On the Markov-modulated insurance risk model with tax

In this paper, we consider the Markov-modulated insurance risk model with tax. We assume that the claim inter-arrivals, claim sizes and premium process are influenced by an external Markovian environment process. The considered tax rule, which is the same as the one considered by Albrecher and Hipp [Blätter DGVFM 28(1):13–28, 2007], is to pay a certain proportion of the premium income, whenever the insurer is in a profitable situation. A system of differential equations of the non-ruin probabilities, given the initial environment state, are established in terms of the ruin probabilities under the Markov-modulated insurance risk model without tax. Furthermore, given the initial state, the differential equations satisfied by the expected accumulated discounted tax until ruin are also derived. We also give the analytical expressions for them by iteration methods.     

A way to construct independence equivalent graphs

Let us denote the independence polynomial of a graph by $I_G\left(x\right)$. If $I_G\left(x\right)=I_H\left(x\right)$ implies that $G?H$ then we say $G$ is independence unique. For graph $G$ and $H$ if $I_G\left(x\right)=I_H\left(x\right)$ but $G$ and $H$ are not isomorphic, then we say $G$ and $H$ are independence equivalent. In [7], Brown and Hoshino gave a way to construct independent equivalent graphs for circulant graphs. In this work we give a way to construct the independence equivalent graphs for general simple graphs and obtain some properties of the independence polynomial of paths and cycles.     

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically.When initial density is piecewise regular with jump discontinuity,we show that there exists a unique global piecewise regular solution.In particular,the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t → +∞.     

Global regularity of the 4D restricted Euler equations

We are concerned with the critical threshold phenomena in the restricted Euler (RE) equations. Using the spectral and trace dynamics we identify the critical thresholds for the 3D and 4D restricted Euler equations. It is well known that the 3D RE solutions blow up. Projected on the 3-sphere, the set of initial eigenvalues which give rise to bounded stable solutions is reduced to a single point, which confirms that the 3D RE blowup is generic. In contrast, we identify a surprisingly rich set of the initial spectrum on the 4-sphere which yields global smooth solutions; thus, 4D regularity is generic.     

Copper corroles: the question of noninnocence

In this paper, the results are presented from a comparative study of the electronic and geometric structure of copper corroles by means of either density functional theory (DFT, using both pure and hybrid functionals) and multiconfigurational ab initio methods, starting from either a complete active space (CASSCF) or restricted active space (RASSCF) reference wave function and including dynamic correlation by means of second-order perturbation theory (CASPT2/RASPT2). DFT geometry optimizations were performed for the lowest singlet and triplet states of copper corrole, both unsubstituted and meso-substituted with three phenyl groups. The effect of saddling on the electronic structure was investigated by comparing the results obtained for planar (C(2v)) and saddled (C(2)) structures. With DFT, the origin of the saddling distortion is found to be dependent on the applied functional: covalent Cu 3d-corrole π interactions with pure functionals (BP86, OLYP), antiferromagnetic exchange coupling between an electron in the corrolate (C(2)) b type π orbital, and an unpaired Cu(II) 3d electron with hybrid functionals (B3LYP, PBE0). The CASPT2 results essentially confirm the suggestion from the hybrid functionals that copper corroles are noninnocent, although the contribution of diradical character to the copper-corrole bond is found to be limited to 50% or less. The lowest triplet state is calculated at 0-10 kcal/mol and conform with the experimental observation (variable temperature NMR) that this state should be thermally accessible.     

Extraction of paeonol from Jisheng Shenqi Wan using supercritical fluid extraction

Supercritical carbon dioxide with or without methanol and 95% ethanol modifiers was used to extract paeonol from the pills of Jisheng Shenqi Wan and high-performance liquid chromatography (HPLC) was used to analyze the extract. The effect of temperature and pressure on the yield of paeonol was tested. The results show that the recovery of paeonol was improved by adding a polar modifier, such as methanol and 95% ethanol in supercritical fluid. The yield obtained after 120 min extraction with 95% ethanol modified-supercritical carbon dioxide was the highest (1.51, w/w at 60 degrees C and 400 bar), while that obtained with supercritical carbon dioxide only at 40 degrees C was the lowest from 0.67 to 0.83 over a range of 200-600 bar.     

Direct electrochemistry and electrocatalysis of myoglobin using an ionic liquid-modified carbon paste electrode coated with Co3O4 nanorods and gold nanoparticles

A nanohybrid biomaterial was fabricated by mixing Co₃O₄ nanorods, gold nanoparticles (Au-NPs) and myoglobin (Mb), and depositing it on the surface of a carbon paste electrode containing the ionic liquid N-hexylpyridinium hexafluorophosphate as the binder. UV–vis and FT-IR revealed the Mb in the composite film to have remained in its native structure. A pair of well-defined redox peaks appears in cyclic voltammograms and indicates direct electron transfer from the Mb to the underlying electrode. The results are attributed to the favorable orientation of Mb in the composite film, to the synergistic effects of Co₃O₄ nanorods and Au-NPs. The modified electrode shows excellent electrocatalytic ability towards the reduction of substrates such as trichloroacetic acid and nitrite, and displays good stability and reproducibility.

An invariant‐region‐preserving limiter for DG schemes to isentropic Euler equations

In this article, we introduce an invariant‐region‐preserving (IRP) limiter for the p‐system and the corresponding viscous p‐system, both of which share the same invariant region. Rigorous analysis is presented to show that for smooth solutions the order of approximation accuracy is not destroyed by the IRP limiter, provided the cell average stays away from the boundary of invariant region. Moreover, this limiter is explicit, and easy for computer implementation. A generic algorithm incorporating the IRP limiter is presented for high order finite volume type schemes as long as the evolved cell average of the underlying scheme stays strictly within the invariant region. For high order discontinuous Galerkin (DG) schemes to the p‐system, sufficient conditions are obtained for cell averages to stay in the invariant region. For the viscous p‐system, we design both second and third order IRP DG schemes. Numerical experiments are provided to test the proven properties of the IRP limiter and the performance of IRP DG schemes.