一类退化椭圆型方程边值问题的适定性

研究一类特殊退化椭圆型方程边值问题的适定性,该类问题与双曲空间中的极小图的Dirichlet问题,曲面的无穷小等距形变刚性问题等等的研究密切相关,而这类方程的特征形式在区域上是变号的,其适定性是值得深入讨论的.最后,得到这类边值问题的H~1弱解的存在性和唯一性.     

细胞自动机方法解小挠度薄板弯曲问题

固体力学中的细胞自动机方法是一种分析固体力学问题的新方法，它将结构的静平衡认为是在力和位移边界条件下，物体元胞间的自组织过程，它不需要象现有有限元那样形成整体刚度矩阵和求解整体平衡方程，对计算机容量要求低，可望成为分析大型结构的有效方法，且特别适宜于并行计算。为拓展其应用范围，本文将其应用于小挠度弹性薄板弯曲的静力计算以检验其可行性。文中给出了详细的计算步骤，以实际算例为基础，探讨了该方法的有效性，并对其优点和目前存在的问题进行了讨论。     

二元Baskakov算子的一致逼近

Baskakov算子也是一类很重要的正线性算子，在其它领域(如概率及其它学科)都应用很广，本文利用多元分解技巧和已有的一元的结论得出多元Baskakov算子的等价一致逼近定理．     

单位圆盘上再生■[z]-模的刚性

主要研究单位开圆盘上■[z]-模的子模的刚性.证明了空间■_α(0<α<1)的子模具有刚性,这和Hardy空间的情况截然不同.本文还证明了Dirichlet空间的一类子模也具有刚性.     

A method for predicting the deflection of reinforced concrete beams strengthened with carbon plates

For strengthening bent beams, plates of reinforced plastics are glued to their tensioned surface. As s result, the beam becomes layered, and it is possible to control its rigidity and deflection. Based on the methods of structural mechanics of layered media, a method is elaborated for determining the deflection of such beams on the entire range of loading up to their ultimate failure. A comparison between the theoretical and experimental results is carried out. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 45–60, January–February, 2006.     

Local Behavior of the Newton Method on Two Equivalent Systems from Linear Programming

Newton's method is a fundamental technique underlying many numerical methods for solving systems of nonlinear equations and optimization problems. However, it is often not fully appreciated that Newton's method can produce significantly different behavior when applied to equivalent systems, i.e., problems with the same solution but different mathematical formulations. In this paper, we investigate differences in the local behavior of Newton's method when applied to two different but equivalent systems from linear programming: the optimality conditions of the logarithmic barrier function formulation and the equations in the so-called perturbed optimality conditions. Through theoretical analysis and numerical results, we provide an explanation of why Newton's method performs more effectively on the latter system.     

Validity and Accuracy of Equivalent Circuit Models of Passive Inductive Meshes. Definition of a Novel Model for 2D Grids

Accuracy of equivalent circuit models of periodic grids is investigated in amplitude and phase in the visible region. The grids studied here are one-dimensional (1D) and two-dimensional (2D) inductive thin metal meshes. They are located in free space and are illuminated by a plane wave under normal incidence. The range of validity and the accuracy of conventional circuit models are defined by comparison with rigorous results obtained with the Finite-Difference Time-Domain (FDTD) method. In particular, it is shown that electrical models of 1D grids are accurate, whereas equivalent circuits of 2D grids should be used very cautiously. Then, a new formulation is proposed to overcome this major drawback. In the non-diffraction region, the agreement between our model and the FDTD results is within 2% for the power reflectivity and 1° for the phase over a very wide range of strip widths.     

Study on the radial composite piezoelectric ceramic transducer in radial vibration

A new type of radial composite piezoelectric transducer in radial vibration is developed and analyzed. The radial composite transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. They are connected together and excited to vibrate in the radial direction. The radial vibrations of a piezoelectric ceramic thin ring and a metal thin circular ring are analyzed, respectively. Their radial electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin ring and the metal thin circular ring in the radial direction, the electro-mechanical equivalent circuit of the radial composite piezoelectric transducer is derived out and the resonance frequency equation is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and the anti-resonance frequencies, the electro-mechanical equivalent circuit parameters are measured. The effective electro-mechanical coupling coefficient and the mechanical quality factor are calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation.     

On gap rigidity problems for compact Hermitian symmetric spaces

We prove a gap rigidity theorem for diagonal curves in maximal polyspheres of irreducible compact Hermitian symmetric spaces of tube type, which is a dual analog to a theorem obtained by Mok. Motivated by the proof we show that the Chow space of certain totally geodesic submanifolds is affine algebraic, which gives a weaker version of gap rigidity for a class of higher dimensional submanifolds.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.