Local 2-Geodesic Transitivity of Graphs

An s-geodesic in a graph Γ is a path connecting two vertices at distance s. Being locally transitive on s-geodesics is not a monotone property: if an automorphism group G of a graph Γ is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. In this paper, we characterise all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics.     

Identifying distress among banks prior to a major crisis using non-oriented super-SBM

We illustrate how data envelopment analysis (DEA) can be used as a forward-looking method to flag bank holding companies (BHCs) likely to become distressed. Various financial performance models are tested in the period leading up to the recent global financial crisis. Results generally support DEA’s discriminatory and predictive power, suggesting that it can identify distressed banks up to 2 years in advance. Robustness tests reveal that DEA has a stable efficient frontier and its discriminatory and predictive powers prevail even after data perturbations. DEA can be used as a preliminary off-site screening tool by regulators, by business managers to ascertain their standing among competitors, and by investors. Attention by regulators can be further directed at potentially distressed banks as some of them would be candidates for closer monitoring. In conclusion, DEA may be useful in making economic decisions because there is an identifiable link between inefficiency and financial distress. To the best of our knowledge, application of DEA to predict financial distress among BHCs prior to a major crisis has not been published.     

Vertex‐Transitive Cubic Graphs of Square‐Free Order

A classification of connected vertex‐transitive cubic graphs of square‐free order is provided. It is shown that such graphs are well‐characterized metacirculants (including dihedrants, generalized Petersen graphs, Möbius bands), or Tutte's 8‐cage, or graphs arisen from simple groups PSL(2, p).     

Gorenstein Global Dimensions and Representation Dimensions for L-R Smash Products

Let H be a Hopf algebra and A an H-bimodule algebra. This paper investigates Gorenstein global dimensions and representation dimensions of L-R smash products \(A\natural H\) . Several well-known results are generalized.     

A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

In this work, we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels. Particularly, we consider the case when the underlying solutions are sufficiently smooth. In this case, the proposed method leads to a fully discrete linear system. We show that the fully discrete integral operator is stable in both infinite and weighted square norms. Furthermore, we establish that the approximate solution arrives at an optimal convergence order under the two norms. Finally, we give some numerical examples, which confirm the theoretical prediction of the exponential rate of convergence.     

自然电位测井的数学模型

自然电位测井是石油开发中一种常用而重要的测井方法。自然电位函数的数学模型可归结为具有间断交界面条件的椭圆型等位面边值问题,在交界面交汇点处,自然电位的跳跃通常不满足相容性条件,此时,这个边值问题不存在分块H1*解,不能使用有限元素法直接求解。本文介绍这一测井方法的数学模型及数值求解方法。     

Globally Hyperbolic Regularization of Grad's Moment System

In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multidimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment system can be analytically given and depend only on the macroscopic velocity and the temperature. The structure of the eigenvalues and eigenvectors of the coefficient matrix is fully clarified. The regularization together with the properties of the resulting moment systems is consistent with the simple one‐dimensional case discussed in ¹. In addition, all characteristic waves are proven to be genuinely nonlinear or linearly degenerate, and the studies on the properties of rarefaction waves, contact discontinuities, and shock waves are included. © 2014 Wiley Periodicals, Inc.     

On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators

Nemirovski’s analysis (SIAM J. Optim. 15:229–251, 2005) indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, a class of Fejér monotone projection and contraction methods is developed. Until now, only convergence results are available to these projection and contraction methods, though the numerical experiments indicate that they always outperform the extragradient method. The reason is that the former benefits from the ‘optimal’ step size in the contraction sense. In this paper, we prove the convergence rate under a unified conceptual framework, which includes the projection and contraction methods as special cases and thus perfects the theory of the existing projection and contraction methods. Preliminary numerical results demonstrate that the projection and contraction methods converge twice faster than the extragradient method.     

小麦液泡膜H~ -ATPase的Ca~(2 )激活特性

纯化小麦液泡膜H -ATPase,测定了纯化的小麦液泡膜H -ATPase 受Mg2 和Ca2 双重激活的特性及两种激活状态下酶的特性. Mg2 激活时酶水解活性受DCCD的抑制,受磷脂酰丝氨酸(PS)影响明显,ATP水解和泵质子活性相偶联.而在Ca2 激活时酶水解活性不受DCCD抑制,受PS影响微弱,Ca2 激活时ATP水解与泵质子活性解偶联. Mg2 和Ca2 对小麦液泡膜H -ATPase的激活作用不具有叠加效应.     

Multigrid algorithm from cyclic reduction for Markovian queueing networks

A multigrid method based on cyclic reduction strategy is proposed to solve huge, nonsymmetric singular linear systems arising from Markovian queueing networks. A simple way to construct the matrix-dependent prolongation and restriction operators is presented in this paper. Numerical results for multiple queues are given to illustrate the efficiency and robustness of our methods.