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The symplectic eigenfunction expansion theorem and its application to the plate bending equation 下载免费PDF全文
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported.It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space.It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem,thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner. 相似文献
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In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP(A) and σ1/P(-A^*) with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results. 相似文献
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This paper deals with a class of upper triangular infinite-dimensional Hamiltonian operators appearing in the elasticity theory.The geometric multiplicity and algebraic index of the eigenvalue are investigated.Furthermore,the algebraic multiplicity of the eigenvalue is obtained.Based on these properties,the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed.It is shown that the completeness is determined by the system of eigenvectors of the operator entries.Finally,the applications of the results to some problems in the elasticity theory are presented. 相似文献
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钨、钼-二苯基乙醇酸-2,2′-联吡啶-钛铁试剂连测体系还未见报道。本文提出了在0.05mol/L的硫酸中,钨与二苯基乙醇酸,2,2′-联吡啶的络合物在-0.79V(vs.SEC)产生一个极其灵敏的极谱催化波,测定完钨后,加入少量钛铁试剂测定钼。钼于-0.20V(vis.SEC)处产生极灵敏的阴极化导数波,波形尖锐对称,易于测量。采用此种连测体系,钨钼的灵敏度都可满足要求,钨和钼的检出限分别为0.004、0.01μg/L。确定最佳条件和拟定了不经分离富集直接测定岩溶地下水中痕量钨和钼的方法。此外还对极谱波性质进行了探讨,讨论了阴、阳离子表面活性物质对极谱催化波的作用机理。 相似文献
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Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory 下载免费PDF全文
This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates. 相似文献
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黄俊杰 《武汉大学学报(理学版)》1979,(4)
在磁记录的检出方式上我们提出了用逻辑电路进行峰值位移的校正方法,在同步方式上,根据磁古的机电性能(木以)出了用无峰值位移的外同步记录加以数学锁相环路进行倍频扦补形成同步讯号,在编码方式上将 Reice 码进行简化,并辅之以其它措施,使得在国产 G—3型磁鼓上获得的存贮容量近于国内中型计算机配套的同型磁鼓存贮容量的4倍,取得了显著的 相似文献