Plastification and Damage in Wheel-Rail Rolling Contact – Case Study on a Crossing

A fully three-dimensional, dynamic model for a wheel running over a crossing is developed using an explicit finite element program. The full mass of the wheel and the crossing and elastic-plastic material behaviour are considered. The damage in the contact area is investigated with a very dense mesh taken from the dynamic model using a submodelling technique. With this kind of calculations the stresses and strains produced in the wheel and the crossing during the cross-over process can be determined, as well as the respective reaction forces in the bedding and the axle. Calculations for different crossing-geometries are performed. Finally a damage indicator is introduced to identify the probable location of crack initiation. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comments on “arithmetic coding as a non-linear dynamical system”

Nagaraj et al. [1], [2] present a skewed-non-linear generalized Luroth Series (s-nGLS) framework. S-nGLS uses non-linear maps for GLS to introduce a security parameter a which is used to build a keyspace for image or data encryption. The map introduces non-linearity to the system to add an “encryption key parameter”. The skew is added to achieve optimal compression efficiency. s-nGLS used as such for joint encryption and compression is a weak candidate, as explained in this communication. First, we show how the framework is vulnerable to known plaintext based attacks and that a key of size 256 bits can be broken within 1000 trials. Next, we demonstrate that the proposed non-linearity exponentially increases the hardware complexity of design. We also discover that s-nGlS cannot be implemented as such for large bitstreams. Finally, we demonstrate how correlation of key parameter with compression performance leads to further key vulnerabilities.     

Study on “double dawn”

The ancient record, “During the first year of King Yi, the day dawned twice at Zheng”, has provided important clues to early Chinese chronicles. The astronomical conditions and visible area distributions related to such a “double dawn” event are discussed, and the precision and current problems in the calculations of ancient astronomical phenomena are shown. On such a basis, all the solar eclipses from 1000 BC to 840 BC are calculated and their associated “double dawn” features investigated. The conclusion that the “double dawn” was a solar eclipse occurring on April 21st, 899 BC is corfirmed to be the most reasonable. Project supported by the Xia-Shang-Zhou Chronology Project and Director Foundation of the Chinese Academy of Sciences.     

谈“a-a=0”和“a/a=1(a≠0)”

<正>代数中的"a-a=0"和"a/a=1(a≠0)"具有统一、简单、对称等数学美,也蕴含着十分重要的数学思想.它的正用有"消元"(加减消元和约分消元)之功能;它的逆用有"构造"(裂项和添项)之功能;这两大功能在数学运用中有着十分重要的作用.所以,这看似简单的两个算式,不仅向人们展示了其数学的思想美和方法美,而且还能拓展我们的逻辑思维能力和创造思维能力.下面举例说明,供大家鉴赏,期望对读者能有启发和帮助.     

Comments on “A Note on the Paper “Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors””

Journal of Optimization Theory and Applications - Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012)....     

Remarks on “Quasi-contraction on a cone metric space”

Recently, D. Ili? and V. Rako?evi? [D. Ili?, V. Rako?evi?, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.     

命题:“若{x≥a,x≤a则x=a”的应用

<正>命题:"若x≥a x≤a,则x=a",体现了"相等"与"不等"的对立统一及其相互转化的关系.命题虽然十分简单,却在解答数学竞赛试题中发挥重要作用.本文举例介绍其应用.一、在求值中的应用例1(2013年全国初中数学联赛)已知实数a,b,c,d,满足:2a2+3c2=2b2+3d2=(ad-bc)2=6,求(a2+b2)(c2+d2)的值.分析与解答一方面,根据菲波那契恒等式和实数的平方是非负数可以得如下不等式:     

Comment on: a two-stage fourth-order “almost” P-stable method for oscillatory problems

In Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118) a fourth-order “almost” P-stable method for y″=f(x,y) is proposed. We claim that it is possible to retrieve this combination of multistep methods by means of the theory of parameterized Runge-Kutta-Nyström (RKN) methods and moreover to generalize the method discussed by Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118).     

A remark on “Connections and Higgs fields on a principal bundle”

The authors show that a unipotent vector bundle on a non–Kähler compact complex manifold does not admit a flat holomorphic connection in general. It was also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold that does not admit any unitary flat connection.     

“a=a·1”在解数学赛题中的运用

在解答数学竞赛题时，若能注意到a=a·1，将会收到意想不到的效果．现采撷几道赛题说明如下．     

证明“线段a=b+c”的基本思路

<正>在初中几何中,三条线段长分别为a,b,c,求证"a=b+c"的证明题是常见问题,尤其对于线段都不在同一直线的情形.本文针对这种情况给出三种基本思路,下面结合一道考试题进行说明.问题如图1,∠B=∠C=90°,AE平分∠DAB,DE平分∠ADC.求证:AD=AB+CD.由于线段AD、AB和CD相互分离,不在同一直线上,因此需要想方设法进行转化,有三种思路.一、将a一分为二此方法将较长线段AD分割成两部分,使