A thermally-insensitive passively Q-switched Cr:YAG/Nd:YAG laser

A passively Q-switched laser with Cr⁴⁺:YAG/Nd:YAG composite crystal using a corner cube prism cavity has been realized, in which the corner cube prism is the key element as it aids the compensation of the thermal lens effect of laser crystal. Compared with plane–plane mirror cavities under the same conditions, the stability of the laser performance using the corner cube prism cavity was improved remarkably over temperatures ranging from −40 to 65 °C. The decrease of Nd:YAG stimulated emission cross section with temperature was considered to be the main reason for the increase of average output pulse energy under the same cycle for the two different cavities when the ambient temperature changed −40 to 65 °C. The mode properties produced by the prism cavity were analyzed, and the theoretical results were verified by experimental observations.     

Corner transfer matrix study of an inhomogeneous Ising model

We consider a planar Ising model with an extended defect described by couplings of the form K(r) = K·(1 + A/r). We determine the spectrum of the corner transfer matrix numerically and analytically and use it to calculate the local magnetization at the defect and the corresponding, non-universal critical exponent.     

CUTTING CORNERS PRESERVES LIPSCHITZ CONTINUITY

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New Trigonometric Basis Possessing Exponential Shape Parameters

Four new trigonometric Bernstein-like basis functions with two exponential shape parameters are constructed, based on which a class of trigonometric Bézier-like curves, analogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an ellipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cubic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape parameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be $C^2$ ∩ $FC^3$ continuous for a non-uniform knot vector, and $C^3$ or $C^5$ continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for $G^1$ continuous joining two trigonometric Bézier-like patches over triangular domain are deduced.     

基于稳定Harris置信度的三步搜索数字稳像方法

提出一种基于稳定Harris角点置信度的三步搜索法数字稳像方法.采用三步搜索法策略进行运动参量的计算,对三步搜索法结果使用稳定Harris角点置信度进行约束,提升运动参量计算准确度.针对分辨率为320×240存在±40个像素范围内抖动的车载运动视频进行稳像处理,实验结果验证此方法有效可行.     

角隅全反镜谐振腔激光器的输出特性

 在高功率脉冲气体激光器中,用角隅反射镜作为全反镜,平行平面镜作为输出镜构成角隅全反镜谐振腔。对角隅腔激光器的输出特性和抗失调稳定性进行了研究,并与平凹腔和平平腔激光器进行了比较。实验结果表明：在角隅全反镜失调角为16 mrad时,角隅腔激光器的单脉冲输出能量下降9.2%,且近场输出光斑没有明显变化;而凹面全反镜失调角仅为0.4 mrad时,平凹腔激光器输出能量下降了9%,近场输出光斑严重变形。在输出镜正前方3.12 m处测量,当角隅镜偏转16.3 mrad时,激光器输出光斑与标准状态时的输出光斑重合;凹面全反镜失调角为0.4 mrad时,激光器输出光斑位移14 mm。经模式仪分析表明,角隅腔激光器近场光强分布均匀。     

A multiple flux boundary element method applied to the description of surface water waves

This paper concerns a two dimensional numerical model based on a high-order boundary element method with fully nonlinear free surface boundary conditions. Multiple fluxes are applied as a method of removing the so-called “corner problem”, whereby the direction of the outward normal at geometric discontinuities is ill-defined. In the present method, both fluxes associated with differing directions of the outward normal at a corner are considered, allowing a single node to be placed at that position. This prevents any loss of information at what can be an important part of the boundary, especially if considering simulations of wave reflection and wave run-up. The method is compared to both the double node approach and the use of discontinuous elements and is shown to be a more accurate technique. The success of the method is further demonstrated by its ability to accurately simulate various problems involving wave transmission and wave-structure interactions at domain corners; the results being achieved without the need for filtering, smoothing or re-gridding of any kind.     

On level sets of marginal functions

The investigation of level sets of marginal functions is motivated by several aspects of standard and generalized semi-infinite programming. The feasible- set M of such a prob­lem is easily seen to be a level set of the marginal function corresponding to the lower level problem. In the present paper we study the local structure of M at feasible bound­ary points in the generic case. A codimension formula shows that there is a wide range of these generic situations, but that the number of active indices is always bounded by the state space dimension. We restrict our attention to two special subcases

In the first case, where the number of active indices is maximalM is shown to be locally diffeomorphic to the non-negative orthant. This situation is well-known from finite and also from standard semi-infinite programming. However, in the second case a generic situation arises which is typical for generalized semi-infinite programming. Here, the active index set is a singleton, and M can exhibit a re-entrant corner or even local non-closedness, depending on whether the Mangasarian-Fromovitz constraint qualifica­tion holds at the active index. If an objective function is minimized over M then in the setting of the second case a local minimizer cannot occur     

Mixed-Integer Cuts from Cyclic Groups

We analyze a separation procedure for Mixed-Integer Programs related to the work of Gomory and Johnson on interpolated subadditive functions. This approach has its roots in the Gomory-Johnson characterization on the master cyclic group polyhedron. To our knowledge, the practical benefit that can be obtained by embedding interpolated subadditive cuts in a cutting plane algorithm was not investigated computationally by previous authors. In this paper we compute, for the first time, the lower bound value obtained when adding (implicitly) all the interpolated subadditive cuts that can be derived from the individual rows of an optimal LP tableau, thus approximating the optimization over the intersection of the Gomory corner polyhedron with the LP relaxation of the original problem formulation. The computed bound is compared with that obtained when only Gomory mixed-integer cuts are used, on a very large test-bed of MIP instances.     

The evolution compressible Navier-Stokes system on polygonal domains

The evolution compressible Navier-Stokes system is considered on polygonal domains. It is shown that the lowest order of the corner singularity of the system is the same as that of the heat equation. In a suitable Banach space the velocity is split into singular and regular parts and the coefficient of the singularity is expressed by convolution of some two functions in the time variable. By a formula of the pressure we observe propagation of the corner singularity along the characteristic lines emanating from the corners and also unboundedness of derivatives of pressure there. An increased regularity for the remainder part is established.