Proposition II (Book I) of Newton’s <Emphasis Type="Italic">Principia</Emphasis>

After preparing the way with comments on evanescent quantities and then Newton’s interpretation of his second law, this study of Proposition II (Book I)— Proposition II Every body that moves in some curved line described in a plane and, by a radius drawn to a point, either unmoving or moving uniformly forward with a rectilinear motion, describes areas around that point proportional to the times, is urged by a centripetal force tending toward that same point. —asks and answers the following questions: When does a version of Proposition II first appear in Newton’s work? What revisions bring that initial version to the final form in the 1726 Principia? What, exactly, does this proposition assert? In particular, what does Newton mean by the motion of a body “urged by a centripetal force”? Does it assert a true mathematical claim? If not, what revision makes it true? Does the demonstration of Proposition II persuade? Is it as convincing, for example, as the most convincing arguments of the Principia? If not, what revisions would make the demonstration more persuasive? What is the importance of Proposition II, to the physics of Book III and the mathematics of Book I?     

水下工程平面定位控制系统

针对大江大河水流环境下的水下工程平面精确定位难题，进行水下工程平面测量定位系统应用性研究。将水下电视技术和多阵元基阵的短基线水声定位技术相结合，解决了传统水声定位精度低的问题。采用多基元短基线定位方法进行快速定位检测，搜寻并确认目标，处理、记录、显示成果，获得了满足工程精度要求的水下平面定位系统，保证了水下工程的质量。     

Geometrical constructions equivalent to non-linear algebraic transformations of the plane in Newton's early papers

Summary The theory of constructive formation of plane algebraic curves in Newton's writings is discussed in § 1: the apparatus by which Newton forms the curves, Newton's theorems on forming unicursal curves, his theory of conics, and his theory of (m, n) correspondence. Special Cremona plane and space transformations obtained by Newton's organic method are dealt with in § 2. The article ends with § 3, which shows two different directions in the theory of the constructive formation of plane algebraic curves in the XVIII-XIXth centuries. A synopsis is appended.Abbreviations MPN The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside, Vols. 1–3, Cambridge, 1967–1969 - Hudson H. Hudson, Cremona Transformations in Plane and Space, Cambridge, 1927 - PT (abridged) Philosophical Transactions of the Royal Society 1665–1800 (abridged), London, 1809 - Andreev ₁ K. A. Andreev, On geometrical correspondences ... (in Russian), Moscow, 1879 - Andreev ₂ K. A. Andreev, On the Geometrical Formation of Plane Curves (in Russian), Kharkov, 1875     

Beitrag zur Theorie der konvexen Bereiche der euklidischen Ebene

Summary The theory of plane convex domains contains some gaps. The present paper contains an exposition, 3 conjectures, one of which is new, as well as partial proofs of the latter conjecture.     

The detection of earnings manipulation: the three‐phase cutting plane algorithm using mathematical programming

The primary goal of this study was to propose an algorithm using mathematical programming to detect earnings management practices. In order to evaluate the ability of this proposed algorithm, the traditional statistical models are used as a benchmark vis‐à‐vis their time series counterparts. As emerging techniques in the area of mathematical programming yield better results, application of suitable models is expected to result in highly performed forecasts. The motivation behind this paper is to develop an algorithm which will succeed in detecting companies that appeal to financial manipulation. The methodology is based on cutting plane formulation using mathematical programming. A sample of 126 Turkish manufacturing firms described over 10 financial ratios and indexes are used for detecting factors associated with false financial statements. The results indicate that the proposed three‐phase cutting plane algorithm outperforms the traditional statistical techniques which are widely used for false financial statement detections. Furthermore, the results indicate that the investigation of financial information can be helpful towards the identification of false financial statements and highlight the importance of financial ratios/indexes such as Days' Sales in Receivables Index (DSRI), Gross Margin Index (GMI), Working Capital Accruals to Total Assets (TATA) and Days to Inventory Index (DINV). Copyright © 2009 John Wiley & Sons, Ltd.     

Nuclear fusion and irregular cytokinesis in binucleate and tetraploid cells ofVicia faba after caffeine treatment

Summary By means of 3 h treatment with 0.2% caffeine solution, binucleate and tetraploid cells were obtained in the lateral root meristem ofVicia faba. During recovery changing rates of fused interphases were noticed. Cell walls were formed in the equatiorial plane of the preceeding division of binucleate and tetraploid cells at interphase and in the course of bimitosis or 4n-mitosis at prophase or metaphase; during bitelophase a constriction of the fused nuclei could be seen. The conclusion is that the basic requirements of cytokinesis are not affected by caffeine.     

Abduction, tomography, and other inverse problems

Charles S. Peirce introduced in the late 19^th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.     

基于语义约束与Graph Cuts的稠密三维场景重建

本文提出一种新颖、有效的稠密三维场景重建算法.在城市建筑场景的重建中,为了快速恢复稠密、准确的深度信息,本文算法首先在视图中对建筑区域进行了语义分割以降低非重建区域(如天空、地面等)的干扰,在提高整体重建速度的同时也增强了采用平面模型对其进行重建的可靠性;然后,在通过基于DAISY特征的空间点扩散方法获取的初始深度图的基础上,针对传统算法难以重建的弱纹理、倾斜表面等区域,本文算法依据场景分段平滑的假设,在超像素级MRF能量优化框架中对其相应的空间平面进行了推断.由于能量函数融合了初始深度图的约束、空间平面先验及空间平面间的几何关系等信息,而且候选平面集通过平面拟合和已知平面约束下的多方向平面扫描两种方法构造,使得相应的两阶段迭代Graph Cuts对能量函数的求解更快速和精确.在标准数据集和真实数据上的实验表明,本文算法能有效克服光照变化、透视畸变、弱纹理区域等因素的影响,快速恢复建筑区域完整的深度图.     

高纯铝再结晶晶界面的择尤取向

相比于传统的晶体择尤取向（晶体织构,简称织构）,晶界面择尤取向是一个新的科学问题.系统地研究晶界面择尤取向的形成规律和演化机制对合理调控显微组织结构以显著改善材料的各种使用性能具有非常重要的科学意义和应用价值.本文利用基于体视学原理和电子背散射衍射技术的晶界特征分布五参数表征分析方法,研究了冷轧变形高纯铝（99.99%）再结晶晶界面的择尤取向问题.结果表明,在再结晶及晶粒长大过程中,晶界面择尤取向由最初的{2 2 3}晶面转变为{1 1 1}晶面,最后取向在{1 0 0}晶面上.分析指出,冷轧变形高纯铝再结晶组织中,小角度晶界（取向差介于2°~15°）是其晶界构成的主体部分;在晶粒长大过程中,晶体织构由{1 1 0}〈1 1 2〉黄铜织构为主转变为以{0 1 1}〈1 0 0〉高斯织构和{0 2 3}〈1 0 0〉织构共存为主,受晶面能和晶体织构的影响,小角度晶界一般择尤取向于可形成能量较低的倾侧型小角度晶界所对应的晶面上.这是导致高纯铝再结晶晶界面择尤取向随晶粒长大而发生上述规律性变化的主要原因.     

Elaboration of an in vivo model, in half life size, for aeronautical purposes]

Toxic effects of combustion products originating from plane cabin constituents are studied, in vivo, in Rats. The model associates an important combustion room, and an experience room containing eight revolving cages for Rats; these cages allow a remote control of the movements of the Rats which can be electrically stimulated and ejected. Such a device permits to study the incapacitance, i.e. the inability to move. For the combustion of a seat, without ventilation, incapacitation appears in 2 to 6 min. Biochemical screening demonstrates on increase of pCO2, carboxyhemoglobin and glycemia and a decrease of pO2.     

基于三层路网优化策略模型的关联交叉口序列研究

以若干个连续交叉口构成的关联交叉口序列为单位,对平面信号交叉口相位的禁／放行状态进行优化建模;建立以减少延误时间和平均排队长度为目标,同时考虑驾驶员的主观心理一生理因素,寻求平面信号最优控制交叉口配时参数为最终目标的三层路网优化控制模型;最后构造出与驾驶加速度紧密关联的、三层模型架构下的目标策略函数。     

<Emphasis Type="Italic">Newton's Argument for Proposition 1 of the</Emphasis> Principia

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center' – we describe two serious flaws in the Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.' (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Galileo’s quanti: understanding infinitesimal magnitudes

In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, Evangelista Torricelli’s theory of indivisibles can be regarded as a natural development of Galileo’s insights about infinitesimal magnitudes, transformed into a geometrical method for calculating the area of unlimited plane figures.     

一种岩石损伤流变模型及数值分析

根据石膏角砾岩的蠕变特性,建立石膏角砾岩的损伤流变模型;推导有限元计算中黏弹塑性损伤流变模型黏性应变的计算公式,结合初应变法的基本原理,分析模型的有限元求解过程;用MATLAB编制了损伤流变模型的平面应变有限元计算程序。利用编制的程序对石膏角砾岩蠕变试验进行有限元分析,有限元计算结果与蠕变试验结果吻合得较好,表明采用统计损伤理论研究岩石的非线性流变是可行、有效的。     

The conduction velocity,number and diameter of unmyelinated fibers in Remak's nerve

Summary Remak's nerve in the chicken was examined ultrastructurally and electrophysiologically to determine the characteristics of fibers in the nerve trunk. The ratio of unmyelinated fibers to myelinated ones was 1111. The mean number of unmyelinated fibers was 3555±232 (SEM, n=5) and they had a mean diameter of 0.502±0.034 (SEM) m. The compound action potential consisted almost entirely of a large diphasic waveform which had a mean peak conduction velocity of 0.62±0.031 (SEM, n=5) m·s^–1 at 37°C.     

Mean Motions in Ptolemy’s <Emphasis Type="Italic">Planetary Hypotheses</Emphasis>

In the Planetary Hypotheses, Ptolemy summarizes the planetary models that he discusses in great detail in the Almagest, but he changes the mean motions to account for more prolonged comparison of observations. He gives the mean motions in two different forms: first, in terms of ‘simple, unmixed’ periods and next, in terms of ‘particular, complex’ periods, which are approximations to linear combinations of the simple periods. As a consequence, all of the epoch values for the Moon and the planets are different at era Philip. This is in part a consequence of the changes in the mean motions and in part due to changes in Ptolemy’s time in the anomaly, but not the longitude or latitude, of the Moon, the mean longitude of Saturn and Jupiter, but not Mars, and the anomaly of Venus and Mercury, the former a large change, the latter a small one. The pattern of parameter changes we see suggests that the analyses that yielded the Planetary Hypotheses parameters were not the elegant trio analyses of the Almagest but some sort of serial determinations of the parameters based on sequences of independent observations.     

An Improved Approach for Estimating the Mean and Standard Deviation of a Subjective Probability Distribution

The literature offers many formulas for estimating the mean and standard deviation of a subjective probability distribution (a well-known example is the PERT formulas). This paper shows that some basic underlying assumptions behind most of these formulas are inappropriate; a more appropriate framework is then proposed. We then develop new formulas that can estimate mean and standard deviation much more accurately than the currently available formulas.©1997 John Wiley & Sons, Ltd.     

Asymmetries in conditional mean and variance: modelling stock returns by asMA‐asQGARCH

We propose a nonlinear time series model where both the conditional mean and the conditional variance are asymmetric functions of past information. The model is particularly useful for analysing financial time series where it has been noted that there is an asymmetric impact of good news and bad news on volatility (risk) transmission. We introduce a coherent framework for testing asymmetries in the conditional mean and the conditional variance, separately or jointly. To this end we derive both a Wald and a Lagrange multiplier test. Some of the new asymmetric model's moment properties are investigated. Detailed empirical results are given for the daily returns of the composite index of the New York Stock Exchange. There is strong evidence of asymmetry in both the conditional mean and the conditional variance functions. In a genuine out‐of‐sample forecasting experiment the performance of the best fitted asymmetric model, having asymmetries in both conditional mean and conditional variance, is compared with an asymmetric model for the conditional mean, and with no‐change forecasts. This is done both in terms of conditional mean forecasting as well as in terms of risk forecasting. Finally, the paper presents some evidence of asymmetries in the index stock returns of the Group of Seven (G7) industrialized countries. Copyright © 2004 John Wiley & Sons, Ltd.