Families of pairs of graphs with a large number of common cards

The vertex‐deleted subgraph G?v, obtained from the graph G by deleting the vertex v and all edges incident to v, is called a card of G. The deck of G is the multiset of its unlabelled vertex‐deleted subgraphs. The number of common cards of G and H (or between G and H) is the cardinality of the multiset intersection of the decks of G and H. In this article, we present infinite families of pairs of graphs of order n ≥ 4 that have at least \begin{eqnarray*}2\lfloor\frac{1}{3}(n-1)\rfloor\end{eqnarray*} common cards; we conjecture that these, along with a small number of other families constructed from them, are the only pairs of graphs having this many common cards, for sufficiently large n. This leads us to propose a new stronger version of the Reconstruction Conjecture. In addition, we present an infinite family of pairs of graphs with the same degree sequence that have \begin{eqnarray*}\frac{2}{3}(n+5-2\sqrt{3n+6})\end{eqnarray*} common cards, for appropriate values of n, from which we can construct pairs having slightly fewer common cards for all other values of n≥10. We also present infinite families of pairs of forests and pairs of trees with \begin{eqnarray*}2\lfloor\frac{1}{3}(n-4)\rfloor\end{eqnarray*} and \begin{eqnarray*}2\lfloor\frac{1}{3}(n-5)\rfloor\end{eqnarray*} common cards, respectively. We then present new families that have the maximum number of common cards when one graph is connected and the other disconnected. Finally, we present a family with a large number of common cards, where one graph is a tree and the other unicyclic, and discuss how many cards are required to determine whether a graph is a tree. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 146–163, 2010     

The card game 24 and its application to math education

The card game 24 is a mathematical game that traditionally engages elementary students to practice their mental computational skills. In this paper, we use probability to formulate and explore the game. We create score of difficulty level for solvable card combination set under various setup of game rules. Based on our findings, we create new playing rules and provide suggestions for different levels of players. Our results may serve as guidelines on introducing the game 24 into the practice of math education.     

互联网环境下消费信贷行为研究

采用结构方程建模方法,实证分析了感知易用性、感知有用性、感知风险、信用卡效应及使用的态度与互联网环境下消费者使用信用卡支付的意愿之间的作用路径关系,从而建立了互联网环境下消费信贷行为影响因素的概念模型．研究表明,除感知风险与使用的意愿之间存在负相关关系外,其余四个因素与使用的意愿之间均存在正相关关系,其中使用的态度对使用的意愿的影响最大．     

水发食品中甲醛含量快速检测的实验研究

利用品红亚硫酸钠溶液与醛类物质反应后颜色深浅与浓度成正比的原理,使用5种标准浓度的甲醛溶液与希夫试剂反应显色后制作标准比色卡。用待测样品显色后的溶液与制作的标准比色卡进行比对,判断甲醛浓度范围。该方法具有现象明显、灵敏准确、药品易得的优点。因此,可用作中学生课外兴趣实验的实施项目,配制的希夫试剂和制作的标准比色卡也可用于家庭检测水发食品中甲醛含量。     

Examination of Polish Identity Documents by Laser-Induced Breakdown Spectroscopy

Laser-induced breakdown spectroscopy (LIBS) was applied to the preliminary examination of Polish documents – passports and identity cards – for forensic purposes. Several security features of potentially high discrimination capability were selected at both the passports (Alphagram, serial number, the contour map of Europe, and emblem) and identity cards (kinegram, the date of birth, and emblem). Different elemental compositions were identified after comparing the spectra recorded from various measurement locations. It was possible to identify characteristic atomic emission from several elements (such as Ti, Ca, K, Fe, Cr, Mg, Na, La, Cd, Li, V, Al, Mn, Ni, and Cu) based on the type of document, issue date, and evaluated area. In the case of passports, the potentially good discriminators with unique elemental composition were identified, e.g., the serial number and the contour map of Europe printed with the use of intaglio printing technique. Identity cards with the cover of polycarbonate foil constitute a very difficult sample to analyze because of the foil’s influence on the laser ablation phenomenon. This study presents the potential of LIBS as an effective and useful technique to analyze Polish passports for forensic purposes. Its many advantages provide a good alternative to the analytical methods routinely used for the examination of these objects.     

抄针周期对纯涤纺梳棉棉结的影响研究

通过在金属针布梳棉机上专门的抄针实验,研究抄针前后不同时刻的棉结粒数的变化规律。结果表明：金属针布在纯涤纺时仍需要抄针,合理的抄针周期应为每两天一次。     

对高校体育“特殊学生群体”体育课的思考

运用文献资料、比较分析、逻辑分析等方法,阐述了高校体育课中"特殊学生群体"的体育课的现状,分析其导致现状的原因有场地、资金紧缺,师资不足,重视程度不够等等,并提出开设体育保健课、运动养身课与棋牌类项目课程等多种课程,以及采用多种教学形式等的对策,并提出建议。     

煤矿专用防护服的研究

煤矿作业首先要保证矿工在工作中的安全与健康,这是一个最基本的前提,也是社会进步的体现。性能优良的矿工防护服在日常工作中保护矿工的身体健康,保障生产安全。本文在分析井下的环境和未来煤矿开采趋势的基础上,详细阐述了煤矿职业安全对矿工防护服的具体要求,从而满足现代化煤矿安全生产要求,为煤矿工作人员构筑一道坚实可靠的安全防线。     

民族元素在服饰品设计中的应用

具有民族特色的服饰品占领着越来越大的市场,民族元素越来越多地被用于服装及服饰品设计。为了传承、保护和开发传统民族服饰,在研究中国民族元素的基础上,选取具有代表性的民族元素,通过筛选和抽象变形的手法,将材质、纹样、色彩、造型、工艺及设计手法等运用于现代服饰品设计中。同时,设计中要注意与流行元素结合,而非生搬硬套。     

用于视频图像数据的ATA接口硬盘存储卡的设计

给出一种视频图像数据ATA接口硬盘存储卡的设计方案,系统采用模块化设计,由图像数据缓冲模块、ATA逻辑模块、ATA接口模块、主机通信模块四部分组成。图像数据缓冲模块选用CPLD加外部FIFO的组合方式来完成,使得系统与不同的外部设备配合工作时,只需要修改CPLD的程序,提高了存储卡的可靠性和可维护性;ATA逻辑模块以及ATA接口模块的功能通过FPGA实现;主机通信模块由AVR芯片配合TUSB6250芯片来共同完成,保证了存储卡具有功耗低、内部短路电路保护等优点。本文所提存储卡方案具有更低的成本,更好地兼容性,易于扩展等优势,尤其适用于视频海量数据的存储。