Forced flexural-and-torsional vibrations of a cantilever beam of constant cross section

The paper addresses the forced flexural-and-torsional vibrations of a cantilever beam of constant cross section. The relevant boundary-value problem is solved. The system of two partial differential equations of the fourth order that describes these vibrations is analyzed in a vector-function space and is subjected to an equivalent transformation to obtain one vector equation of the fourth order with two matrices as coefficients. One is an idempotent matrix; the other is a diagonal matrix. This makes it much easier to construct a Cauchy vector function as an analytic function of these matrices __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 102–114, August 2007.     

Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed.     

利用无网格方法分析斜拉破坏钢筋混凝土梁

从传统的混凝土分离裂缝模型和弥散裂缝模型出发，使用不同的模型模拟不同发展阶段的混凝土裂缝，并利用无网格方法可以灵活布置节点和边界的优点，使分离裂缝模型的使用得到很大的简化。通过在宏观裂缝表面布置基于试验结果的混凝土与混凝土界面单元，正确地模拟了裂缝表面抗剪能力的变化。算例表明，使用本文方法可以准确模拟斜拉破坏混凝土梁的破坏过程，且精度和数值稳定性要高于传统的有限元弥散裂缝方法。     

Disappearing Wakes and Dispersion in Numerically Simulated Flows Through Tube Bundles

Flow through a staggered array or bundle of parallel rigid cylinders of diameter D is computed with the help of a three-dimensional direct numerical simulation (DNS) at various values of Reynolds number between 50 and 6000. Two different spacings L of the tubes, i.e. L/D= 2 and L/D= 3, have been considered. When Re 500 the flow is laminar. In that case the converging flow between a pair of adjacent cylinders brings the oppositely signed vorticity at the two edges of the wake closer together behind the upstream cylinder so that the vorticity decreases quickly due to cancellation by diffusion. At Re 6000, when the flow is highly turbulent, the wake vorticity disappears rather by turbulent diffusion. This disappearance of the wakes in the closely packed flows (i.e. L/D 2) causes the mean flow in a cell, which consists of the region around a single cylinder, to be effectively independent of that in other cells. Another consequence is that the mean velocity field can be very well approximated by potential flow except in a thin boundary layer along the cylinder and a short wake behind it. The results have been applied to the transport of scalars in closely packed arrays. As in other complex flows, the dispersion of the scalars is dominated by the divergence and convergence of the streamlines around the cylinder rather than by the wake turbulence. Approximate expressions are derived for this topologically influenced dispersion in terms of the geometry of the array. The fact when most of the flow in the array can be approximated by a potential flow, allows us to introduce a fast approximate calculation method to compute the dispersion.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

Amenability properties of Banach algebra valued continuous functions

Let X be a compact Hausdorff space and A   a Banach algebra. We investigate amenability properties of the algebra C(X,A)$C(X,A)$ of all A  -valued continuous functions. We show that C(X,A)$C(X,A)$ has a bounded approximate diagonal if and only if A has a bounded approximate diagonal; if A   has a compactly central approximate diagonal (unbounded) then C(X,A)$C(X,A)$ has a compactly approximate diagonal. Weak amenability of C(X,A)$C(X,A)$ for commutative A is also considered.     

大型稀疏矩阵的不完全因子分解法及预处理

本文对大型稀疏阵线性方程组的不完全因子分解及预处理法进行了研究。对对称正定阵和Ｌ阵分别提出了非对角元乘子不完全因子分解法的分解公式。对分解Ａ＝Ｍ－Ｎ，得到了当Ａ为对称正定时，Ｍ亦为对称正定，当Ａ为Ｌ阵时，分解为正规分裂等结果。并研究了预处理ＣＧ加速，最后的数值例子表明本文给出了的算法效果是良好的。     

A note on generalized nonlinear diagonal dominance

In this paper, an open problem, proposed by A. Frommer, about nonlinear generalized diagonal dominance, is solved on some weak restriction, a counterexample is presented if such a restriction is omitted, and some new properties of nonlinear generalized diagonally dominant functions are investigated.     

g-循环矩阵的谱分解和Jordan块结构

首先证明了n级非奇异g-循环矩阵必定可以对角化，并且给出了它的谱分解。其次，当（n,g）=1时，给出了n级奇异g-循环矩阵相似于某些对角阵和某些幂零Jordan块的直和，进一步给出了其中幂零Jordan块的幂零指数的计算法。     

用对角质量矩阵时有限单元特征值问题的准确度

本文讨论的对角化质量矩阵是在动能积分的公式中将积分点取在有限单元的结点上而得到的,本文给出了用这种矩阵时,固有频率、固有振型和对应的应力的对角化误差与动能积分的代数精确度、插值位移场的多项式的阶次、应变能中导数的最高阶数的关系,利用这些关系和多个算例讨论了对角化质量矩阵的应用性问题。