基于有限域GF上圆锥曲线的公钥密码算法

圆锥曲线密码学是一种新型的公钥密码学,迄今对圆锥曲线密码学的研究成果都是以有限域GF(p)上的圆锥曲线为基础的.本文将有限域GF(p)上的圆锥曲线C(GF(p))推广为有限域GF(2ⁿ)上的圆锥曲线C(GF(2ⁿ)),证明了圆锥曲线C(GF(2ⁿ))上的点和加法运算构成有限交换群(C(GF(2ⁿ)),),并给出了圆锥曲线群(C(GF(2ⁿ)),)的阶的计算.此外,提出了使用有限域GF(2ⁿ)上的圆锥曲线群构造公钥密码系统,并给出了ElGamal加密方案和数字签名算法(DSA)在圆锥曲线C(GF(2ⁿ))上模拟的算法,最后分析其安全性.     

一般增长曲线模型参数阵的BLU估计

考虑一般增长曲线模型：Ｙ＝Ｘ１ＢＸ２＋εＥ（Ｖｅｃ（ε））＝０Ｖ（Ｖｅｃ（ε））＝σ２ＶＩｎ（Ｖ０）本文对任一可估函数ＫＢＬ给出了它的ＢＬＵ估计（最佳线性无偏估计），并得到了方差σ２的一个无偏估计．     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

A critique of the unsaturable trap model of radiation damage in metals

The unsaturable trap model, which attributes the increase of the electrical resistivity of fcc metals during electron irradiation in the temperature regime of Stage-II recovery to the trapping of Stage-I_E interstitials at impurity atoms, is shown to be in serious disagreement with the experiments, contrary to opposite statements in the literature. As shown recently, the predictions of the unsaturable trap model are independent of the dimensionality of the diffusion of the Stage-I_E interstitials. Previous attempts to rule out a one-dimensional migration of the Stage-I_E interstitials (and hence the two-interstitial model) on the basis of the alleged agreement of the unsaturable trap model with Stage-II damage curves are thus meaningless. On the contrary, it is demonstrated that the two-interstitial model accounts for minute details of the measured Stage-II damage curves in a natural way.     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

An Algorithm for Computing the Singularity of the Generic Germ of a Pencil of Plane Curves

Abstract

We give an algorithm that describes the singularity of all but finitely-many germs in a pencil generated by two arbitrary germs of plane curve.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

Boolean operations on rasterized shapes represented by chain codes using space filling curves

This paper introduces a new algorithm for Boolean operations on rasterized geometric shapes that are represented with chain codes. The algorithm works in three steps. Firstly, the chain code symbols are transformed in the Hilbert space, where the overlaid chain code symbols are recognised. After that, a suitable starting cell is determined. Finally, the walk-about through the sequence of the initial chain code symbols is performed to obtain the sequence of chain code symbols representing the shape of the required Boolean operation. The algorithm is demonstrated on Freeman chain code in four directions. The time and space complexity of the proposed algorithm is linear, which was proven theoretically and confirmed by experiments.     

A new method for the automated selection of the number of components for deconvolving overlapping chromatographic peaks

Mathematical deconvolution methods can separate co-eluting peaks in samples for which (chromatographic) separation fail. However, these methods often heavily rely on manual user-input and interpretation. This is not only time-consuming but also error-prone and automation is needed if such methods are to be applied in a routine manner.