APPLICATION OF PARAMETRIC DERIVATION METHOD TO THE CALCULATION OF PEIERLS ENERGY AND PEIERLS STRESS IN LATTICE THEORY

Applying the parametric derivation method, Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory, while the results obtained by the power-series expansion according to sinusoidal law can be deduced as a limiting case of non- sinusoidal law. The simplified expressions of Peierls energy and Peierls stress are obtained for the limit of wide and narrow. Peierls energy and Peierls stress decrease monotonically with the factor of modification of force law. Present results can be used expediently for prediction of the correct order of magnitude of Peierls stress for materials.

A NEW DERIVATIVE FREE OPTIMIZATION METHOD BASED ON CONIC INTERPOLATION MODEL

In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.

A NEW METHOD FOR THE PREPARATION OF PHENOLS AND ITS DERIVATIVES

a-Oxo ketene dithioacetals 2 via 1,2-nucleophilie addition by methallyl magnesius chloride afforded corresponding alcohols (3). Treated with water or methanol and catalyzed by Lewis acid, the alcohols 3 were converted regiospecifical ly to substituted phenols 5' or related phenol methyl ethers 5 respectively. This reaction is a novel approach to the synthesis of phenols and their derivatives starting from non-aromatic precursors.

Study on State of Terbium Ion in Liposome by One order Derivative Fluorescence Quenching Method

The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the concentration of PC is beyond CMC, most of Tb3+ is dimerized, the dimerization constant is about 3.92×104L/mol. In PC?CH?H2O system, the binding constant of Tb3+?CH complex 2.93×104L/mol is obtained.

Variational iteration method for solving time-fractional diffusion equations in porous the medium

The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.

Retrieval of Sea Surface Height from CYGNSS Data with Tropospheric Delay

An analysis of the delay Doppler maps(DDMs) data from the CYGNSS satellites is implemented to derive the sea surface height(SSH). An SSH estimation algorithm, the leading edge derivation(LED) method which is applied to the delay waveforms, is applied to the DDMs, while the tropospheric delay methods, the Saastamoinen method(SM)and the numerical method(NM) are used. The results show that when the SSH from Jason-2 is referred to as the truth, if the tropospheric delay is corrected, the SSH bias can decrease. The resulted SSH bias from the Jason-2 SSH by the LED retrieval method is of order meter. The resulted SSH deviation from the truth by the NM scheme is half as small as that by the SM scheme. Since the SM scheme is not applicable to the nonhydrostatical condition, the resulted bias is larger.The work can be applied to the Beidou system in the future.

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise

The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.

An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.

2N + 1-soliton Solutions of Boussinesq-Burgers Equation

2N + 1-soliton solutions of Boussinesq-Burgers equation are obtained by using the Hirota bilinear derivative method and the perturbation technique.Further,we give the graphs of corresponding three-and five-soliton solutions.

A Derivative Recovery Spectral Volume Model for the Analysis of Constituents Transport in One-Dimensional Flows

The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and the continuous structure of analytic solutions. In this paper, a derivative reconstruction approach is proposed in the context of spectral volume methods, for the approximation of diffusive fluxes, aiming at the reconciliation of this conflict. Two different reconstructions are used for advective and diffusive fluxes： the advective reconstruction makes use of the information contained in a spectral cell, and allows the formation of discontinuities at the spectral cells boundaries; the diffusive reconstruction makes use of the information contained in contiguous spectral cells, imposing the continuity of the reconstruction at the spectral cells boundaries. The method is demonstrated by a number of numerical experiments, including the solution of shallow-water equations, complemented with the advective-diffusive transport equation of a conservative substance, showing the promising abilities of the numerical scheme proposed.

A Structure-Preserving Numerical Method for the Fourth-Order Geometric Evolution Equations for Planar Curves

For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a structure-preserving method based on a discrete variational derivative method.Furthermore,to prevent the vertex concentration that may lead to numerical instability,we discretely introduce Deckelnick’s tangential velocity.Here,a modification term is introduced in the process of adding tangential velocity.This modified term enables the method to reproduce the equations’properties while preventing vertex concentration.Numerical experiments demonstrate that the proposed approach captures the equations’properties with high accuracy and avoids the concentration of vertices.

EXPRESSION OF rhBMP-7 GENE IN TRANSDUCED BONE MARROW DERIVED STROMAL CELLS

OBJECTIVE: To explore the possibility of expression of exogenous gene in transduced bone marrow derived stromal cells (BMSCs). METHODS: The marker gene, pbLacZ, was transferred into cultured BMSCs and the expression of transduced gene by X-gal staining was examined. Then plasmid pcDNA3-rhBMP7 was delivered to cultured BMSCs. Through immunohistochemical staining and RT-PCR assay, the expression of rhBMP7 gene was detected. RESULTS: The exogenous gene could be expressed efficiently in transduced BMSCs. CONCLUSION: The present study provided a theoretical basis to gene therapy on the problems of bone and cartilage tissue.

A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT

The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.

A rapid compensation method for launch data of long-range rockets under influence of the Earth＇s disturbing gravity field

Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

STUDIES ON THE EXPOSITION OF HYDROXYL RADICAL FROM HEMATOPORPHYRIN DERIVATIVE SOLUTION TO LIGHT BY SPIN-TRAPPING METHOD

That the photosensitive action of hematoporphyrin can damage tumor cells, has attracted much attention recently. However, its mechanism of action is not very clear. Some reported that the damage is due to the production of singlet oxygen （1O2）, a cy-

Implementation of Some Methods of Shape Design for Variational Inequalities

In this paper we present some results concerning the optimal shape design problem governed by the fourth-order variational inequalities. The problem can be considered as a model example for the design of the shapes for elastic-plastic problem. The computations are done by finite element method, and the performance criterion is minimized by the material derivative method. We also discuss the error estimates in the appropriate norm and present some numerical results. An example is used to clearly illustrate the essential elements of shape design problems.

Conformable Fractional Nikiforov–Uvarov Method

We introduce conformable fractional Nikiforov–Uvarov(NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schr¨odinger equation(SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods–Saxon potential, and Hulthen potential.

Studies on aeroservoelasticity semi-physical simulation test for missiles

Missiles may be damaged when aeroservoelastic problem occurs,which is caused by the interaction of structure flexibility and flight control system.Because of the limit of wind tunnel test condition,numerical methods are mostly used in previous aeroservoelastic studies.However,series of assumptions and simplification on structures,aerodynamics and flight control systems are unavoidably introduced,and various nonlinear factors are also ignored,therefore,they result in considerable errors.A novel method called aeroservoelasticity semi-physical simulation test is proposed in this paper,which takes the flexible missile with control system as the test object.Vibration signals at several locations of the missile are measured by accelerometers,then corresponding unsteady aerodynamics is computed based on the fact that airflow at high Mach is nearly quasi-steady,and finally unsteady aerodynamics is exerted simultaneously by shakers at certain locations of the missile.The aeroservoelasticity semi-physical simulation test system can be constructed after the control system is closed.Open loop transfer function test and closed loop stability test are carried out in sequence.The test principle and method proposed in this paper are verified by the concordance between the results of numerical simulation and experiment.

Novel nanoparticles composed of chitosan and β-cyclodextrin derivatives as potential insoluble drug carrier

This research was aim to develop novel cyclodextrin/chitosan （CD/CS） nanocarriers for insoluble drug delivery through the mild ionic gelation method previously developed by our lab. A series of different β- cyclodextrin （β-CD） derivatives were incorporated into CS nanoparticles including hydroxypropyl-β- cyclodextrin （HP-β-CD）, sulphobutylether-β-cyclodextrin （SB-β-CD）, and 2,6-di-O-methy-βcyclodex- trin （DM-β-CD）. Various process parameters for nanoparticle preparation and their effects on physicochemical properties of CD/CS nanoparticles were investigated, such as the type of CD derivatives, CD and CS concentrations, the mass ratio of CS to TPP （CS/TRP）, and pH values. In the optimal condition, CDICS nanoparticles were obtained in the size range of 215-276 nm and with the zeta potential from 30.22 mV to 35.79 mY. Moreover, the stability study showed that the incorporation of CD rendered the CD/CS nanocarriers more stable than CS nanoparticles in PBS buffer at pH 6.8. For their easy preparation and adjustable parameters in nanoparticle formation as well as the diversified hydrophobic core of CD derivatives, the novel CD/CS nanoparticles developed herein might represent an interesting and versatile drug delivery platform for a variety of poorly water-soluble drugs with different physicochemical properties.