Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

Modeling the effect of deep traps on the capacitance–voltage characteristics of p-type Si-doped GaAs Schottky diodes grown on high index GaAs substrates

Numerical simulation, using SILVACO-TCAD, is carried out to explain experimentally observed effects of different types of deep levels on the capacitance–voltage characteristics of p-type Si-doped GaAs Schottky diodes grown on high index GaAs substrates. Two diodes were grown on (311)A and (211)A oriented GaAs substrates using Molecular Beam Epitaxy (MBE). Although, deep levels were observed in both structures, the measured capacitance–voltage characteristics show a negative differential capacitance (NDC) for the (311)A diodes, while the (211)A devices display a usual behaviour. The NDC is related to the nature and spatial distribution of the deep levels, which are characterized by the Deep Level Transient Spectroscopy (DLTS) technique. In the (311)A structure only majority deep levels (hole traps) were observed while both majority and minority deep levels were present in the (211)A diodes. The simulation, which calculates the capacitance–voltage characteristics in the absence and presence of different types of deep levels, agrees well with the experimentally observed behaviour.     

In vivo evaluation of a mucoadhesive polymeric caplet for intravaginal anti-HIV-1 delivery and development of a molecular mechanistic model for thermochemical characterization

Context and objective: The aim of this study was to develop, characterize and evaluate a mucoadhesive caplet resulting from a polymeric blend (polymeric caplet) for intravaginal anti-HIV-1 delivery.

Materials and methods: Poly(lactic-co-glycolic) acid, ethylcellulose, poly(vinylalcohol), polyacrylic acid and modified polyamide 6, 10 polymers were blended and compressed to a caplet-shaped device, with and without two model drugs 3′-azido-3′-deoxythymidine (AZT) and polystyrene sulfonate (PSS). Thermal analysis, infrared spectroscopy and microscopic analysis were carried out on the caplets employing temperature-modulated DSC (TMDSC), Fourier transform infra-red (FTIR) spectrometer and scanning electron microscope, respectively. In vitro and in vivo drug release analyses as well as the histopathological toxicity studies were carried out on the drug-loaded caplets. Furthermore, molecular mechanics (MM) simulations were carried out on the drug-loaded caplets to corroborate the experimental findings.

Results and discussion: There was a big deviation between the T_g of the polymeric caplet from the T_g's of the constituent polymers indicating a strong interaction between constituent polymers. FTIR spectroscopy confirmed the presence of specific ionic and non-ionic interactions within the caplet. A controlled near zero-order drug release was obtained for AZT (20 d) and PSS (28 d). In vivo results, i.e. the drug concentration in plasma ranged between 0.012–0.332?mg/mL and 0.009–0.256?mg/mL for AZT and PSS over 1–28 d.

Conclusion: The obtained results, which were corroborated by MM simulations, attested that the developed system has the potential for effective delivery of anti-HIV-agents.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

A Constitutive Equation of Thermoelasticity for Solid Materials

A new constitutive equation of thermoelasticity for crystals is presented based on the interatomic potential and solid mechanics at finite temperature. Using the new constitutive equation, the calculations for crystal copper and graphene are carried out under different loading paths at different temperatures. The calculated results are in good agreement with those of the previous thermoelasticity constitutive equation based on quantum mechanics, which clearly indicates that our new constitutive equation of thermoelasticity is correct. A lot of comparisons also show that the present theory is more concise and efficient than the previous thermal stress theory in the practical application.     

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials

We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.Mathematics subject classification 1991. 65N35, 65N22, 65F05, 35J05     

大牛地气田异常修正等时试井资料求取产能方法

大牛地气田为低渗-致密气田,因存在启动压力梯度等因素,修正等时试井曲线按常规方法处理出现异常,无法准确获取气井的产能方程.采用LIT法和异常曲线校正法对气田异常试井资料进行了重新处理,最终获得气井产能方程,为同类气藏产能试井可能出现的异常资料处理解释探索了新的途径.     

差分跳频通信系统的特点及性能

文章介绍了一种新型的短波跳频通信技术——差分跳频,分析了差分跳频技术区别于常规跳频技术的主要特点。针对按序列检测的信号接收方法,对差分跳频通信系统在AWGN信道下的性能进行了理论分析,同时做出相应的计算机仿真,证实了差分跳频通信技术和按序列检测方法的结合,使通信系统在AWGN信道下的性能得到了比较显著的提升。     

A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

波动方程数值模拟的隐式差分法

在有限差分波动方程数值模拟中,通常采用高阶差分方法来提高空间导数的数值逼近精度,以实现降低数值频散,提高数值模拟精度的目的。首先对差分频散进行了理论分析;然后讨论了估计一阶空间导数的隐式差分格式,并与通常采用的高阶精度显式差分格式进行了对比分析,结果表明,隐式差分格式能够在更宽的波数范围使差分频散控制在可接受的水平,如8阶精度的显式差分格式所适应的波数带宽约为O．55kmax,而隐式差分格式所适应的波数带宽约为0．7kmax;最后通过模型试算,对隐式差分格式的有效性进行了验证。模拟结果表明,用隐式差分格式在一定程度上降低了差分频散,提高了模拟精度。