Monoid-labeled transition systems

Given a -complete (semi)lattice , we consider -labeled transition systems as coalgebras of a functor ⁽⁻⁾, associating with a set X the set ^X of all -fuzzy subsets. We describe simulations and bisimulations of -coalgebras to show that L⁽⁻⁾ weakly preserves nonempty kernel pairs iff it weakly preserves nonempty pullbacks iff L is join infinitely distributive (JID).Exchanging for a commutative monoid , we consider the functor ⁽⁻⁾_ω which associates with a set X all finite multisets containing elements of X with multiplicities m M. The corresponding functor weakly preserves nonempty pullbacks along injectives iff 0 is the only invertible element of , and it preserves nonempty kernel pairs iff is refinable, in the sense that two sum representations of the same value, r₁ + … + r_m = c₁ + … + c_n, have a common refinement matrix (m_{(i, j)}) whose k-th row sums to r_k and whose l-th column sums to c_l for any 1≤ k ≤ m and 1 ≤ l ≤ n.     

Catadioptric Projective Geometry

Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system.     

On local convergence of a Newton-type method in Banach space

In this study we are concerned with the local convergence of a Newton-type method introduced by us [I.K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear equations in Banach spaces, Appl. Math. Lett. 5 (1992), pp. 7–9.] for approximating a solution of a nonlinear equation in a Banach space setting. This method has also been studied by Homeier [H.H.H. Homeier, A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math. 157 (2003), pp. 227–230.] and Özban [A.Y. Özban, Some new variants of Newton's method, Appl. Math. Lett. 17 (2004), pp. 677–682.] in real or complex space. The benefits of using this method over other methods using the same information have been explained in [I.K. Argyros, Computational theory of iterative methods, in Studies in Computational Mathematics, Vol. 15, C.K. Chui and L. Wuytack, eds., Elsevier Science Inc., New York, USA, 2007.; I.K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear equations in Banach spaces, Appl. Math. Lett. 5 (1992), pp. 7–9.; H.H.H. Homeier, A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math. 157 (2003), pp. 227–230.; A.Y. Özban, Some new variants of Newton's method, Appl. Math. Lett. 17 (2004), pp. 677–682.]. Here, we give the convergence radii for this method under a type of weak Lipschitz conditions proven to be fruitful by Wang in the case of Newton's method [X. Wang, Convergence of Newton's method and inverse function in Banach space, Math. Comput. 68 (1999), pp. 169–186 and X. Wang, Convergence of Newton's method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000), pp. 123–134.]. Numerical examples are also provided.     

一类拟线性椭圆型方程弱解P-指标的稳定性

该文利用拟线性椭圆型方程弱解梯度的一致估计,在区域Ω的边界满足一致p-厚的条件下,使用一致p-厚的边界Sobolev不等式,Hlder不等式和Young不等式,得到了此类方程弱解关于p-指标的稳定性。     

概率约束规划逼近最优解集的几乎处处上半收敛性

对概率约束规划逼近最优解集序列的几乎处处上半收敛性进行讨论．利用概率测度方法建立随机规划模型,将带有约束的随机规划问题转化成与其等价的无约束随机规划问题．以概率测度弱收敛的性质给出概率约束规划可行解的几乎处处收敛性条件,得到概率约束规划逼近最优解集序列的几乎处处上半收敛性．     

HEC—RAS在溢洪道水面线计算中的应用

HEC—RAS软件是一款在国内外河道水面线计算中广泛运用的软件,但是在中小型水库溢洪道水面线计算中应用较少。通过工程实例将HEC—RAS计算结果与传统水面线计算结果相比较,该软件计算溢洪道水面线既省时又精确,还可获得流速、水头等其它结果,所以可在今后的设计中推广应用。     

基于改进蒙特卡洛法的框架强柱弱梁可靠度分析

针对蒙特卡洛方法存在的计算量大,计算时间长的缺点,借助曲线拟合的思想,提出了改进的蒙特卡洛可靠度分析方法。基于该方法并考虑计算模式、材料强度、几何尺寸的随机性,对抗震设计规范所提出的抗震概念设计进行了讨论,分析了钢筋混凝土结构的节点强柱弱梁可靠性。得出了不同抗震等级下节点强柱弱梁设计的可靠度,最后确定了2010版建筑抗震设计规范中框架柱端弯矩增大系数的调整对强柱弱梁的失效概率的影响规律,新规范调整后的柱端弯矩增大系数使强柱弱梁设计可靠性大大增加,达到了规范调整的目的。     

BEMD在复杂背景下弱小目标检测中的应用

针对复杂背景下的弱小目标检测与识别问题,提出了一种基于二维经验模态分解(Bidimensional Empirical Mode Decomposition,BEMD)的检测算法。待检测的原图像经过BEMD分解筛选出多个二维的内蕴模函数(Intrinsic Mode Functions,IMF)和趋势图像,使用全局门限法分割各个IMF,将处理后的IMFs综合成一个分割出待检测目标的结果图像。实验结果表明,该方法使用简洁的步骤,有效、准确地检测出弱小目标。     

三弧段型面联接的数控加工

论述了三弧段型面曲线的形成及其曲线参数方程,编制了三弧段型面的数控加工宏程序,适用于各种不同参数的三弧段型面的加工,且能够满足加工精度的要求。     

Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of quasi-static and transient dynamic problems in two-dimensional (2-D) nonhomogeneous linear viscoelastic media. A unit step function is used as the test functions in the local weak form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The correspondence principle is applied to such nonhomogeneous linear viscoelastic solids where relaxation moduli are separable in space and time variables. Then, the LBIEs are formulated for the Laplace-transformed viscoelastic problem. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-D problems. The moving least squares (MLS) method is used for approximation of physical quantities in LBIEs.