正弦函数式进料对膜污染的影响及流体力学计算

以腐植酸溶液模拟污水,研究正弦函数式进料方式对膜通量的影响。实验结果表明,当阀门开度为50%时,正弦式进料周期和占空时间均为9 s时,膜通量明显提高。扫描电镜结果显示,正弦式函数进料后,膜表面不同程度的沾附有颗粒物质;而稳定流进料后,膜表面有滤饼层形成,造成较严重的污染。当采用正弦函数式进料能将其对膜口的剪切力提高至27×10^5N,约为稳定流进料的4倍,为改变流体流动形态减轻膜污染的原因提供理论依据。

函数y=Asin(ωx+)+k是一个原型(高一)

教材对函数y=Asin(ωx+(?))+k的图象和性质有详尽的分析.本文说明不少正余弦函数式可以化为这个原型,使问题迎刃而解. 例1 求函数y=sinx+cosx的最大值和单调增区间.

Monotonicity Results and Inequalities for Inverse Hyperbolic Sine

In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.