基于固定序的Bellman-Ford算法的改进

固定序算法是Bellman-Ford算法的一种基本改进算法。为了改变固定序算法在稀疏图上的劣势,本文通过预先订制参与迭代的点的计算顺序,对该算法进行了改进。实验表明,在稀疏图上, 改进后的算法相对于原算法计算效率提高了近50%, 并能够与国际流行的先进先出算法相媲美。本文的工作表明,固定序算法不仅在大规模稠密图上具有明显的优势,而且在稀疏图上也具有很强的竞争力。     

整数扩展欧几里得矩阵序列的选择项算法的修正

Wang和Pan提出了一个计算整数扩展欧几里得矩阵序列的选择项的算法,并把此算法应用于模有理数重构问题和数值有理数重构问题.这个算法仅消耗接近线性的时间复杂度,与目前已知的整数gcd算法的最佳时间复杂度相一致,而整数gcd算法只是此算法的一个特殊情形.分析了这个算法,指出了算法中由于考虑的不够全面而存在的错误,补充了矩阵序列性质的理论部分,并修正这个算法.     

基于精英区域学习的多种群自适应的差分进化算法

为了进一步提高差分进化算法的收敛速度、算法精度和稳定性,采用多种群技术来增加算法收敛速度和降低复杂度;利用精英区域学习策略来对算法的全局搜索能力和算法精度进一步提升,引进自适应免疫搜索策略,以实现自适应修正差分算法的变异因子和交叉因子。通过五个测试函数,把本文算法与最新文献中的算法进行对比,表明算法在收敛速度、精度和高维问题寻优能力方面的优越性。     

经过改进的求解TSP问题的蚁群算法

介绍了一种求解TSP问题的算法—改进的蚁群算法,算法通过模拟蚁群搜索食物的过程,可用于求解TSP问题,算法的主要特点是:正反馈、分布式计算、与某种启发式算法相结合.通过对传统蚁群算法的改进可以得到较好的结果.计算机仿真结果表明了该算法的有效性.     

线性规划的新算法

提出一种求解LP的新思想 ,基于这种思想给出了一种求解LP的新算法 ,其中从一个基准面到更深层基准面的推进算法是按算法与模型一体化思想构思的 ,借助切割面 ,把推进的模型与算法化为一维单峰函数求优的特殊模型与算法 ,既简单又初等 ,无需矩阵求逆 ,计算量很少 .新算法的另一个意义在于 ,它的核心算法可以有效地改进单纯形算法、Karmarkar算法和一种新椭球算法的迭代过程 ,还充分利用迭代过程解x^k 的全部信息     

蚂蚁算法和小生境遗传算法的融合

蚂蚁算法是一种新型的模拟进化算法,也是一种随机型智能搜索算法.较为系统的总结了算法的基本理论,分析了其基本算法解决TSP问题的模型,针对蚂蚁算法易出现停滞的缺点,把小生境遗传算法和蚂蚁算法融合,仿真比较实验结果表明优于基本蚂蚁算法.     

基于混合细菌趋药性的聚类分割算法

为解决模糊C均值算法对初始值敏感、容易陷入局部极值的问题,提出基于混合细菌趋药性的聚类分割算法,在简单细菌趋药性算法的基础上,将粒子群算法引入.新算法使用粒子群算法、细菌趋药性算法两步优化得到的结果作为模糊C均值算法的初始值,同时新算法中引入精英保持策略,进一步提高算法效率.实验结果表明,新算法具有较快的收敛速度,.同时能够获得较好的图像分割效果和质量.     

基于混合单纯形算法的模糊均值图像分割

针对模糊C均值算法用于图像分割时对初始值敏感、容易陷入局部极值的问题,提出基于混合单纯形算法的模糊均值图像分割算法.算法利用Nelder-Mead单纯形算法计算量小、搜索速度快和粒子群算法自适应能力强、具有较好的全局搜索能力的特点,将混合单纯形算法的结果作为模糊C均值算法的输入,并将其用于图像分割.实验结果表明:基于混合单纯形算法的模糊均值图像分割算法在改善图像分割质量的同时,提高了算法的运行速度.     

偏微分方程的局部保结构算法

讨论偏微分方程的局部保结构算法,它是原来的整体保结构算法的自然推广. 当边界条件适宜时, 局部保结构算法自然是整体保结构算法, 但整体保结构算法却不一定是局部保结构算法. 局部保结构算法的概念能解释不同保结构算法之间的差异性, 也能为分析和构造性能较好的保结构算法提供理论基础. 不仅如此, 合适的边界条件不再是局部保结构算法可应用于偏微分方程的必要条件, 从而拓宽了保结构算法的适用性. 还讨论了局部保结构算法的应用和系统构造问题, 得到了非线性Klein-Gordon方程的一些新的格式.     

GA-BP嵌套算法的理论及应用

分析了BP算法、遗传算法以及GA-BP-APARTING算法的特点,提出了GA-BP-NESTING算法.在人工神经网络的在线学习和离线学习方式下,分别对BP算法、GA算法、GA-BP-APARTING算法和GA-BP-NESTING算法进行了比较研究,研究发现:第一,网络初始权值的赋值对人工神经网络训练影响很大;第二,离线学习方式下GA-BP-NESTING算法效果最佳.     

Physicomechanical characteristics of a disperse-filled polytetrafluoroethylene

Composite polymer materials based on PTFE containing ultradisperse -sialon (1–10 wt.%) as the cross-linking agent are studied. It is shown that the injection of small amounts of fillers (1–2 wt.%) increases the degree of composite crystallinity. A correlation between the structure, element distribution on the surface layers of samples, and tribotechnical characteristics of composites is found. The change in the physicomechanical characteristics is associated with the effect of the interstructural plasticization.Ammosov Yakutsk State University, Yakutsk, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 797–806, November–December, 1999.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [M. Elad, Why simple shrinkage is still relevant for redundant representations? IEEE Trans. Inform. Theory 52 (12) (2006) 5559–5569], a new iterative method called parallel coordinate descent (PCD) was devised. We provide herein a convergence analysis of the PCD algorithm, and also introduce a form of the regularization function, which permits analytical solution to the coordinate optimization. Several other recent works [I. Daubechies, M. Defrise, C. De-Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. LVII (2004) 1413–1457; M.A. Figueiredo, R.D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Process. 12 (8) (2003) 906–916; M.A. Figueiredo, R.D. Nowak, A bound optimization approach to wavelet-based image deconvolution, in: IEEE International Conference on Image Processing, 2005], which considered the deblurring problem in a Bayesian methodology, also obtained element-wise optimization algorithms. We show that the last three methods are essentially equivalent, and the unified method is termed separable surrogate functionals (SSF). We also provide a convergence analysis for SSF. To further accelerate PCD and SSF, we merge them into a recently developed sequential subspace optimization technique (SESOP), with almost no additional complexity. A thorough numerical comparison of the denoising application is presented, using the basis pursuit denoising (BPDN) objective function, which leads all of the above algorithms to an iterated shrinkage format. Both with synthetic data and with real images, the advantage of the combined PCD-SESOP method is demonstrated.     

Superapproximation and Commutator Properties of Discrete Orthogonal Projections for Continuous Splines

This paper builds upon the L_p-stability results for discrete orthogonal projections on the spaces S_h of continuous splines of order r obtained by R. D. Grigorieff and I. H. Sloan in (1998, Bull. Austral. Math. Soc.58, 307–332). Properties of such projections were proved with a minimum of assumptions on the mesh and on the quadrature rule defining the discrete inner product. The present results, which include superapproximation and commutator properties, are similar to those derived by I. H. Sloan and W. Wendland (1999, J. Approx. Theory97, 254–281) for smoothest splines on uniform meshes. They are expected to have applications (as in I. H. Sloan and W. Wendland, Numer. Math. (1999, 83, 497–533)) to qualocation methods for non-constant-coefficient boundary integral equations, as well as to the wide range of other numerical methods in which quadrature is used to evaluate L₂-inner products. As a first application, we consider the most basic variable-coefficient boundary integral equation, in which the constant-coefficient operator is the identity. The results are also extended to the case of periodic boundary conditions, in order to allow appplication to boundary integral equations on closed curves.     

Effect of the adhesion interaction and the degree of filling on the internal stresses in finely divided crystalline fillers of epoxy composites

Two kinds of model composite materials with finely divided (1) crystal fillers—LiF or polyethylene-filled epoxy resin cured by polyethylenepolyamine — are investigated by X-ray diffractometry. It is found that tensile stresses arise in LiF crystals, which show a strong adhesion interaction with the binder, for all degrees of filling (from =2.2 to =74 vol.%) examined. Their values remain constant up to a degree of filling at which the boundary layers come into contact with one another. Then, the inner stresses decrease with increasing . In the crystalline regions of polyethylene, where the adhesion between the binder and crystals is weak, the inner stresses are compressive. It is shown that the thickness of the boundary layer of the matrix on the surface of filler particles can be evaluated by the method used.Institute of Polymer Mechanics, Latvian University, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 807–820, November–December, 1999.     

Rigid isotopy classification of real algebraic curves of bidegree (3,3) on quadrics

A rigid isotopy of nonsingular real algebraic curves on a quadric is a path in the space of such curves of a given bidegree. We obtain the rigid isotopy classification of nonsingular real algebraic curves of bidegree (3, 3) on a hyperboloid and on an ellipsoid. We also study of the space of real algebraic curves of bidegree (3, 3) with a single node or cusp. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 810–815, December, 1999.     

Embeddings of the classesH ω

In this paper we study functions belonging to the classesV _ε and ΛBV, which are encountered in the theory of Fourier trigonometric series. Necessary and sufficient conditions for the embedding of the classesH _ω in the classesV _ϕ and ABV are obtained. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 713–719, November, 1998. This research was supported by the program “Leading Scientific Schools” under grant No. 96/97-15-96073.