Using variational methods and Morse theory, we obtain some existence results of multiple solutions for certain semilinear problems associated with general Dirichlet forms.
In this paper,with the relative Morse index,we will study the existence of solutions of(1.1)under the assumptions that V satisfies some weaker conditions than those in[2].
Li DAR点云为小尺度地表形态的提取与表达提供了精确的数据源,但其高密度性与不确定性,导致应用Morse理论提取的特征点中含有大量的"伪特征点"。这里首先通过定义特征点指数等一系列概念,模拟特征点周围区域的地表形态,建立...Li DAR点云为小尺度地表形态的提取与表达提供了精确的数据源,但其高密度性与不确定性,导致应用Morse理论提取的特征点中含有大量的"伪特征点"。这里首先通过定义特征点指数等一系列概念,模拟特征点周围区域的地表形态,建立特征点重要性度量指标与计算方法;然后给出了地表重要特征点的提取算法;最后,进行了试验验证与分析。结果表明:提出的算法优于现有的持续值法与自然法则法,可以有效剔除"伪特征点",实现基于Li DAR点云小尺度复杂地形的特征点精确提取与多层次表达。展开更多
A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ...A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.展开更多
基金supported by National Natural Science Foundation of China - NSAF (10976026)National Natural Science Foundation of China (11271305)
文摘Using variational methods and Morse theory, we obtain some existence results of multiple solutions for certain semilinear problems associated with general Dirichlet forms.
基金Supported by DEU of Henan(Grant No.19A110011)and PSF of China(Grant No.188576).
文摘In this paper,with the relative Morse index,we will study the existence of solutions of(1.1)under the assumptions that V satisfies some weaker conditions than those in[2].
文摘A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.
