Waggling conical pendulums and visualization in mechanics

Students often find mechanics a difficult area to grasp. This paper describes an equation of motion for a waggling conical pendulum. A wide range of pendulum dynamics can be simulated with this model. The equation of motion is embedded in a graphical user interface (GUI) for its numerical solution in MATLAB. This allows a student's focus to be on the influence of different parameters on the pendulums dynamics. The simulation tool can be used as a dynamics demonstrator in a lecture or as an educational tool driven by the imagination of the student. By way of demonstration, the simulation tool has been applied to two damped pendulums and an inverted damped pendulum. The model has also been used to simulate resonance and has shown that there is a wide range of behaviour possible depending on the type of forcing applied. Finally, a forced conical pendulum as a system for harnessing wave energy is considered.     

倒数代换在极限计算中的应用

倒数代换是解决极限问题的一种好方法.正确、恰当地运用倒数代换会使问题简化、易解.     

互反判断阵比对值对满意一致性的影响

满意一致性是互反判断阵可否作为决策依据的指标.对CR>1的互反判断阵,一般是通过比对值的修正,使之达到满意一致性要求.利用多元隐函数偏导数及行列式基本性质,可以得出各比对值变化对满意一致性的影响比例.在已知影响比例情况下,比对值如何修正、修正多少就有了理论上的依据.     

基于两点累积信息原／倒变量展开的对偶优化方法的收敛性分析

基于两点累积信息原／倒变量展开的对偶优化方法的收敛性分析邢誉峰（北京航空航天大学固体力学研究所）钱令希（大连理工大学工程力学所）ＡＭＡＴＨＥＭＡＴＩＣＡＬＣＯＮＶＥＲＧＥＮＣＥＡＮＡＬＹＳＩＳＯＦＴＨＥＤＵＡＬＭＥＴＨＯＤＢＹＥＸＰＡＮＳＩＯＮＯＦＯ...     

应用功的互等定理计算弹性圆薄板挠曲面方程

本文在文献[1],[2]的基础上,进一步将功的互等定理推广应用于弹性圆薄板.提出一种求解具有复杂边界条件,受复杂载荷作用的圆板挠曲面方程的简便,通用的新方法.     

A reciprocal confluence tree unit and its applications

A theorem by Jaeschke is generalized in this paper and a fast and efficient implementation called Reciprocal Confluence Tree unit for implementing the new theorem is sketched. We shall show that it can be used to solve two problems: a hashing algorithm design problem and an access control mechanism design problem.     

Least-squares orthogonalization using semidefinite programming

We consider the problem of constructing an optimal set of orthogonal vectors from a given set of vectors in a real Hilbert space. The vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors. We show that the design of the optimal vectors, referred to as the least-squares (LS) orthogonal vectors, can be formulated as a semidefinite programming (SDP) problem. Using the many well-known algorithms for solving SDPs, which are guaranteed to converge to the global optimum, the LS vectors can be computed very efficiently in polynomial time within any desired accuracy.By exploiting the connection between our problem and a quantum detection problem we derive a closed form analytical expression for the LS orthogonal vectors, for vector sets with a broad class of symmetry properties. Specifically, we consider geometrically uniform (GU) sets with a possibly non-abelian generating group, and compound GU sets which consist of subsets that are GU.     

A simple procedure to obtain the extreme core allocations of an assignment market

Given an assignment market, we introduce a set of vectors, one for each possible ordering on the player set, which we name the max-payoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn out to give the extreme core allocations of the market. When the assignment game has a large core, all the max-payoff vectors are extreme core allocations.     

Divergences without probability vectors and their applications

In general, divergences and measures of information are defined for probability vectors. However, in some cases, divergences are ‘informally’ used to measure the discrepancy between vectors, which are not necessarily probability vectors. In this paper we examine whether divergences with nonprobability vectors in their arguments share the properties of probabilistic or information theoretic divergences. The results indicate that divergences with nonprobability vectors share, under some conditions, some of the properties of probabilistic or information theoretic divergences and therefore can be considered and used as information measures. We then use these divergences in the problem of actuarial graduation of mortality rates. Copyright © 2009 John Wiley & Sons, Ltd.     

Recognizing conic TDI systems is hard

In this note we prove that the problem of deciding whether or not a set of integer vectors forms a Hilbert basis is co-NP-complete. Equivalently, deciding whether a conic linear system is totally dual integral or not, is co-NP-complete. These statements are true even if the vectors in the set or respectively the coefficient vectors of the inequalities are 0?C1 vectors having at most three ones.     

Sequences of vectors that are orbits of operators

This paper characterizes sequences of vectors that are the orbits of a linear operator and sequences of vectors in a Hilbert space that are orbits of a unitary operator. The latter is applied to time series. Sequences of vectors in a Hilbert space that generalize random walks are also shown to be the orbits of a bounded linear operator.     

Balanced biorthogonal scaling vectors using fractal function macroelements on

Geronimo, Hardin et al. have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on [0,1]. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on [0,1] is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with two specific constructions with desirable properties in each case. The constructions will use macroelements supported on [0,1], some of which will be fractal functions.     

Optimal estimates of random vectors using information criteria

Information criteria are applied for estimation of random vectors. Normal random vectors and random vectors with an unknown distribution are considered. Both linear estimates and estimates represented by a measurable function of observations are derived.Translated from Vychislitel'naya i Prildadnaya Matematika, No. 62, pp. 105–113, 1987.     

Vector-Stability of Univariate Refinable Vectors

Stability is an expected property for refinable vectors, which is widely considered in the study of refinement equations. There are two types of stability for refinable vectors. One is the ordinary-stability, another is the vector-stability. The ordinary-stabilityconsiders the stability of entries of refinable vectors, but the vector-stability considers the stability of refinable vectors when they are considered as elements of super-Hilbert spaces. In this article, we give a necessary and sufficient condition for refinable vectors to be vector-stable. Our results improve on some known ones.     

Load-deformation relations in second-order elasticity

A method for determining overall load-deformation relations for small-strain elastic deformations has been adapted so that second-order elastic effects can be included in certain overall quantities, such as bending stiffness, without explicit determination of the second-order solution. The approach uses Betti's Reciprocal Theorem. The strains are considered small enough that third-order effects can be neglected but there is no restriction on the magnitude of the displacements. The method is applied to obtain the resultant force and moment to second order for cylindrical bars with arbitrary cross section under torsion, extension and torsion, bending by an end load, and twisting and bending to helical form.     

The sub-lattice structure of linear congruential random number generators

Sequences of pseudo-random numbers are discussed which are generated by the linear congruential method where the period is equal to the modulus m. Such sequences are divided into non-overlapping vectors with n components. In this way for each initial number exactly m/gcd(n, m) different vectors are obtained. It is shown that the periodic continuation (with period m) of these vectors forms a grid which is a sub-grid of the familiar grid generated by all m overlapping vectors. A sub-lattice structure also exists for certain multiplicative congruential generators which are often used in practice.     

基于GA-PLS和AdaBoost的故障诊断方法

提出一种基于GA-PLS和AdaBoost的液压系统故障诊断方法。该方法用遗传算法与偏最小二乘法相结合(Genetic algorithm-partial least squares,GA-PLS)的算法对初始特征向量进行筛选,提取出与故障信息相关程度高的特征向量,把该特征向量作为输入,运用AdaBoost(Adaptive Boost)方法建立分类器,以识别液压系统的工作状态和故障类型。对实验数据分析的结果说明,该方法能准确地选择出特征向量,并有效地应用于液压系统的故障诊断。     

Theory and Computation of Covariant Lyapunov Vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.     

Geometry of isometric reflection vectors

In this paper we study the geometry of isometric reflection vectors. In particular, we generalize known results by proving that the minimal face that contains an isometric reflection vector must be an exposed face. We also solve an open question by showing that there are isometric reflection vectors in any two dimensional subspace that are not isometric reflection vectors in the whole space. Finally, we prove that the previous situation does not hold in smooth spaces, and study the orthogonality properties of isometric reflection vectors in those spaces.     

Moments of Limits of Lightly Trimmed Sums of Random Vectors in the Generalized Domain of Normal Attraction of Non-Gaussian Operator-Stable Laws

Existence and nonexistence for moments of limiting random vectors of normalized, lightly trimmed sums of random vectors in the generalized domain of normal attraction of non-Gaussian operator-stable laws are studied. The idea of representing the limiting random vectors by infinite series is essentially used in the proofs.