极坐标方程的通式、特式与曲线的周期

对于曲线的极坐标方程,文[1]引进了通式、特式的概念,有效地解决了文[2]所指出的有关极坐标的问题.文[3],[4]为方便画图而引进了曲线周期的概念,然而出现了比较复杂的问题[5],因此文[1]主张舍弃这个概念,但是用文[1]的方法解决极坐标画图问题仍然感到不便.     

具有两个中心点的平面二次系统

<正> 本文给出二次系统具有两个中心点的充要条件,及双中心情形下四种全局拓扑结构的判别方法.文[1]用若干不变量给出上述充要条件,文[2]讨论了至少具有一个中心点的二次系统的全局拓扑结构,其中有关双中心的四种之一似有误.在本文送审期间,我们见到了文[3]的工作,它用[1]的方法,改进并完善了[2]的结果.对于某些常见的方     

受轴力作用的平面杆的圣维南问题

本文利用文[1]中讨论的主轴应力坐标上的平衡微分方程,通过假设平面杆在轴力作用下的主轴应力曲线,获得了该问题的圣维南问题的解,指出剪应力的衰减速度是a3/y3,轴力趋于常数的速度是a2/y2.     

曲线拐点充分条件证明中的常见错误

文[1]给出了判别曲线拐点的两个充分条件,文[2]给出了一个充分条件,但三个定理的证明都是错误的.同时,文[1]的两个推论也是错误的.本文通过反例分析了其错因,并给出了文[1]中一个拐点充分条件的正确证明.     

二次系统极限环线的(3,1)分布

<正> 文[1],[2]指出:在有限部分具有两个奇点,在无穷远只有一个简单奇点,而且是鞍点情况下,二次系统可以至少出现四个极限环,且呈(3,1)分布结构.文[1]举出二阶细焦点方程,文[2]举出三阶细焦点方程,都用[?]扰动方法使极限环产生(3,1)分布结果.     

实轴上无限个间断点的Riemann问题

本文将讨论实轴上的如下Riemann边值问题:其系数和自由项都可能有可数个第一类间断点。当边界L是实轴上可数个互不衔接的线段。{L_k}_1~∞的并集,而且加上某些限制时的齐次Riemann问题的讨论见于文[1]。我们的讨论对边界L的限制大大放宽,而且考虑了非齐次问题。本文将沿用文[2]的记号、概念和结果。故凡在文[2]中已加说明的,本文不再重复。     

四边形两个优美性质的深入探究

文[1]、[2]分别给出了圆内接四边形中有关三角形内切圆、旁切圆的两个几何恒等式,并综合运用三角、代数知识给出了证明.这两个恒等式"优美"的几何背景是什么?如何用几何方法给出它们的证明?笔者对此作了进一步探究,得到了圆内接四边形一个非常优美的几何性质,由此很容易证得文[1]与文[2]中的有关性质.     

一个"通法"的完善

为解决问题:"圆锥曲线上存在两点关于某直线对称,求某一参变量的取值范围",文[1]给出了四个与圆锥曲线弦的中点的相关结论,并运用这些结论简捷地解决了上述问题.文[2]认为,掌握这四个结论并非轻松之事(笔者也有同感),并研究得到解决这一问题的"通法":……     

三角形的一个向量性质再探究

文[1]给出了三角形重心向量的一个性质,并进行了空间拓广.文[2]对三角形内任一点的向量性质进行了探究,并进行了空间拓广.文[3]对文[1]的性质进行再探究,本文类比文[3]对文[2]的性质进行再探究,得到了两个定理,现叙述如下.定理1如图1所示,已知△ABC及其内部一点P,若λ1PA λ2PB     

对数学问题1720的再研究

《数学通报》(文[1])2008年2期问题1720为:△ABC中,以BC为轴(长轴或短轴均可)作一椭圆交AB于E,交AC于F(如图1).设M、N分别是点E、F关于直线BC的对称点,EN交FM于D.求证:AD⊥BC. 文[2]中供题者利用伸缩变换给出了上述问题的证法,文[3]给出了该问题的常规解法,并把它进行了探究得出以下结论(文[3]中的性质12),同时把结论拓展到双曲线.     

On Meeting Energy Balance Errors in Co-Simulations

The term co-simulation denotes the coupling of some simulation tools for dynamical systems into one big system by having them exchange data at points of a fixed time grid and extrapolating the received data into the interval, while none of the steps is repeated for iteration. From the global perspective, the simulation thus has a strong explicit component. Frequently, among the data passed across subsystem boundaries there are flows of conserved quantities, and as there is no iteration of steps, system-wide balances may not be fulfilled: the system is not solved as one monolithic equation system. If these balance errors accumulate, simulation results become inaccurate. Balance correction methods which compensate these errors by adding corrections for the balances to the signal in the next coupling time step have been considered in past research. But establishing the balance of one quantity a posteriori due to the time delay in general cannot establish the balances of quantities that depend on the exchanged quantities, usually energy. In most applications from physics, the balance of energy is equivalent to stability. In this paper, a method is presented which allows users to choose the quantity that should be balanced to be that energy, and to accurately balance it. This establishes also numerical stability for many classes of stable problems.     

等效均衡函数的性质及均衡函数的构造

从均衡函数的等效性出发研究均衡函数的性质,证明了等效的均衡函数之和、积以及数乘仍为均衡函数,并且得到的新均衡函数与原均衡函数等效,这些性质表明等效的均衡函数关于加法和乘法运算均具有半群的代数结构。另外,进一步讨论了构造均衡函数的方法,给出了两个构造均衡函数的定理,该方法具有一般性,现有文献中的均衡函数几乎都能由其构造得到。     

Balance in complete cohomology

The balance of complete cohomology for modules that admit complete resolutions has been established by Christensen and Jorgensen (2013), as well as by Enochs, Estrada and Iacob (2012), by using two types of constructions on a given bicomplex. In this paper, we show that these constructions are closely related to each other. We also present an alternative proof of balance, which is based on the corresponding assertion for ordinary cohomology.     

A nonlinear model for rotor-shaft joints of high speed rotor systems with internal damping

Viscous internal damping in joints of high speed rotor systems causes instabilities above a certain frequency of revolution. In the majority of cases a nonlinearity adjusts the stability margin towards higher frequencies. In this paper an analytical solution of a nonlinear four degrees of freedom rotor model with internal damping is proposed, which enables to clearly analyse the influence of shaft stiffness, connection stiffness, rotor mass and shaft mass. The steady state solution of the unbalance case and the stability boundaries are deduced analytically. The stabilizing effect of the nonlinearity is shown. The analytical solutions are in good agreement with numerical results obtained by FERAN, a rotor dynamic simulation tool. A model, representing the rotor–shaft connection with an o–ring has been analyzed by a hydro pulse rig. Beneath the linear way, two further approaches to describe the measured hysteresis, a cubic and a bilinear force law are shown in the paper. The different analytical and numerical results for the whole rotor system with these three approaches are compared. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hyperbolic Balance Laws with a Non Local Source

This paper is devoted to hyperbolic systems of balance laws with non local source terms. The existence, uniqueness and Lipschitz dependence proved here comprise previous results in the literature and can be applied to physical models, such as Euler system for a radiating gas and Rosenau regularization of the Chapman–Enskog expansion.     

On the determination of the worst sampling error in a communication system for pulse amplitude modulated signals. Part II: The finite dimensional model

This paper is dedicated to the problem of optimizing the transmission properties of a Pulse Amplitude Modulation (PAM) system. The system is disturbed by a random timing jitter in the sampling device which periodically evaluates the continuous output signal at discrete times. Mathematically the timing jitter is a random variable with unknown probability distribution. So, our optimization problem turns out to be actually a minimax problem, for which mathematical game theory with its powerful concepts becomes the suitable frame for our analysis.In the first part [4] we have established a general existence theorem for the minimax problem, and we have worked out some properties of solutions in the case that the feasible impulse responses form a space of infinite dimension.This part summarizes results which we obtain, if we allow only for impulse responses lying in a certainn-dimensional subspace of the original space (see [2, 3]). By general results from semi-infinite optimization (see [1]) we know that, writing the minimax problem as a semi-infinite optimization problem, we can reduce the number of restrictions from infinity to a numbersn+1. On the basis of our special model we present a theory of uniformly singular quadratic forms, which has been developed (see [3]) in order to get additional statements abouts.In this way we supplement the work of Krabs [6], who was the first to present such a finite dimensional model, arguing that it is impossible for an engineer to construct a system in a way that an arbitrary impulse response is realized, unless this impulse response has a simple structure (for instance a low pass filter).The first two paragraphs have been taken almost literally from part I in order to render the lecture more comfortable. The interesting parts, however, are the following ones, where the results specific for the finite dimensional case are worked out.     

An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks

Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in response to environmental stimuli can be quantified using flux balance analysis by parameterizing the linear program with respect to extracellular conditions. However, for most large, genome-scale metabolic networks of practical interest, the resulting parametric problem has multiple and highly degenerate optimal solutions, which are computationally challenging to handle. An improved multi-parametric programming algorithm based on active-set methods is introduced in this paper to overcome these computational difficulties. Degeneracy and multiplicity are handled, respectively, by introducing generalized inverses and auxiliary objective functions into the formulation of the optimality conditions. These improvements are especially effective for metabolic networks because their stoichiometry matrices are generally sparse; thus, fast and efficient algorithms from sparse linear algebra can be leveraged to compute generalized inverses and null-space bases. We illustrate the application of our algorithm to flux balance analysis of metabolic networks by studying a reduced metabolic model of Corynebacterium glutamicum and a genome-scale model of Escherichia coli. We then demonstrate how the critical regions resulting from these studies can be associated with optimal metabolic modes and discuss the physical relevance of optimal pathways arising from various auxiliary objective functions. Achieving more than fivefold improvement in computational speed over existing multi-parametric programming tools, the proposed algorithm proves promising in handling genome-scale metabolic models.     

Ordered spatial sampling by means of the traveling salesman problem

In recent years, spatial sampling has been the subject of a flourishing literature. Its use had become widespread due to the availability of topographical information about statistical units, especially in the environmental context. New algorithms enable us to take advantage of spatial locations directly. In this paper, we present a new way of using spatial information by using traditional sampling techniques as systematic sampling. By means of a famous optimization method, the traveling salesman problem, it is possible to order the statistical units in a way that preserves the spatial correlation. Next ordered sampling methods are applied on the statistical units. Therefore we can render spatial some non-spatial methods. An economic application on real data is presented and different spatial and non-spatial methods are tested. Results are compared in terms of variance estimation and spatial balance, in order to establish the possibility of spatializing traditional sampling methods and of implementing them on data of different nature, among which economic ones.     

关于广义蝶图的平衡指标集

In this paper, we introduce the concept of the general butterfly graph B[m, n; d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m, n; d] to exist.     

基于IMO-SLFDA的大规模分布式光伏并网的智能配电网相位平衡研究

分布式光伏的大量接入智能配电网后,可能导致三相电流的失衡,进而破坏配电系统的安全稳定性。对此,本文构建了以电流不平衡和电能损失最小化为目标的含分布式光伏的配电网优化的多目标模型,旨在解决大规模分布式光伏发电并网后配电网相位平衡的问题;然后,用随机单纯形法对混合蛙跳算法进行优化,改进了蛙跳算法求解优化问题时极易陷入局部最优以及计算效率较低的缺点,并和决策算法相结合,提出适用本文算例的改进的多目标混合蛙跳决策算法,确保能以极快的搜索速度和较高的计算精度得到最优解;最后,以IEEE-123节点三相不平衡测试系统为例,通过控制变量的相关操作实现配电系统的三相平衡。对比分析基础案例和优化算例的差异,验证了本文所提算法的先进性和实用性。