正规Cayley图

综述了自１９９０年以来１２－传递图研究的一些新成果，正规Ｃａｙｌｅｙ图的相关结论。     

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.     

Nonlinear Normal Modes of a Parametrically Excited Cantilever Beam

We investigate theoretically thenonlinear normal modes of a vertical cantilever beam excited by aprincipal parametric resonance. We apply directly the method ofmultiple scales to the governing nonlinear nonautonomousintegral-partial-differential equation and associated boundary conditions.In the absence of damping, it is shown that the system has nonlinear normal modes, as defined by Rosenberg, even in the presence of the parametric excitation.We calculate the spatial correction to the linear mode shapedue to the effects of the inertia and curvature nonlinearities andthe parametric excitation. We compare the result obtained withthe direct approach with that obtained using a single-mode Galerkindiscretization.The deviation between the two predictions increases as the oscillationamplitude increases.     

On Affine Normal Forms and a Classification of Homogeneous Surfaces in Affine Three-Space

We classify homogeneous surfaces in real and complex affine three-space. This is achieved by choosing affine coordinates so that the surface is defined by a function whose Taylor series is in a preferred normal form.     

Metric Inequality, Subdifferential Calculus and Applications

In this paper we establish characterizations of Asplund spaces in terms of conditions ensuring the metric inequality and intersection formulae. Then we establish chain rules for the limiting Fréchet subdifferentials. Necessary conditions for constrained optimization problems with non-Lipschitz data are derived.     

On non-null distributions connected with testing that a real normal distribution is complex

The exact and the asymptotic non-null distribution of the maximal invariant corresponding to testing that the covariance matrix of a 2m-dimensional real normal distribution has complex structure is obtained.     

幂零群的若干充分条件

本文利用Ｃ－正规子群的性质，得到了若干有限群为幂零群的充分条件，推广了一些著名定理，如Ｔｈｏｍｐｓｏｎ定理及Ｉｔ＾ｏ定理。     

沿法线方向改进非DEA有效DMU

现有的非DEA有效DMU的改进方法造成DMU的投入或产出的波动太大,因而难以进行改进.提出了沿法线方向改进非DEA有效DMU的新方法.可以使非DEA有效DMU尽快到达有效前沿面,成为DEA有效,减小了波动幅度,并结合12所重点理工高校效评价的实际,验证了本方法的优势.     

k-systems, k-networks and k-covers

The concepts of k-systems, k-networks and k-covers were defined by A. Arhangel’skii in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among k-systems, k-networks and k-covers are further discussed and are established by mk-systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of mk-systems.     

A Novel Fiber Taper for Efficient Optical Interconnection

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｅｒｃｏｎｎｅｃｔｉｏｎｓｏｆｏｐｔｉｃａｌｗａｖｅｇｕｉｄｅｃｏｍｐｏｎｅｎｔｓｗｉｔｈｄｉｆｅｒｅｎｔｍｏｄａｌｓｐｏｔｓｉｚｅｓ，ｐａｒｔｉｃｕｌａｒｌｙｆｏｒｔｈｅｃｏｎｎｅｃｔｉｏｎｏｆ（１）ｌａｓｅｒｓｏｕ...