Description of the thermodynamic properties and fluid-phase behavior of aqueous solutions of linear,branched, and cyclic amines

The SAFT-γ Mie group-contribution equation of state is used to represent the fluid-phase behavior of aqueous solutions of a variety of linear, branched, and cyclic amines. New group interactions are developed in order to model the mixtures of interest, including the like and unlike interactions between alkyl primary, secondary, and tertiary amine groups (NH₂, NH, N), cyclic secondary and tertiary amine groups (cNH, cN), and cyclic methine-amine groups (cCHNH, cCHN) with water (H₂O). The group-interaction parameters are estimated from appropriate experimental thermodynamic data for pure amines and selected mixtures. By taking advantage of the group-contribution nature of the method, one can describe the fluid-phase behavior of mixtures of molecules comprising those groups over broad ranges of temperature, pressure, and composition. A number of aqueous solutions of amines are studied including linear, branched aliphatic, and cyclic amines. Liquid–liquid equilibria (LLE) bounded by lower critical solution temperatures (LCSTs) have been reported experimentally and are reproduced here with the SAFT-γ Mie approach. The main feature of the approach is the ability not only to represent accurately the experimental data employed in the parameter estimation, but also to predict the vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria, and LCSTs with the same set of parameters. Pure compound and binary phase diagrams of diverse types of amines and their aqueous solutions are assessed in order to demonstrate the main features of the thermodynamic and fluid-phase behavior.     

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations, are obtained using the exp_a function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.     

Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

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.     

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.     

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     

凝胶渗透色谱法测定基础油PAO的相对分子质量及分布

聚α-烯烃是一种性能优良的润滑油基础油，其相对分子质量及分布直接影响宏观性能。本研究建立了一种用于表征1-癸烯齐聚物相对分子质量及分布的方法。采用带示差折光检测器的凝胶渗透色谱系统，综合考虑分离效果和测试可操作性，优化了流动相流速和凝胶色谱柱的组合方式。以四氢呋喃为流动相，流速为0.8 mL/min，色谱柱组合方式为Styragel HR 0.5,Styragel HR 1,PLGEL 3μm MIXED-E三柱串联，以聚苯乙烯作为标准样品，采用普适校正方法处理色谱流出曲线。此方法测得样品的质均相对分子质量与凝胶渗透色谱-光散射法所测定结果相比较，相对误差相对偏差在3%以内。     

A Novel Approach to Analyzing the Occupancy of the Geo/Geo/∞ Queueing System

Discrete time queueing systems have been successfully used to model packet queues in computer and digital communications systems. In this article we introduce a novel approach to analyzing the Geo^X/Geo^Y/∞ queueing system, which is suitable for modelling high speed computer and communications systems. The approach is based on characterizing the system by a functional equation which is then solved recursively to give identical results to those obtained using other approaches.     

Moving Least-Squares Differential Quadrature Method for Free Vibration of Antisymmetric Laminates

In this paper, the moving least-squares differential quadrature (MLSDQ) method is employed for free vibration of thick antisymmetric laminates based on the first-order shear deformation theory. The generalized displacements of the laminates are independently approximated with the centered moving least-squares (MLS) technique within each domain of influence. The MLS nodal shape functions and their partial derivatives are computed quickly through back-substitutions after only one LU decomposition. Subsequently, the weighting coefficients in the MLSDQ discretization are determined with the nodal partial derivatives of the MLS shape functions. The MLSDQ method combines the merits of both the differential quadrature and meshless methods which can be conveniently applied to complex domains and irregular discretizations without loss of implementation efficiency and numerical accuracy. The natural frequencies of the laminates with various edge conditions, ply angles, and shapes are calculated and compared with the existing solutions to study the numerical accuracy and stability of the MLSDQ method. Effects of support size, order of completeness of basis functions, and node irregularity on the numerical accuracy are investigated in detail.     

带参数的一阶脉冲微分方程边值问题

利用上下解和单调迭代法。讨论了带参数的一阶脉冲微分方程。获得了单边Lipschitz条件下这类方程边值问题的解的存在性。