定积分中值定理的推广

对定积分中值定理作了推广，使之有更广泛的结论，并给出了关于两个积分商的中值定理。     

周期函数的几个判定定理

周期函数是数学中比较重要的概念之一,本文给出了几个周期函数的定理并加以证明.     

试论网络吸收变换定理及其应用

阐述建立在双口网络定理基础上的吸收变换定理，这是一种新的网络分析方法。文中举例说明当双口网络的两端口负载及基内部某一特定支路（包括含源支路）元件参数变化时，应用吸收变换法来求解，将使分析过程大大简化。     

教学实践中对中值定理的讨论

在高等数学中,三个中值定理十分重要,因而其在教学过程中如何教好也显得尤为关键。而如何教好这节内容特别是对如何构造出辅助函数的讲解是一个难重点,经过摸索可采用启发性教学以及用综合分析法来构造辅助函数。     

Numerical weight function method for the structural analysis of ships: a speedy direct calculation with condensed structural information

The weight function method was originally derived for crack problems to calculate stress intensity factors for arbitrary loading conditions. In this article, a numerical weight function method has been extended to formulate the structural response analyses of two-dimensional elasticity, plate-bending, and three-dimensional plate-structures by using the finite-element method. The solution procedure is based on the well-known Maxwell–Betti reciprocal theorem, which is applied to the original and properly defined auxiliary problems. The present numerical weight function may be considered as a finite-element version of a Green’s function in an integral equation solution scheme. Although ship structures are certainly analysed by the finite-element method in a practical design procedure, the weight function approach has not yet been realized. The method is very useful for the analysis of structures subjected to a vast range of loading conditions, because structural responses can simply be calculated by the inner product of the universal weight function and load vectors. The validity and convergence characteristics of the present method are investigated by two-dimensional elastic and plate-bending problems, respectively. Finally, the method is applied to the calculation of the response amplitude operator of a stress component at a critical structural detail of a double-hull tanker, and the speed and efficiency of the method are quantitatively discussed based on the practical results.     

一类p-Laplacian方程周期解的存在唯一性

利用 Man＆#225;sevich-Mawhin 连续定理研究一类二阶 p-Laplacian 方程（p（x＇））＇= f（t，x，x＇）- e（t）周期解的存在与唯一性，在非线性项 f = g ＋ h 分别满足一定增长性的条件下，得到了一个新的周期解存在唯一性定理。     

三带紧支撑正交内插尺度函数的构造

提出了设计同时具有紧支撑、正交性、内插性和正则性的3-带尺度函数的方法,从而利用Walter小波采样定理能够快速而准确地重构多分辨空间Vj(φ)的信号f(t),除了计算机的有限字长误差外,没有任何截断误差。     

二维地效翼气动性能计算研究

从格林定理出发,在边界上布置Rankine源和偶极子,分别用定常和非定常方法对二维地效翼的性能进行计算,构建一种处理地效翼问题的计算模型.详细介绍这种方法的理论推导和计算过程,并经过试算确定了适当的模型参数.通过对多个参数的变化调整,讨论离地间隙、攻角对二维地效翼升力的影响.大量的数值计箅和与试验数据的比较,证实该法作为地效翼问题的一个支撑模型是可行、可靠的.     

曲柄滑块机构中连杆加速度瞬心位置的确定

提出了确定曲柄滑块机构中连杆加速度瞬心位置的方法,从而可直接求解连杆上任意点的加速度问题。     

基于射流理论的空气中水射流轨迹及扩展范围计算方法

基于射流理论基础,引入射流卷吸假定和动量分析方法,建立计算空气中水射流运动轨迹及扩展范围的射流-动量模型,运用耙吸挖泥船艏喷、吹泥管线等实测数据对模型进行验证和分析,并与部分现有模型进行对比分析。结果表明:射流-动量模型计算射流轨迹与现有模型相当,与实测值基本一致,计算扩展范围与实测值符合较好,较现有模型更具实用性。针对艏喷和吹泥管线的工况特性,推荐了适用的射流扩展系数、吸入空气流速系数这两个射流-动量模型重要特性参数的取值。     

On the realization of nonlinear wave profiles using the Banach fixed-point theorem: Stokes wave in a finite depth

A new mathematical formulation for the realization of nonlinear wave profiles and its nonlinear solution procedure, based on the Banach fixed-point theorem, is proposed. To apply the formulation, a nonlinear equation for the Stokes wave in a finite depth was derived, and some numerical solutions are given. A numerical study showed that the proposed iteration method, based on linear progressive wave potential only, enabled us to realize the Stokes nonlinear wave profiles in a finite depth. The nonlinear strategy of iteration has a very fast convergence rate, i.e., only about 6–10 iterations are required to obtain a numerically converged solution.     

考虑流体静压时充液圆柱壳的输入能量流特性

研究了内部流体静压力对充液圆柱壳的受迫振动能量流的影响。静压力作为预应力计入壳体振动方程当中,壳体和流体分别采用Fliigge方程和Helmholtz波动方程。分析了耦合系统在周向线分布余弦载荷下的动态响应．用傅立叶变换和反变换实现空间域与波数域之间的相互转换,采用留数定理求取系统的响应并得到耦合系统的输入能量流。结果表明,周向模态数n=0时,静压力对耦合系统的输入能量流影响很小;n较大时,在中低频下静压力使输入能量流曲线沿频率轴右移,由于输入能量流的峰值点处的频率对应于频散曲线中各支传播波的截止频率,对应传播波的截止频率升高,高频时则基本无影响。随着静压力以及周向模态数的增大,输入能量流受到的影响程度也增大。     

振动翼推进性能计算及试验研究

采用非定常边界元法基于格林定理构建振动翼计算模型,讨论相关的构建过程、程序结构;采用时变尾涡面和时间步进法在时域中处理振动翼的尾涡存储效应,在尾涡面上应用等压Kutta条件并通过New-ton-Raphson法进行迭代求解,对在无限域中的振动翼水动力特性进行计算和研究;通过数值计算结果与试验数据对比,证实本方法的有效性。