Approximate analytical solutions to a conservative oscillator using global residue harmonic balance method

In the current research paper, a conservative system comprising of a mass grounded by linear and nonlinear springs in series connection is studied. The equation of motion for the aforementioned system has been derived as a nonlinear ordinary differential equation with inertia and static–type cubic nonlinearities. The global residue harmonic balance method is applied to obtain an approximate analytical frequency and periodic solution of the problem. Using the obtained analytical expressions, the influences of the hardening and softening nonlinear spring on the non–dimensional frequency are investigated. The results show that developing the system nonlinearity leads the displacement of the mass and the deflection of linear spring to approach each other. Moreover, comparison of the results obtained using the proposed procedure with those achieved by other methods such as numerical method, variational iteration method and harmonic balance approach demonstrates the accuracy and advantages of the current approach.     

An approximate treatment of reflection coefficient in the phased beam tracing method for the simulation of enclosed sound fields at medium frequencies

The phased beam tracing method (PBTM) was suggested as a medium-frequency simulation technique for the calculation of impulse response, although main assumptions of geometric acoustics still hold. The phased method needs the reflection coefficient for characterizing the acoustic property of a surface and the complex wave number for describing the propagation characteristics. In this study, two types of approximate real reflection coefficients derived from the measured absorption coefficient were tested for a practical applicability. As a test example, pressure impulse responses and energy impulse responses computed from the PBTM were compared with those from the measurement and the ordinary beam tracing method. The PBTM employing the approximate reflection coefficients greatly increased the accuracy of the prediction compared to the ordinary beam tracing method, in particular at the medium-frequency range in octave bands above the Schroeder cutoff frequency. A comparison was made between angle-dependent and angle-independent reflection coefficients in the calculation of acoustic measures. Although the angle-dependent reflection coefficient yielded best matched results with measured data, but the simple angle-independent reflection coefficient can be also used with a reasonably good precision.     

狭长封闭声场的近似圆锥束跟踪法模拟研究

狭长空间声传播特性研究对于地铁，长廊等场所的音质设计是非常有意义的，本文提出了模拟狭长封闭声场的近似圆锥束跟踪法，利用它研究了矩形和非矩形狭长声场的空间分布特性。仿真结果表明，对于狭长声场，经典扩散场理论并不适用，而利用本文的数值模拟方法能正确地分析这类声场的特性。     

APPROXIMATE SOLUTION TO THE PARABOLIC EQUATIONS AND THEIR PICTURE DISPLAY ON THE COMPUTER

In this paper, we consider the approximate solution of the type Ⅰ , Ⅲ initial boundary valued problems of the second order linear parabolic partial differential equations. We use a new difference scheme by suitably combining the difference and the basic recursion of elements in the bivariate spline space S21(Δmn(2)) to construct the approximate solutions. We have proved their convengence. And we will give a flow diagraph to display curved surface on a computer, and give an example.     

Limiting behavior of the approximate second-order subdifferential of a convex function

Hiriart-Urruty and the author recently introduced the notions of Dupin indicatrices for nonsmooth convex surfaces and studied them in connection with their concept of a second-order subdifferential for convex functions. They noticed that second-order subdifferentials can be viewed as limit sets of difference quotients involving approximate subdifferentials. In this paper, we elaborate this point in a more detailed way and discuss some related questions.The author is grateful to the referees for their helpful comments.     

A second-order upwind finite-volume method for the Euler solution on unstructured triangular meshes

A scheme for the numerical solution of the two-dimensional (2D) Euler equations on unstructured triangular meshes has been developed. The basic first-order scheme is a cell-centred upwind finite-volume scheme utilizing Roe's approximate Riemann solver. To obtain second-order accuracy, a new gradient based on the weighted average of Barth and Jespersen's three-point support gradient model is used to reconstruct the cell interface values. Characteristic variables in the direction of local pressure gradient are used in the limiter to minimize the numerical oscillation around solution discontinuities. An Approximate LU (ALU) factorization scheme originally developed for structured grid methods is adopted for implicit time integration and shows good convergence characterisitics in the test. To eliminate the data dependency which prohibits vectorization in the inversion process, a black-gray-white colouring and numbering technique on unstructured triangular meshes is developed for the ALU factorization scheme. This results in a high degree of vectorization of the final code. Numerical experiments on transonic Ringleb flow, transonic channel flow with circular bump, supersonic shock reflection flow and subsonic flow over multielement aerofoils are calculated to validate the methodology.     

具有高阶分界线环的多项式微分系统的近似系统

利用Hamilton系统的挑动系统得到了构造具有高阶分界线环的多项式微分系统的近似系统的一种方法，并举出了具体例子．     

Brouwer-Schauder-Tychonoff不动点定理的进一步推广

最近,Wu和Yuan将Brouwer-Schauder-Tychonoff不动点定理推广到H-空间.本文首先建立一个逼近选择定理,然后使用这个结果建立一个新的不动点定理,很大地改进和推广了Wu和Yuan的结果.     

Feasible algorithms for approximate reasoning using fuzzy logic

Deductive reasoning with classical logic is hampered when imprecision is present in the variables, although human reasoning can cope quite adequately with vague concepts. A new approach to reasoning which allows imprecise conclusions to be drawn consistently from imprecise premises was introduced by Baldwin [2]. This method is economical in calculation as it avoids the high dimensionality that fuzzy set representations often involve.This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method. A feasible algorithm for computing each process is then presented.It is assumed that the reader is familiar with the concept of, and operations on, fuzzy sets introduced by Zadeh [14].