On analytical solutions of the Black–Scholes equation

This work presents a theoretical analysis for the Black–Scholes equation. Given a terminal condition, the analytical solution of the Black–Scholes equation is obtained by using the Adomian approximate decomposition technique. The mathematical technique employed in this work also has significance in studying some other problems in finance theory.     

Compressible navier-stokes equations with density-dependent viscosity, vacuum and gravitational force in the case of general pressure

This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.     

Strong convergence of an iterative method for nonexpansive mappings with new control conditions

The purpose of this paper is to study the convergence problem of an iterative method for nonexpansive mappings in Banach spaces under some new control conditions on parameters.     

参数曲线的全局凸性判别条件

基于平面曲线的二次微商,导出了二重点的判别条件,结合参数曲线的局部凸性条件,得到了参数闭曲线的充要条件。给出了参数曲线的拐点判别条件,从而得到了参数曲线局部凸的充要条件。     

Construction and performance characteristics of new fentanyl-selective plastic membrane electrode.

The construction and performance characteristics of an ion-selective electrode for fentanyl-drug cation, based on an ion-pair complex with tetrakis[3,5-bis-(trifluoromethyl)phenyl]borate anion in a PVC matrix were studied. A linear response for 1 x 10(-5) mol dm-3 to 1 x 10(-2) mol dm-3 drug with a slope of 57.9 +/- 0.5 mV/decade was established. The optimum pH range was 2 to 6. The lower detection limit was 6.29 x 10(-6) mol dm-3 fentanyl citrate (2.1165 micrograms cm-3 fentanyl). There were negligible interferences from a number of inorganic cations, structural analogues, and some common drug additives in injections. The electrode proposed has been successfully applied to determine fentanyl citrate in injections. The results correlated well with those obtained by the United States Pharmacopoeia standard procedure.     

Dynamics of a small vibro-impact pile driver

A mathematical model is developed to study periodic-impact motions and bifurcations in dynamics of a small vibro-impact pile driver. Dynamics of the small vibro-impact pile driver can be analyzed by means of a three-dimensional map, which describes free flight and sticking solutions of the vibro-impact system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the Poincaré map. The piecewise property is caused by the transitions of free flight and sticking motions of the driver and the pile immediately after the impact, and the singularity of map is generated via the grazing contact of the driver and the pile immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularities and parameter variation on the performance of the vibro-impact pile driver is analyzed. The global bifurcation diagrams for the impact velocity of the driver versus the forcing frequency are plotted to predict much of the qualitative behavior of the actual physical system, which enable the practicing engineer to select excitation frequency ranges in which stable period one single-impact response can be expected to occur, and to predict the larger impact velocity and shorter impact period of such response.     

Study on Chromium‐Containing Aluminophosphate CrAPO‐5 via Density Functional Theory

Various structures of CrAPO‐5 clusters are studied via density functional B3LYP exchange‐correlation method. The optimized structures are compared with data from X‐ray absorption. Their total energies and atomic net charges are also analyzed. Results indicate that the substitution of the aluminum site of an AFI framework by chromium is in general not feasible. The chromium ion is more likely docked in between two neighboring 12‐membered rings of the framework of AFI. To further verify our claim, the excitation energies of the representative chromium structures of CrAPO‐5 clusters are calculated via the TDDFT method. The results for excitation energies further support that Cr³⁺ is not incorporated into the framework.     

Synthesis, structure and physicochemical characterization of a noncentrosymmetric, quaternary thiostannate: EuCu2SnS4

EuCu₂SnS₄ was prepared by a stoichiometric combination of the elements heated to 700 °C for 125 h. The structure was determined by single crystal X-ray diffraction methods. The compound crystallizes in the noncentrosymmetric, orthorhombic space group Ama2 with a=10.4793(1) Å, b=10.3610(2) Å, c=6.4015(1) Å, Z=4, R1=0.99% and wR2=2.37%. The structure type is that of SrCu₂GeSe₄. The structure can be described as a three-dimensional network built from near perfect SnS₄ and distorted CuS₄ tetrahedra together with EuS₈ square antiprisms. The dark red compound is a semiconductor with an optical bandgap of 1.85 eV.