一类出现在燃烧理论中的奇摄动边值问题

研究了一类出现在燃烧理论中的奇摄动边值问题。在一定的条件下,通过选取适当的具有边界层性质和角层性质的函数构造出一对界定函数,应用微分不等式理论证明了具有角层性质的解的存在性,并给出解的渐近估计。     

奇摄动非线性系统的内层现象

本文研究二阶非线性系统的内部角层和冲击现象，在适当假设条件下利用微分不等式理论证明了奇摄动问题解的存在性，并讨论了当ε→0^ 时解的各种性态。     

一个燃烧反应扩散的奇摄动问题

讨论了一个燃烧反应扩散方程的奇摄动Dirichlet问题。首先，构造了代数型角层形式的解，分别得到了左边界层、右边界层和内层性质的校正项，然后，构造了上、下解，并对相应的关系式的非线性项进行了泰勒展开，再用中值定理得到了有关不等式，最后，利用微分不等式理论，证明了问题解的存在性，并得到了解的渐近估计。     

恰当处理目标角 正确解答三角题

在求三角函数值或角的问题中,为了避免出现错解、漏解、增解,需要深刻理解题设条件,善于分析题设条件与结论中的角的相互关系,仔细探索目标角的实际范围,现举例说明如下。     

恰当处理目标角正确解答三角题

在求三角函数值或角的问题中,为了避免出现错解、漏解、增解,需要深刻理解题设条件,善于分析题设条件与结论中的角的相互关系,仔细探索目标角的实际范围,现举例说明如下.     

十三讲 解直角三角形

解直角三角形就是根据一个直角三角形中已知的边与角求出这个三角形中的未知的边与角．解直角三角形的依据是：     

《代数与初等函数》(上册) 第六章 “解三角形”的学习辅导

本章主要内容是解三角形。我们知道,一个三角形,或是直角三角形,或是斜三角形,它们都包括三条边和三个角等六个元素。所谓解三角形,就是由三角形中已知的边和角,来计算得出未知的边和角。怎样由三角形中已知的边和角,来计算得出未知的边和角呢?就解直角三角形来说,主要是明确三角形中边与角的关系,这在前两章已经学习过了,重要的是,要记住这些关系式。解斜三角形,还要学习并掌握正弦定理和余弦定理,并能熟练地运用这些定理。此外,还要理解、掌握并能熟练地     

三角函数问题中怎样“缩角”?

在三角函数求角求值时,经常遇到要考虑角的范围以确定解的个数,也就是要根据已知条件缩小角的范围,以排除其中的增解的问题.那么,怎样缩小角的范围呢?     

三角函数解题中一个值得注意的问题

在解三角题中,角的取值范围是十分重要的条件,为了解题合理、正确,既要考虑角的取值范围的明显条件,还应考虑角的取值范围的隐含条件.而不少同学在解题过程中往往疏忽,使解不完整,甚至错解.现举例分析,以飨读者.一、算术根的化简     

三角问题中缩小角范围的六法

由于三角函数是周期函数，即自变量与三角函数值是多对一的对应关系，所以，解三角问题时要特别注意确定角的实际变化范围，尽可能地缩小角的范围，否则会出现增解．下面介绍缩小角的范围的六种方法．     

Singular perturbation of a second-order three-point boundary value problem for nonlinear systems

This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.     

Steady-state response of a saturated half-space with an overlying dry layer subjected to a moving load

In this paper, the steady-state response of a saturated half-space with an overlying dry layer subjected to a moving rectangular load is investigated. The governing partial differential equations are solved using the Fourier transform. The solutions in time-space domain are expressed in terms of infinite Fourier type integrals, which can be evaluated only by numerical quadrature. Numerical results show that the influence of a drained or undrained interface on the response is related to the permeability of the underlying saturated soil. Moreover, the effect due to the upper dry layer is associated with the thickness of the layer.     

台风顶部辐散流出层流线方程及转向半径

本文把质点动力学的Lagrange表述法和流体力学惯用的Euler表述法结合起来,建立了描述台风顶部辐散流出层Coriolis旋流的独特的二维微分方程组。该方程组有精确解,得到了流线方程.台风流出层气流先表现为气旋性流出,然后转化为反气旋性流出,本文求得了转向点的位置,理论计算的结果与由观测资料得到的Fujita模式符合得较好,并且导得强台风流出层转向半径与流入层转向半径相等的结论。     

平板层流边界层的新速度分布函数

采用积分关系式方法求解平板层流边界层问题,在满足基本边界条件的基础上提出以雅克比椭圆正弦函数作为新的近似速度分布函数,用最小二乘法确定函数中的待定系数.分析表明新分布函数精度有明显提高,且形式简单,便于工程应用。     

物理学中的守恒定律及其地位

从时间的均匀性可推得机械能守恒定律,从空间的均匀性和空间的各向同性可分别推出动量守恒定律和角动量守恒定律。如果没有时间对称性、就根本谈不上物理学。因此,守恒定律是物理学的基石,它与基本定 律和各种物理现象一层层地构成了整个物理大厦。     

一类一阶二次微分方程解的探究

为了探究一类一阶二次微分方程的解析解,先提出独立通解（UGS）的概念,可以得到齐次微分方程的解,其通解是由若干个独立通解共同构成的．对于非齐次情形,其解是由若干个特解共同构成,并验证了这些特解线性相关．     

Analytical model for straight hemming based on minimum energy method

An analytical model for straight hemming was developed based on minimum energy method to study the effect of flanging die corner radius on hemming qualities. In order to calculate plastic strain and strain energy more exactly, the neutral layer of specimen corner after hemming is assumed to be a half ellipse with its major semi-axis unknown. Isotropic hardening rule is adopted to describe bending and reverse bending processes neglecting Bauschinger effect. The model takes into account the material property parameters in order to satisfy a wide application range of different materials. Specimen profile, creepage/growing (roll-in/roll-out) and maximum equivalent strain are predicted, which are greatly influenced by the flanging die corner radius. Experimental facilities were designed and hemming experiments were undertaken. The predicted results of the present analytical model were compared to experimental data as well as finite element (FE) simulation results. It was confirmed that they are in good agreement, and the model can be used to evaluate whether the material used as an outer panel for hemming is appropriate and to optimize process parameters when the material used for hemming is changed.     

Effects of vortex generator jet on corner separation/stall in high-turning compressor cascade

The effects of the vortex generator jet(VGJ)attached at the endwall on the corner separation/stall control are investigated by numerical simulation in a high-turning linear compressor cascade. The results show that the corner separation could be reduced significantly, which results in a wider operation range as well as a more uniform exit flow angle and total pressure profile. At the near-stall operation point, the maximum relative reduction of the total pressure loss is up to 32.5%,, whereas the jet mass ratio is less than 0.4%,. Based on the analysis of the detailed flow structure, three principal effects of the VGJ on the endwall cross flow and corner separation are identified. One is to increase the tangential velocity component opposite to cross flow, thus inhibiting the endwall secondary flow near the jet exit. The second is to suppress the pitchwise extension of the passage vortex as an air fence. The third is to sweep the low energy fluids towards the mainstream on the up-washed side and to transport the mainstream fluids to the endwall to reenergize the boundary layer on the down-washed side.     

自适应有限元方法在凹角域椭圆问题上最佳误差估计

完整给出由‖·‖ L∞(Ω) 范数最佳误差估计推出的一种关于线性椭圆问题近似解的自适应有限元方法 .本方法对给定误差能自动剖分 ,且不需要关于精确解的先验信息 ,通过在凹角域详细分析此过程 ,证明该方法是有效的 .在实例中也得到了所期望的结果 .