基于模糊集合论的实物期权定价方法

实物期权的定价在风险投资决策过程中具有重要意义.传统的实物期权定价方法忽略标的资产价值和投资成本的模糊性,从而可能导致错误的投资决策.本文主要研究了具有模糊标的的资产价值和投资成本情形时的实物期权定价模型.文中将这些模糊因素分别视为模糊数和模糊变量,然后运用模糊集合论,结合B-S期权定价理论,对实物期权进行定价,得到了基于模糊集合论的实物期权定价模型.     

水下爆炸柱形高压气泡膨胀过程的RGFM和高精度格式数值模拟

为了对柱形装药水下爆炸高压气泡膨胀过程进行三维数值模拟,用level set方法追踪气水界面,详细描述了精确对柱形气泡进行level set建模;对于流场,使用Euler方程描述,并用高精度格式(五阶WENO和四阶R-K法)离散空间项和时间项;对于level set方程,使用五阶HJ-WENO离散;用RGFM处理气水界面附近网格节点。给出了水下流场不同时刻的压力云图、柱形高压气泡的形状演变以及流场中几个指定点的压力峰值。通过三维建模和计算验证,用RGFM结合高精度格式可以很好地对柱形高压气泡膨胀问题进行三维数值模拟,同时也可以较精确地追踪高密度比、高压力比的三维气水界面。计算结果表明,柱形高压气泡在膨胀过程中,形状逐渐向椭球形变化;位于固壁附近的柱形高压气泡受固壁反射波的影响,在固壁法线方向上的膨胀会受到抑制;双圆柱形高压气泡膨胀产生的冲击波,可以彼此抑制对方的膨胀。

     

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.     

快中子照相中的点扩展函数计算

 快中子照相中,基于反冲核原理探测快中子的有机闪烁体平板是普遍采用的快中子辐射转换体。模拟了D-T中子垂直入射BC400闪烁体平板,计算了不同厚度平板闪烁体的点扩展函数,对14.1 MeV快中子照相中闪烁体固有分辨率随厚度的变化进行了研究。计算结果表明,在不考虑二次中子与闪烁体作用及背景噪声等情况时,点扩展函数几乎不依赖于闪烁体厚度。同时,计算还表明在一定的分辨率范围内,由于荧光收集效率的限制,闪烁体厚度增加并不会改善图像对比度。     

3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Segmentation of three-dimensional (3D) complicated structures is of great importance for many real applications. In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model. Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations. Instead, the minimum cut on a special designed graph need to be computed. The method is tested on data with complicated structures. It is rather stable with respect to initial value and the algorithm is nearly parameter free. Experiments show that it can solve large problems much faster than traditional approaches.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

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.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Ends,tangles and critical vertex sets

We show that an arbitrary infinite graph G can be compactified by its ends plus its critical vertex sets, where a finite set X of vertices of an infinite graph is critical if its deletion leaves some infinitely many components each with neighbourhood precisely equal to X. We further provide a concrete separation system whose ?₀‐tangles are precisely the ends plus critical vertex sets. Our tangle compactification is a quotient of Diestel's (denoted by ), and both use tangles to compactify a graph in much the same way as the ends of a locally finite and connected graph compactify it in its Freudenthal compactification. Finally, generalising both Diestel's construction of and our construction of , we show that G can be compactified by every inverse limit of compactifications of the sets of components obtained by deleting a finite set of vertices. Diestel's is the finest such compactification, and our is the coarsest one. Both coincide if and only if all tangles are ends. This answers two questions of Diestel.