非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

Equivalent nonlinear beam model for the 3-D analysis of shear-type buildings: Application to aeroelastic instability

Tower buildings can be very sensitive to dynamic actions and their dynamic analysis is usually carried out numerically through sophisticated finite element models. In this paper, an equivalent nonlinear one-dimensional shear–shear–torsional beam model immersed in a three-dimensional space is introduced to reproduce, in an approximate way, the dynamic behavior of tower buildings. It represents an extension of a linear beam model recently introduced by the authors, accounting for nonlinearities generated by the stretching of the columns. The constitutive law of the beam is identified from a discrete model of a 3D-frame, via a homogenization process, which accounts for the rotation of the floors around the tower axis. The macroscopic shear strain in the equivalent beam is produced by the bending of columns, accompanied by negligible rotation of the floors. A coupled nonlinear shear–torsional mechanical model is thus obtained. The coupling between shear and torsion is related to a non-symmetric layout of the columns, while mechanical nonlinearities are proportional to the slenderness of the columns. The model can be used for the analysis of the response of tower buildings to any kind of dynamic and static excitation. A first application is here presented to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions and on the postcritical behavior of tower buildings, based on a quasi-steady model of aerodynamic forces.     

Allyl sulfides and α‐substituted acrylates as addition–fragmentation chain transfer agents for methacrylate polymer networks

The rapid and uncontrolled nature of network formation from di(meth)acrylate monomers produces high shrinkage stress and results in polymers with oftentimes brittle mechanical properties. Methods for regulating polymerization and network formation are sought. One option is the use of addition–fragmentation chain transfer (AFCT) agents, which are well known to control molecular weight and molecular weight distribution of monofunctional (meth)acrylates. A series of novel and previously described AFCT reagents were synthesized and screened with laser flash photolysis to determine reactivity. Well‐performing AFCT reagents were then tested in polymerizations with monofunctional and difunctional methacrylates. With monofunctional monomers, the molecular weight and polydispersity of the resultant linear polymers tend to decrease with the addition of AFCT agent. In copolymerization with dimethacrylate monomers, the AFCT agents were found to substantially lower and sharpen the glass transition. Sharpness of the glass transition is here indicative of a more regular and homogenous network. After coupling of the instruments, photorheology was performed simultaneously with real‐time IR to show an increase in monomer conversion at the time of gelation, which appears to have a positive effect on reducing shrinkage stress. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 394–406     

Issue Information

An integrated finite element method (FEM) is proposed to simulate incompressible two‐phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2‐iso‐Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic‐type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi‐implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1‐integrated FEM coupled with the semi‐implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.     

A mixed-ligand approach for building a N-rich porous metal-organic framework for drug release and anticancer activity against oral squamous cell carcinoma

Abstract

A new Zn(II) metal-organic framework (MOFs), [Zn(BTC)(HME)]·(DMAc)(H₂O) (1, H₃BTC =1,3,5-benzenetricarboxylic acid, HME?=?protonated melamine, DMAc?=?N,N-dimethylacetamide), has been synthesized under solvothermal conditions. In the structure of 1, the four-coordinate Zn(II) ions are connected by BTC^3? ligands into a 3-D framework with (3)-connected utg-type topology. This MOF shows permanent porosity after lattice solvent removal with a calculated pore size distribution around 0.72?nm. With abundant N-donor sites and suitable pore size, the desolvated 1 (1a) was used as a drug carrier for the loading of anticancer drug 5-fluorouracil (5-Fu) molecules. Moderate 5-Fu loading capacity and long drug release time were observed for 1a. The computational simulation results reveal that strong H-bond interactions between the 5-Fu molecules and the nitrogen sites allow slow release of the drug 1a. In addition, the in vitro cytotoxicity of 1 and 5-Fu loaded 1a were also evaluated using MTT assays against human oral squamous cell carcinoma (SCC-251 and HSC-4).     

3D finite element simulation of explosive welding of three-layer plates

A 3D finite element model of the explosive welding process of three-layer plates with materials of steel-copper-copper is established. Based on the presented model, the bonding mechanism is simulated and analyzed, different detonation modes are also comparatively studied to indicate the driving force spread in few microseconds. The results show that the three layer plates bond together after many times of impact between the flyers and the base driven by detonation wave, which is damping rapidly at each impa...     

Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side.     

Temperature dependence of volume and surface symmetry energy coefficients of nuclei

The thermal evolution of the energies and free energies of a set of spherical and near-spherical nuclei spanning the whole periodic table are calculated in the subtracted finite-temperature Thomas–Fermi framework with the zero-range Skyrme-type KDE0 and the finite-range modified Seyler–Blanchard interaction. The calculated energies are subjected to a global fit in the spirit of the liquid-drop model. The extracted parameters in this model reflect the temperature dependence of the volume symmetry and surface symmetry coefficients of finite nuclei, in addition to that of the volume and surface energy coefficients. The temperature dependence of the surface symmetry energy is found to be very substantial whereas that of the volume symmetry energy turns out to be comparatively mild.     

The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection with the τ-function representation is discussed.     

Dislocation-density-based constitutive modelling of tensile flow and work-hardening behaviour of P92 steel

The flow and work-hardening behaviour of tempered martensitic P92 steel have been investigated using phenomenological constitutive model in the temperature range 300–873 K for the strain rates ranging from 3.16 × 10^?5 to 1.26 × 10^?3 s^?1. The analysis indicated that the hybrid model reduced to Estrin–Mecking (E–M) one-internal-variable model at intermediate and high temperatures. Further, the analysis also indicated that dislocation dense martensite lath/cell boundaries and precipitates together act as effective barriers to dislocation glide in P92 steel. The flow behaviour of the steel was adequately described by the E–M approach for the range of temperatures and strain rates examined. Three distinct temperature regimes have been obtained for the variations in work-hardening parameters with respect to temperature and strain rate. Signatures of dynamic strain ageing in terms of the anomalous variations in work-hardening parameters at intermediate temperatures and the dominance of dynamic recovery at high temperatures have been observed. The evaluation of activation energy suggested that deformation is controlled by the dominance of cross-slip of dislocations at room and intermediate temperatures, and climb of dislocations at high temperatures.