擂台赛

擂台1 翻硬币问题(coin) 现行我们把4X4=16个硬币放在桌上排成一个方阵。这些硬币的正面是白色的,反面是黑的。现在我们只可以对这些硬币进行一种操作,就是把一个硬币和它上下左右相邻的四个硬币一起翻面。求最少的操作次数,使得所有的硬币都变成正面向上或反面向上。     

有理插值的广义QD算法

在Pade表的研究与计算中,Rutishauser的QD算法起着重要作用。该算法可用于构造Pade表中的一个下降阶梯上的元素,即若级数f(z)=sum from i=0 to ∞(c_iz~i)正规(对于所有m和n,Hankel矩阵H(m,n,n)非奇异,那么对于任何k≥1,存在连分式 。_b。0。。b。n0。。b。 f_k(z)=c_0+c_1z+…+c_(k-1)z~(k-1)+((c_kz~k)/1)-((q_1~kz)/1)-((e_1~kz)/1)-((q_2~kz)/1)-((e_2~kz)/1)-…,     

基于两步测量方法及其最少观测次数的任意量子纯态估计

量子状态层析所需要的完备观测次数d~2(d=2~n)随着状态的量子位数n的增加呈指数增长,这使得对高维量子态的层析变得十分困难.本文提出一种基于两步测量的量子态估计方法,可以对任意量子纯态的估计提供最少的观测次数.本文证明:当选择泡利观测算符,采用本文所提出的量子态估计方法对d=2n维希尔伯特空间中的任意n量子位纯态进行重构时,如果为本征态,那么所需最少观测次数memin仅为memin=n;对于包含l(2 6 l 6 d)个非零本征值的叠加态,重构所需最少观测次数msmin满足msmin=d+2l..3,此数目远小于压缩传感理论给出的量子态重构所需测量配置数目O(rd log d),以及目前已发表论文给出的纯态唯一确定所需最少观测次数4d..5.同时给出最少观测次数对应的最优观测算符集的构建方案,并通过仿真实验对本文所提出的量子态估计方法进行验证,实验中重构保真度均达到97%以上.     

n个元素分类(sort)的一个算法

本文给出的是分类 n 个元素的一个递归算法,其时间复杂性为n log n-5/4 n+1og n~(1/2)+C,这个值已经和分类问题的理论下界相当接近。目前所知的和它同级的分类法,如堆分类法(Heapsort)和合并分类法(Mergesort)等,虽然都是 O(nlogn)级的,但所需比较次数都比本文提供的算法多。本文共分三部分:1.最少插入分类法2.时间复杂性3.作者的猜想     

多输出弹性k-旋转对称布尔函数的存在性与构造

多输出布尔函数可由多个单输出布尔函数表示,在分组密码中有着广泛的应用.多输出k-旋转对称布尔函数(k-RSBF)是多输出旋转对称布尔函数(RSBF)的扩展.本文首先研究多输出旋转对称函数和多输出k-旋转对称函数的轨道分布情况,给出了计算两类函数中长度相同轨道个数的方法.其次研究了平衡多输出k-旋转对称布尔函数的存在性,给出了在选择合适的k的前提下,n=pr、n=2pr和n=2r时,平衡(n,m)k-RSBF的构造方法.之后研究弹性多输出k-旋转对称布尔函数的存在性,分别给出了r≥3,n=2r,2≤m≤2r-r,k=2时1阶弹性(n,m)k-RSBF的构造方法,以及p为奇素数,r≥2,n=pr,2≤m≤p-1,k=p时1阶弹性(n,m)k-RSBF的构造方法.最后我们还对两种方法得到的1阶弹性多输出k-旋转对称布尔函数进行仿真测试.     

一种基于数据分块的快速原地归并算法

与其它排序算法相比,二路归并最适合于对两个有序子表进行排序.归并长度分别为m和n的两个有序子表,经典算法有两种.第一种算法完成归并需要○(m+n)的附加空间,○(m+n)次比较和移动.第二种算法是原地的,但完成归并需要○(m+n)次比较和○(m×n)次移动.经过长期研究,提出了一种基于数据分块的快速原地归并算法.新算法通过将数据分块、对数据块排序等方法最多用○((m+n)log2√m+n次比较和○((m+n)3/2)次移动完成两个有序子表的原地归并.实验证明,该算法与经典的原地算法相比,极大地降低了元素的移动次数和算法的运行时间.     

最少比较排序问题中S(15)和S(19)的解决

最少比较排序问题就是要研究在最坏情况下,对n个元素完成排序所需要的最少比较次数S(n)。1965年M.Wells用穷举法证明了S(12)=30。2002年和2004年,M.Peczarski通过计算先后得到S(13)=34,S(14)=38,S(22)=71。文章在Wells算法和Peczarski算法基础上,设计了一个新的PS算法,并改进了线性扩展计数算法,在并行机"南开之星"上计算得到S(15)=42,S(19)=58。     

n中取m代码的完全自校验(TSC)校验口的一种新的设计方法

本文提出了为n中取m代码设计有效的完全自校验(TSC)校验■的一种新方法。该方法基于把输入码变量划分成任意的r类。本文确定了在m,n和r中必须保持必要的设计条件。校验■基本上由与1/2到1/2子校验■连接的m/n到1/2子校验■组成。所进行的成本分析指出,对于 n≤4m 的多由m/n 代码,r值导于3或4获得最经济的校验■。同早期的一些设计相比较,逻辑复杂性和测试复杂性方面有了很大的改进。     

春小麦新品种“沈农一号”育成简况

1.选育经过“沈农1号”是我专业系统选育出来的春小麦新品种。1963年,黑龙江省农科院提供我院一批进行小麦秆锈多小种试验的材料。经过成株鉴定,在“辽春1号”和“克刚”杂交的选系中,发现有4个单株对秆锈小种21群(即:21,21c_1,21c_2,21c_3),194,19,34c_1,和40号及对自然流行的叶锈,表现高度抵抗,编号为     

用参数法求一些特殊的线性代数方程组的数值解

本文将求解线性方程组数值解的双参数法进行推广,得到(?)种求解一些特殊的线性方程组的较为(?)般的方法-参数法,并具体给出利用三组参数求解拟二对角方程组和拟Hessen-berg方程组的算法.此算法具有明显的优越性.比如,在求解拟二对角方程组时,和利用LU分解法相比,乘除运算的次数由11n-16变为9n+20,所需要设定的向量组由5个降为4个.在求解拟Hessenberg方程组时,和Gauss消去法相比,除法运算的次数由1/2n(n+1)变为3n-4.这对求解大型的拟三对角方程组和拟Hessenberg方程组非常有利.当然,此种方法还可以用来求解其它一些方程组。     

How to detect a counterfeit coin: Adaptive versus non-adaptive solutions

In an old weighing puzzle, there are n?3 coins that are identical in appearance. All the coins except one have the same weight, and that counterfeit one is a little bit lighter or heavier than the others, though it is not known in which direction. What is the smallest number of weighings needed to identify the counterfeit coin and to determine its type, using balance scales without measuring weights? This question was fully answered in 1946 by Dyson [The Mathematical Gazette 30 (1946) 231-234]. For values of n that are divisible by three, Dyson's scheme is non-adaptive and hence its later weighings do not depend on the outcomes of its earlier weighings. For values of n that are not divisible by three, however, Dyson's scheme is adaptive. In this note, we show that for all values n?3 there exists an optimal weighing scheme that is non-adaptive.     

Statistical edge-based feature selection for counterfeit coin detection

Multimedia Tools and Applications - The number of counterfeit coins released into circulation is persistently increasing. According to official reports, the mass majority of these coins are...     

一种硬币鉴别系统的设计与实现

介绍了一种可用于我国现行流通硬币的鉴别系统.该系统以电涡流传感器、光电传感器为检测手段,以LM3S1138微控制器为控制核心,设计并实现了对硬币面值的快速识别及实时显示、对假币的辨伪和清退,系统鉴别精度高,成本低,具有一定的应用价值.     

The effect of rounding on payment efficiency

Theory predicts that dismissing the 1 and 2 euro cent coins from the denominational range of the euro facilitates payment efficiency. To examine whether this theory holds true in practice, data were collected for the Netherlands before and after September 2004, which marks the day that retail stores were allowed to round all amounts at 5 euro cents. The data consist of wallet contents for three cross sections of individuals. As the amounts of various coins in wallets are correlated, a multivariate Poisson-log Normal model is proposed to analyze these data. It is found that rounding leads to less 1 and 2 cent coins in wallets, but that still other coins are over or underrepresented, thereby suggesting that the euro range does not yet lead to fully efficient payment behavior.     

最少钱币数量的计算与钱币面额的确定

钱币种类的发行和确定在相对长的一段时间内会保持一定程度的稳定性，钱币的总量和面额是一个国家在中长期通过规划和预算来进行确定的。那么怎么来确定钱币的面额，使得尽可能方便人们使用，不但便于计算，也要尽可能降低使用频率，这是一个比较实际和实用的问题。对于给定范围、给定钱币面额，借助埃拉托色尼筛法、迪杰斯特拉算法、图的广度优先遍历算法思想，设计了一个快速计算每个数值的最小钱币数量方法，即最少钱币数量筛法来计算平均纸张数量；对于给定范围、给定数量的钱币种类如何确定最优钱币组合问题，给出了3种钱币最优组合的寻找过程，即通过分析最优组合中每一个钱币的数值特征，找出其中的规律，并通过最小二乘法原理拟合出最优组合中每个钱币面额的拟合曲线，通过拟合曲线的限制，大大减少寻找最优钱币组合的遍历次数。     

浅谈假冒伪劣元器件的规避方法

针对当前大量假冒元器件被用户错误选用的情况,文中分析了假冒元器件的种类和危害,介绍了DPA的发展情况及其在检查假冒电子元器件中的应用,结合NASA公布的企业发现假冒元器件的途径,对整机设备客户如何规避假冒元器件提出了一些建议,以期对假冒元器件的错误选用起到一定的遏制作用。     

An Investigation of the Confusability of a New,Non-Circular Coin

Two experiments are reported in each of which subjects were shown photographs of assorted coins and were asked to count the number of coins of a specified denomination. Experiment 1, using only decimal coins, showed that people made few errors when counting new, 7-sided coins (50p), but many errors when counting circular coins (50p) having the same diameter as the new coin. Experiment 2 showed: (a)errors when counting (10p) coins were fewer in an assortment of £sd coins than when among decimal coins-with in the £sd coinage no other coin had the same diameter as l0p; (b) the l0p error rate could be reduced by enlarging the diameter of the 50p coin. These results suggest that the new 7-sided coin was not itself difficult to discriminate when it was tho search objective, but that it was sometimes mistakenly classified as the circular l0p when people were searching for lOp coins. To explain this asymetric confusability between the circular and non-circular coins, it is suggested that people vary tho salient dimensions used when searching for different coins-using predominantly shape for a non-circular coin, and predominantly size for a circular coin.     

高阶统计与局部几何特征结合的货币图像识别

由于硬币具有多样性特点及现代假币手段的隐蔽性,这给硬币鉴伪带来了很大的困难,为此提出了一种基于高阶统计量与局部几何特征相结合的硬币图像识别方法。利用图像边缘纹理和图像面积的比值不变性,给出了一种变阈值的Robert边缘检测算法。将边缘图像的不变矩、纹理特征以及区域占有率等高阶统计量,以及不同版本硬币的局部几何特征量作为硬币图像的特征向量,采用模糊C均值聚类方法对其进行聚类分析,从而实现硬币的分类识别。实验结果表明该方法的识别率可以达到98．5％以上,并对环境光照的变化有很强的适应性。     

A game-theoretic approach of mixing different qualities of coins

Perpetrators leverage the untraceable feature to conduct illegal behaviors leading security issues with respect to mixing coins. Generally, bad coins are blocked based on a common blacklist. However, the blacklist may not be updated in time, which results in that bad coins escape the blocking. Consequently, perpetrators can still conduct illicit behaviors such as money laundering. In this paper, we apply game theory under imperfect information to study how coins' quality restrain these illicit behaviors under the incomplete scenario. More specifically, we propose a strategy for participants to submit deposits if they hope to mix coins with others even if they are not in blacklist at this time. The deposits will not be refunded when participants are included in the blacklist after mixing. Therefore, no participants have incentives to mix with bad coins. At the last part of this paper, we also simulate the incomes for participants, which indicates that deposits strategy is effective to prevent illicit behaviors.     

纸质传感器在点伪钞机中的应用

对点伪钞机识别假币的关键器件─纸质传感器（近紫外线传感器）进行了研究，有效地解决了识别假币的三个关键问题，即传感器的响应速度、灵敏度及温漂问题，提高了点伪钞机识别假币的准确性。