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A Markov observation model with dividend is defined and the interpretation of the practical significance is given. We try to use an irreducible and homogeneous discrete-time Markov chain to modulate the inter-observation times and embed a dividend strategy. In the Markov observation model with dividend, a system of liner equations for the expected discounted value of dividends until ruin time is derived. Moreover, an explicit expression is obtained and proved. Finally, some interesting properties are illustrated by numerical analysis and by comparing with the complete compound binomial model with dividend.     

Bloch Constant on α-Bloch Mappings of the Unit Ball

This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of Cn with critical points.Furthermore,the estimates of Bloch constant with respect to these subclasses are given.     

Cobalt ferrite for direct cracking of methane to produce hydrogen and carbon nanostructure: Effect of temperature and methane flow rate

Cobalt ferrite (CoFe₂O₄) was used as a catalyst for direct methane cracking. The reaction was accomplished in a fixed bed reactor at normal atmospheric pressure, while gas flow rate (20–50 mL/min) and reaction temperature (800–900 °C) were varied. The fresh CoFe₂O₄ morphology is sponge-like particle with inverse spinel structure as revealed from SEM and XRD results. The methane conversions and hydrogen formation rate were increased with reaction temperature, while catalyst stability and induction period decreased. Increases of gas flow rate > 20 mL/min led to a decrease the overall catalytic activity of CoFe₂O₄ for methane cracking. The XRD results of spent catalysts revealed that CoFe alloy was the active phase of methane cracking. TGA analysis showed that the largest amount of deposited carbon was 70.46 % at (20 mL/min, 900 °C), where it was 34.40 % at (50 mL/min, 800 °C). The deposited carbon has the shape of spherical carbon nanostructures and/or nano sprouts as observed with SEM. Raman data confirmed the graphitization type of the deposited carbon.     

A Theoretical Account of the Coupling between Metal- and Ligand-centred Spins

This study addresses the magnetic interaction between paramagnetic metal ions and the radical ligands taking the [Cu^II(hfac)₂(imVDZ)] and [M^II(hfac)₂(pyDTDA)] (imVDZ=1,5-dimethyl-3-(1-methyl-2-imidazolyl)-6-oxoverdazyl; hfac=(1,1,1,5,5,5)hexafluroacetylacetonate; pyDTDA=4-(2′-pyridyl)-1,2,3,5-dithiadiazolyl), (M=Cu, Ni, Co, Fe, Mn) compounds as reference systems. The coupling between the metal and ligand spins is quantified in terms of the exchange coupling constant (J) in the platform of density functional theory (DFT) and the wave function-based complete active space self-consistent field (CASSCF) method. Application of DFT and broken symmetry (BS) formalism results ferromagnetic coupling for all the transition metal complexes except the Mn(II) complex. This DFT-BS prediction of magnetic nature matches with the experimental finding for all the complexes other than the Fe(II)-pyDTDA complex, for which an antiferromagnetic coupling between high spin iron and the thiazyl ligand has been reported. However, evaluation of spin state energetics through the multiconfigurational wave function-based method produces the S=3/2 ground spin state for the iron-thiazyl in parity with experiment. Electronic structure analyses find the overlap between the metal- and ligand-based singly occupied molecular orbitals (SOMOs) to be one of the major reasons attributing to different extent of exchange coupling in the systems under investigation.     

Sensitivity enhancement of capillary electrophoresis-frontal analysis-based method for characterization of drug-protein interactions using on-line sample preconcentration

Capillary electrophoresis-frontal analysis is one of the most frequently used approaches for the study of plasma protein-drug interactions as a substantial part of new drug development. However, the capillary electrophoresis-frontal analysis typically combined with ultraviolet-visible detection suffers from insufficient concentration sensitivity, particularly for substances with limited solubility and low molar absorption coefficient. The sensitivity problem has been solved in this work by its combination with an on-line sample preconcentration. According to the knowledge of the authors this combination has never been used to characterize plasma protein-drug binding. It resulted in a fully automated and versatile methodology for the characterization of binding interactions. Further, the validated method minimalizes the experimental errors due to a reduction in the manipulation of samples. Moreover, employing an on-line preconcentration strategy with capillary electrophoresis-frontal analysis using human serum albumin-salicylic acid as a model system improves the drug concentration sensitivity 17-fold compared to the conventional method. The value of binding constant (1.51 ± 0.63) · 10⁴ L/mol obtained by this new capillary electrophoresis-frontal analysis modification is in agreement with the value (1.13 ± 0.28) ·10⁴ L/mol estimated by a conventional variant of capillary electrophoresis-frontal analysis without the preconcentration step, as well as with literature data obtained using different techniques.     

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.     

Calculation of the anharmonic effect on the main reactions referring to ethylbenzene combustion mechanism

About 11 reactions related to ethylbenzene are studied in this paper using transition state theory. The YL method proposed by Yao and Lin is utilized to calculate the anharmonic and the harmonic rate constants in these reaction processes in the temperature range of 300–4,000 K, energy diagram and the temperature dependence of the rate coefficients are also presented. The calculations indicate that the harmonic rate constants are larger than the anharmonic rate constants in most cases. Especially, there is a temperature junction between the high and low relationship between the anharmonic and harmonic rate constants in several reactions. Furthermore, the calculated values are in good agreement with other theoretical ones within the allowable error. Finally, the kinetic parameters and the thermodynamic parameters are calculated. To sum up, it can be concluded that the anharmonic effect in these reactions is very significant and cannot be ignored.     

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds

The ferromagnetic and antiferromagnetic wave functions of the KMnF₃ perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and β electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and β eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons. When a pseudopotential is used, such a spin polarization of the core functions of Mn and F can obviously not take place. The importance of such a spin polarization can be appreciated by comparing (i) the spin density at the Mn and F nuclear position, and then the Fermi contact constant, a crucial quantity for the hyperfine coupling, and (ii) the ferromagnetic–antiferromagnetic energy difference, when obtained with an all electron or a pseudopotential scheme, and exploring how the latter varies with pressure. This difference is as large as 50% of the all electron datum, and is mainly due to the rigid treatment of the F ion core. The effect of five different functionals on the core spin polarization is documented.     

Comonotone approximation with interpolation at the ends on an interval

Let a function f ∈ C[-1, 1], changes its monotonisity at the finite collection Y := {y1,… ,ys} of s points yi ∈ (-1, 1). For each n ≥ N(Y), we construct an algebraic polynomial Pn, of degree ≤ n, which is comonotone with f, that is changes its monotonisity at the same points yi as f, and |f(x)-Pn(x)|≤c(s)ω2(f,(√1-x2)/n), x∈[-1,1],where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s and ω2 (f, t) is the second modulus of smoothness of f.     

Tailoring the polarity of polymer shell on BaTiO_3 nanoparticle surface for improved energy storage performance of dielectric polymer nanocomposites

Nanocomposites comprising flexible polymers and high dielectric constant inorganic nanoparticles are considered to be one of the promising candidates for electrostatic capacitor dielectrics.However,the effect of interfacial property on electrical ene rgy storage of dielectric polymer nanocomposites is still not clear.Herein,the role of the polarity of the interfacial region is investigated.For this purpose,three polymers with different polarity,polymethyl methacrylate(PMMA),polyglycidyl methacrylate,and polymethylsulfonyl ethyl methacrylate(PMSEMA) are attached onto BaTi03(BT) na noparticle surface via surface-initiated reversible addition-fragmentation chain transfer polymerization.It is found that the polarity of shell polymers shows an apparent effect on the dielectric and energy storage of dielectric polymer nanocomposites.For example,PMSEMA@BT(shell polymer possesses the highest polarity)increases dielectric loss and decreases the breakdown strength of the nanocomposites,leading to lower ene rgy storage capability.However,PMMA@BT(shell polymer possesses the lowest polarity) can induce higher breakdown strength of the nanocomposites.As a result,the PMMA@BT nanocomposite exhibits the highest electrical energy sto rage capability among the three nanocomposites.This re search provides new insight into the design of core-shell nanofillers for dielectric energy storage applications.