Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.     

Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments

We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.     

大型稀疏无约束最优化问题的行列修正算法

本文提出了一类适用于大型稀疏最优化问题的简单易行的行列修正算法，获得了新算法的局部超一性收敛性，大量的数值试验表明这是一个较为理想的修正算不。新算法同样可以用来求解大型对称性非线性方程组。     

无严格互补松驰条件的序列线性方程组新算法

该文通过构造特殊形式的有效集来逼近KKT点处的有效集，给出了一个任意初始点下的序列线性方程组新算法，并证明了该算法在没有严格互补松驰条件的情况下具有全局收敛性和一步超线性收敛性。      

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

Prediction of the retention indices of methyl pyridines and pyrazines in capillary gas chromatography based on the non-linear additivity of the sorption energy

Summary Methylbenzenes, pyridines and pyrazines were investigated on fused-silica and glass capillary columns coated with SE-30 and PEG-40M/KF liquid phases, at two temperatures, 80° and 110°C. The contribution of the methylene groups to the partial molar free sorption energy was determined for methylpyridines and pyrazines. Equations are proposed for the calculation of the retention indices of methyl pyridines and pyrazines. These equations are based on the ortho- and α-effects of the methyl groups. The predicted indices have been experimentally tested for six dimethyl- and trimethylpyridines, and four methylpyrazines. Good accuracy of the calculation permits to use this method for the identification of methylpyridines and pyrazines in complex mixtures. Enlarged text of the paper presented at the Eighth International Symposium on Capillary Chromatography, Riva del Garda, Italy, May 19–21, 1987.     

Predictive models to describe VLE in ternary mixtures water + ethanol + congener for wine distillation

The modeling of liquid–vapor equilibrium in ternary mixtures that include substances found in alcoholic distillation processes of wine and musts is analyzed. In particular, vapor–liquid equilibrium in ternary mixtures containing water + ethanol + cogener has been modeled using parameters obtained from binary mixture data only. The congeners are substances that although present in very low concentrations, of the order of part per million, 10⁻⁶ to 10⁻⁴ mg/L, are important enological parameters [1] and [2]. In this work two predictive models, the PSRK equation of state and the UNIFAC liquid phase model and two semipredictive activity coefficient models: NRTL and UNIQUAC have been used. The results given by these different models have been compared with literature data and conclusions about the accuracy of the models studied are drawn, recommending the best models for correlating and predicting the phase equilibrium in this type of mixtures.     

Sample capacity in open tubular and micro-packed columns for GC

Equations have been derived from which the maximum sample size which may be loaded on a column without significantly affecting the performance may be calculated. It is shown that micro-packed columns can handle a sample which is as much as forty times larger than that which can be loaded onto wall-coated open tubular columns with comparable conditions.     

Equations describing lamellar structure parameters and melting points of polyethylene-<Emphasis Type="Italic">co</Emphasis>-(butene/octene)s

Time- and temperature-dependent SAXS-experiments were used to determine the effect of octene and butene co-units on the lamellar structure and the melting properties of polyethylene. As expected, melting points decrease with increasing co-unit content, but crystal thicknesses are not affected and depend on the crystallization temperature only. Results can be cast into some simple equations which describe the dependence:

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.