期权定价公式的一般推导方法

一、引言我们知道，布莱克—斯科尔斯（ＢｌａｃｋＳｃｈｏｌｅｓ）期权定价公式可以这样来推导。假设股票价格遵循下面的随机微分方程ｄＳ＝μＳｄｔ＋σＳｄｚ其中Ｓ是股票的价格，μ是股票价格的期望增长率，σ是股票价格的波动率，ｚ是维纳过程。如果没有税收和交易...

针灸方的分类

本文通过对古代针灸方的系统考察将其分为 3类 ,即经验方、腧穴主治方及推导方。经验方主要来源于临床实践 ,具有较高的临床信度与效度 ,值得进一步用现代科学研究的手段去加以验证和升华 ;腧穴主治方不是源自实践而是改编自文献的一类针灸方 ,推导方是指用中医传统理论和现代医学研究成果推导出来的针灸方 。

洛仑兹变换的一种导出

洛仑兹变换的一种导出邢玉珍在普通物理学教材中的相对论部分，在推导洛仑兹变换的过程中，往往用到一个前提条件：Ｓ＇系相对于Ｓ系的速度为ｖ，则Ｓ系相对于Ｓ＇系的速度为一ｖ。［１］１９７９年，朱保如指出。在推导之初，从Ｓ系看Ｓ＇系原点的运动速度为ｖ，无法断定...

Effective stress in soils under different saturation conditions

BISHOP’s effective stress or two state stress variables are unsatisfactory for unsaturated soils where one of fluid phases is discontinuous, so new expressions of effective stress should be founded. The approach for derivation was according to the principle of equilibrium of forces (i.e., the stress-sharing principle), and it was firstly validated by demonstrating TERZAGHI’s principle of effective stress. And then, the derivations were subdivided into four parts according to different pore air states: 1) air bubbles were spherical and suspended in pore water; 2) air bubbles were bound on soil skeleton; 3) air bubbles held almost the single section of pore; 4) air phase was continuous. The different formulae of effective stress were presented. Conclusions are drawn as follows: 1) For nearly-saturated soils, the "real" effective stress would be a little smaller than TERZAGHI’s effective stress; 2) For soils in which air phase is discontinuous in the form of bubbles, a new concept of pore air elastic pressure is put forward, and the total stress can be constituted by effective stress, pore water pressure and pore air elastic pressure; 3) For soils in which air phase is continuous, effective stress is equal to the value of the total stress plus suction; 4) Suction can be divided into two parts: one is the effect caused by additional pressure, and the other is the contract action by the "skin".

Oxidation kinetics regularity in spontaneous combustion of gas coal

In order to investigate the oxidation kinetics of gas coal at low temperatures, we derived a rate equation of oxygen consumption during low-temperature oxidation of gas coal and deduced an E-c equation, expressing the relation between active energy E and oxygen concentration c. The reaction order n and active energy E were calculated with this equation based on experiments of static oxygen consumption tests. In addition, we proved the rationality of the E-c equation using a kinetic compensation effect and obtained the isokinetic temperature Tc. The results show that： 1） the gas coal oxidizes easily with increasing temperature and the oxidation tends to be spontaneous at higher temperatures; 2） the oxygen concentration c affects oxygen consumption very much at lower temperatures but has only a small effect at higher temperatures; 3） the isokinetic temperature Tc was 127 ℃ which has been experimentally validated as the key turning point during low-temperature spontaneous combustion of gas coal.

Rock burst induced by roof breakage and its prevention

Based on the research on rock burst phenomenon induced by the breakage of thick and hard roof around roadways and working faces in coal mines, a criterion of rock burst induced by roof breakage （RBRB） was proposed and the model was built. Through the model, a method calculating the varied stresses induced by roof breakage in support objects and coal body was proposed and a unified formula was derived for the calculation of stress increment on support objects and coal body under different breaking forms of roof. Whilst the formula for calculating dynamic load was derived by introducing dynamic index Kd. The formula was verified in Huating Mine by stress measurement. According to the formula for stress increment calculating, the sensitivities of dynamic load parameters were further studied. The results show that the thickness and breaking depth of roof, width of support objeet are the sensitive factors. Based on the discussion of the model, six associated effective methods for rock burst prevention are obtained.

Modal analysis on transverse vibration of axially moving roller chain coupled with lumped mass

The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equations were derived by means of Lagrange's equations.The effects of the parameters,such as the axially moving velocity of the chain,the tension force,the weight of lumped mass and its time-variable assign position in chain span,on the modal characteristics of transverse vibration for roller chain were investigated.The numerical examples were given.It is found that the natural frequencies and the corresponding mode shapes of the transverse vibration for roller chain coupled with lumped mass change significantly when the variations of above parameters are considered.With the movement of the chain strand,the natural frequencies present a fluctuating phenomenon,which is different from the uniform chain.The higher the order of mode is,the greater the fluctuating magnitude and frequency are.

Derivation of the Equation Nernst-Aibassov in a Magnetic Field

The influence of magnetic field on the redox potentials of the Nernst equation. The author offered the new formula Nernst equation in a magnetic field. Our proposed formula takes into account the influence of the magnetic field on the redox processes.

Droplet Contact Angle Measurement on Microstructures of Octocoral Sclerites-ESEM Image Analysis

This work explores the methodology for micron-scale water droplet contact angle derivation for the warty surface of octocoral sclerites. The calcite-made sclerites of the Red Sea octocoral Dendronephthya hemprichi have been chosen as a model for this study. Water droplet condensation on the sclerites has been in-situ investigated using Quanta 200 FEG （field emission gun） ESEM （environmental scanning electron microscope） under wet environmental conditions. Two different analysis methods of droplet top and side views have been applied to determine the contact angle based on the secondary electron images. The ESEM image analysis for the sclerites indicates that their surface is hydrophilic. The microscopic contact angle is measured to be 45.3°±6.3°. The macroscopic contact angle has been calculated by using the Wenzel model for the surface texturing of the sclerites.

Quadrant based incremental planning for mobile robots

Path planning of a mobile robot in the presence of multiple moving obstacles is found to be a complicated problem.A planning algorithm capable of negotiating both static and moving obstacles in an unpredictable(on-line)environment is proposed.The proposed incremental algorithm plans the path by considering the quadrants in which the current positions of obstacles as well as target are situated.Also,the governing equations for the shortest path are derived.The proposed mathematical model describes the motion(satisfying constraints of the mobile robot)along a collision-free path.Further,the algorithm is applicable to dynamic environments with fixed or moving targets.Simulation results show the effectiveness of the proposed algorithm.Comparison of results with the improved artificial potential field(iAPF)algorithm shows that the proposed algorithm yields shorter path length with less computation time.

The Method for Inferring a Buried Fault from Resistivity Tomograms and Its Typical Electrical Features

Electrical resistivity tomography (ERT) has been used to experimentally detect shallow buried faults in urban areas in the past a few years, with some progress and experience obtained. According to the results from Olympic Park, Beijing, Shandong Province, Gansu Province and Shanxi Province, we have generalized the method and procedure for inferring the discontinuity of electrical structures (DES) indicating a buried fault in urban areas from resistivity tomograms and its typical electrical features. In general, the layered feature of the electrical structure is first analyzed to preliminarily define whether or not a DES exists in the target area. Resistivity contours in resistivity tomograms are then analyzed from the deep to the shallow. If they extend upward from the deep to the shallow and shape into an integral dislocation, sharp flexure (convergence) or gradient zone, it is inferred that the DES exists, indicating a buried fault. Finally, horizontal tracing is be carried out to define the trend of the DES. The DES can be divided into three types-type AB, ABA and AC. In the present paper, the Zhangdian-Renhe fault system in Zibo city is used as an example to illustrate how to use the method to infer the location and spatial extension of a target fault. Geologic drilling holes are placed based on our research results, and the drilling logs testify that our results are correct. However, the method of this paper is not exclusive and inflexible. It is expected to provide reference and assistance for inferring the shallow buried faults in urban areas from resistivity tomograms in the future.

On Camassa-Holm Equation with Self-Consistent Sources and Its Solutions

Regarded as the integrable generalization of Camassa-Holm (CH) equation, the CH equation with selfconsistent sources (CHESCS) is derived. The Lax representation of the CHESCS is presented. The conservation laws for CHESCS are constructed. The peakon solution, N-soliton, N-cuspon, N-positon, and N-negaton solutions of CHESCS are obtained by using Darboux transformation and the method of variation of constants.

Elastic stability of shallow pin-ended parabolic arches subjected to step loads

Buckling could be induced when shallow arches were subjected to vertical step loads. In-plane static and dynamic buckling of shallow pin-ended parabolic arches with a horizontal cable was investigated. Based on the equations of motion derived from Hamilton's principle, nonlinear equilibrium equations and static buckling equilibrium equations were deduced. Through the pseudo-static analysis, approximate solutions to the lower and upper dynamic buckling loads under step loads were obtained, for shallow parabolic arches. The results show that dynamic buckling and snap-through buckling are impossible when modified slenderness ratio λ<λc and λ>λs, where λc and λs denote critical slenderness ratios of bucking and snap-through buckling, respectively; effects of the stiffness of the horizontal cable on the dynamic buckling are significant; and the dynamic buckling loads under a equivalent central concentrated step load are lower than the loads under a distributed load appreciably.

Nonlinear static response of piezoelectric plates considering electro-mechanical coupling

Nonlinear static analysis of piezoelectric plates has been carried out using nonlinear finite element method considering electro-mechanical coupling,The geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the plate thickness,The governing equations are obtained using potential energy and Hamilton's principle that includes elastic and piezoelectric effects.The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements,Results are presented for piezoelectric plate under different mechanical boundary conditions,Numerical results for the plate are given in dimensionless graphical forms.Effects of boundary conditions on linear and nonlinear response of the plate are also studied.The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.

Analysis on effective stress formula and consolidation of gassy muddy clay

In order to found an applicable equation of consolidation for gassy muddy clay, an effective stress formula of gas-charged nearly-saturated soils was introduced. And then, a consolidation equation was derived. Subsequently, supposing soils were under tangential loading, the expressions of pore water pressure were presented. The analytic solution of pore water pressure was attempted to be validated by the measured values in a real embankment. The parameters in the expressions of pore water pressure were gotten by the method of trial. The result shows that the consolidation model is rational and the analytic solution of pore water pressure is correct. The following conclusions can be made: 1) the influence of bubbles on the compressibility of pore fluid should be considered; 2) the effective stress would be influenced by bubbles, and the consolidation would depend on the compressibility of soil skeleton: the softer the soils are, the more distinct the influence of bubbles is; for normal clay, the influence of bubbles on the effective stress may be commonly neglected.

Linear quadratic stochastic integral games and related topics

This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.

Influence of phase shift drift and splitting ratio on 80 GHz optical mm-wave generation

For the scheme of 80 GHz optical millimeter-wave(mm-wave) generation using two cascaded Mach-Zehnder modulators(MZMs),an exact analytical solution for the optical mm-wave affected by phase shift drift and splitting ratio is derived with the method of expanding Bessel series.The results show that for the carrier and the fourth-order sideband,the influence caused by phase shift drift is dominant,while the first-order,the second-order and the third-order sidebands are influenced by both phase shift drift and splitting ratio.It follows that the undesired sideband suppression ratio is at least 35.9 dB when the splitting ratio deviation is 0.001,and the phase shift drift is 1o.The performance of the system is perfect if the accuracy is achieved.

A Time-Marching Throughflow Model and its Application in Transonic Axial Compressor

A throughflow model based on the time-marching finite volume approach is described in this paper. The governing equations are derived by circumferentially averaging the three-dimensional Navier-Stokes equations neglecting the circumferentially non-uniform and viscous terms. An inviscid blade force model similar to the Large-particle method is derived. The viscous blade force has been modeled by the distributed loss model. The convective fluxes of the governing equation are discretized with the Edward’s low-diffusion flux-splitting (LDFSS) scheme. And a point-iterative Symmetric Gauss-Seidel (SGS) scheme is used in the temporal discretization. The throughflow model has been applied to the NASA Rotor 67 and a high-load transonic fan stage ATS-2. The reasonable good agreements with the experiments and the 3D viscous computations show the potential of the method.

Investigation of model development for deterministic correlations associated with impeller-diffuser interactions in centrifugal compressors

The average-passage equation system(APES)provides a rigorous framework to account for the deterministic unsteady effects by the so-called deterministic correlations(DC),which include both deterministic stress correlations(DCS)and deterministic total enthalpy correlations(DCH).These correlations should be modeled to close the system of equations.In this paper,the distribution of DC in a transonic centrifugal compressor is presented,and its relative importance is revealed.The assumption made by Adamczyk that the pure unsteady fluctuation is significantly smaller than the spatial fluctuation is verified at the impeller-diffuser interface.The decomposition of DCH is also discussed to determine its two different physical mechanisms.Finally,the transport equations in terms of DCS in cylindrical coordinates are derived,and the terms are evaluated to determine the ones that are necessary to model.All these analyses significantly contribute to our model development for DC in centrifugal compressors.

Theoretical shape analysis of tapered fibers using a movable large-zone furnace

To estimate the shape of tapered fibers using tapering machines with movable large-zone furnaces, a new calculation method is proposed based on the discrete deducing method and the principle of the volume conservation of the fiber materials. This method can estimate the tapering results, i.e., the shape of the tapered fibers, based on arbitrary moving parameters of the large-zone furnace and the fiber holders. The theoretical estimated results agree with the experimental measuring shape of the tapered fibers quite well.