpose of this paper is to extend some results of the potential theory of an elliptic operator to the fractional Laplacian (−Δ)^α/2, 0<α<2, in a bounded C^1,1 domain D in Rⁿ. In particular, we introduce a new Kato class K_α(D) and we exploit the properties of this class to study the existence of positive solutions of some Dirichlet problems for the fractional Laplacian.     

Reduced Graphene Oxide|Carbon Ceramic Electrode Modified with CdS‐Hemoglobin as a Sensitive Hydrogen Peroxide Biosensor

A sensitive hydrogen peroxide (H₂O₂) biosensor was developed based on a reduced graphene oxide|carbon ceramic electrode (RGO|CCE) modified with cadmium sulfide‐hemoglobin (CdS‐Hb). The electron transfer kinetics of Hb were promoted due to the synergetic function of RGO and CdS nanoparticles. The transfer coefficient (α) and the heterogeneous electron transfer rate constant (k_s) were calculated to be 0.54 and 2.6 s^?1, respectively, indicating a great facilitation achieved in the electron transfer between Hb and the electrode surface. The biosensor showed a good linear response to the reduction of H₂O₂ over the concentration range of 2–240 µM with a detection limit of 0.24 µM (S/N=3) and a sensitivity of 1.056 µA µM^?1 cm^?2. The high surface coverage of the CdS‐Hb modified RGO|CCE (1.04×10^?8 mol cm^?2) and a smaller value of the apparent Michaelis? Menten constant (0.24 mM) confirmed excellent loading of Hb and high affinity of the biosensor for hydrogen peroxide.     

Parameter estimation of a bivariate compound Poisson process

In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likelihood approach. This approach ensures that the estimated model remains in the class of multivariate compound Poisson processes. A simulation study investigates the small sample behaviour of the MLEs, where we also suggest a new simulation algorithm. Finally, we apply our method to Danish fire insurance data.     

Comparative evaluation on the thermal properties and stability of MWCNT nanofluid with conventional surfactants and ionic liquid

Journal of Thermal Analysis and Calorimetry - Conventional surfactants such as CTAB (cetrimonium bromide), SDS (sodium dodecyl sulphate), SDBS (sodium dodecyl sulphonate) are combined with...     

The Hydrothermal Synthesis of Petalite Mineral Phases and their Morphological Changing by Increasing of Temperature

In this investigation the Petalite minerals were synthesized hydrothermally at different temperatures from a glass with the composition Li₂CO₃:Al₂O₃: SiO₂ and the relation 1: 1: 8. On that occasion the following mineral phases arised:

• at low temperatures (410°C) α-petalite (unit cell å = 11.737 Å/b̊ = 5.17 Å/c̊ = 7.63 Å, space group P₂/a);
• At 490 °C α-petalite was splitted to quartz and an orthorhombic β₁-petalite (unit cell å = 18.24 Å/c̊ = 10.54 Å/c̊ = 10.57 Å, space group P_mC_n). β₁-petalite could be observated until 1000 °C.
• at 560 °C tetragonal β₂-petalite (unit cell å = 7.50 Å/c̊ = 9.07 Å, space group P 4₃2₁2) in parallel with β₁-petalite;
• Behind 750 °C β₂-petalite was not observed.
• Behind 900 °C a pseudohexagonal mineral phase developed from β₁-petalite. May be it is possible to indicate this phase as hexagonal (unit cell å = 5.217 Å/c̊ = 5.464 Å, space group P 6₂22 or P 6₄22). The author suggests to denote this phase as β₃-petalite.

     

The Hydrothermal Effect on Crystal Development and Electrical Conductivity of Li2CO3

Lithiumcarbonat was treated hydrothermally in the range of temperature from 80 °C to 600 °C. The Li₂CO₃-crystals of the starting material were monoclinic with the unit cell a = 8.39 Å, b = 5.00 Å, c = 6.21 Å, β = 114.5° and the space group C2/c (Zemann). During the increase of temperature the habit of the Li₂CO₃-crystals changed in the ranges of higher temperatures that they could be described as pseudocubic. In parallel with this development the electrical conductivity of the crystals also changed.     

The Morphology of Some Hydrothermally Synthesized Li-Minerals: A-Zeolite, α-Eucryptite, β-Spodumene and β-Eucryptite

The hydrothermal treatment of glass with the composition 2 LiF, Al₂O₃, 3 SiO₂ at 1 kbar in the range of 150 °C to 850 °C gave rise to the formation of A-zeolite with orthorhombic unit cell with å = 10.31 Å/b̊ = 8.18 Å/c̊ = 5.0 Å (space group Pna2₁), α-eucryptite, trigonal, å = 13.4 Å/bº = 13.4/Å/cº = 9.0 Å (space group R 3 ), β-spodumene, pseudocubic/tetragonal, å = 7.53 Å/b̊ = 7.53 Å/c̊ = 9.15 Å (space group P4₃2₁2), β-eucryptite, monoclinic, å = 7.75 Å/b̊ = 5.2 Å/c̊ = 11.16 Å (space group P6₂22). The morphology and development of the mineral phases depend on the temperature of formation.