On the Spectrum of Mutually r-orthogonal Idempotent Latin Squares

Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they are all idempotent. In this paper, we show that for any integer v≥28, there exists an r-MOILS（v） if and only if r∈[v, v^2]／ {v ＋ 1, v^2-1}.

Nonequidistant two-dimensional antenna arrays based on Latin squares

Non-equidistant sparse antenna arrays constructed on the basis of Latin squares are considered. A method for their construction and a synthesis algorithm are proposed,and the properties of two-dimensional antennas based on them,which ensure,at a high degree of rarefaction,a sufficiently small lateral radiation are studied. The features and main characteristics of such antennas are studied.

Further Results on Mutually Nearly Orthogonal Latin Squares

Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearly orthogonal Latin squares are provided.It is proved that there exist 3 MNOLS（2m） if and only if m ≥3 nd there exist 4 MNOLS（2m） if and only if m ≥4 with some possible exceptions.

The Fine Structures of Three Symmetric Latin Squares with Even Orders

Denote by SFin（v） the set of all integer pairs （t, s） for which there exist three symmetric Latin squares of order v on the same set having fine structure （t, s）. We completely determine the set SFin（2n） for any integer n ≥ 5.

Existence of Weakly Pandiagonal Orthogonal Latin Squares

A weakly pandiagonal Latin square of order n over the number set {0, 1, . . . , n-1} is a Latin square having the property that the sum of the n numbers in each of 2n diagonals is the same. In this paper, we shall prove that a pair of orthogonal weakly pandiagonal Latin squares of order n exists if and only if n ≡ 0, 1, 3 （mod 4） and n≠3.

CONSTRUCTING SELF-CONJUGATE SELF-ORTHOGONAL DIAGONAL LATIN SQUARES

In this paper, we give some constructions of self-conjugate self-orthogonal diagonal Latinsquares (SCSODLS). As an application of such constructions we disproof the conjecture aboutSCSODLS and show that there exist SCSODLS of order V, whenever w=1 (mod 12), with thepossible exception of v∈ {13, 85, 133}.

Constructing Pandiagonal Snowflake Magic Squares of Odd Order

The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.

An Upper Bound for the Number of Normalized Latin Square

In this note, the author find an upper bound formula for the number of the p × p normalized Latin Square,the first row and column of which are both standard order 1, 2,…p.

Using the Latin Square Design Model in the Prioritzation of Network Security Threats: A Quantitative Study

Society is becoming increasingly dependent on cyberspace for both business and pleasure. Cyber attackers continue to attack organizational computer networks, as those same computer networks become increasing critical to organizational business process. Strategic planning and managing IT security risks play an important role in the business and government planning process. Deploying defense in depth security measures can ensure that organizations continue to function in times of crisis. This quantitative study explores whether the Latin Square Design (LSD) model can be effectively applied to the prioritization of cybersecurity threats and to the linking of information assurance defense in-depth measures to those threats. The methods used in this study consisted of scanning 10 Cybersecurity Websites such as the Department of Homeland Security US CERT (United States-Computer Emergency Readiness Team [1]) and the SANS Institute (SysAdmin, Audit, Network and Security [2]) using the Likert Scale Model for the Website’s top ten list of cyber threats facing organizations and the network defense in depth measures to fight those threats. A comparison of each cybersecurity threats was then made using LSD to determine whether the Likert scale and the LSD model could be effectively applied to prioritize information assurance measures to protect organizational computing devices. The findings of the research reject the H0 null hypothesis that LSD does not affect the relationship between the ranking of 10 Cybersecurity websites top ten cybersecurity threats dependent variables and the independent variables of defense in depth measures used in protecting organizational devices against cyber-attacks.

Impairment of Continuous Insulin Delivery Therapy and Analysis from Graeco-Latin Square Design Model

The desire to deliver measured amount of insulin continuously to patients with type I diabetes, for glycemic control, has attracted a lot of attention. Continuous subcutaneous insulin infusion has seen some success in recent years. However, occlusion of insulin delivery may prevent the patient from receiving the prescribed dosage, with adverse consequence. An in vitro study of insulin delivery is performed, using different insulin pumps, insulin analogs and operating conditions. The aim is to identify incidences of occlusion due to bubble formation in the infusion line. A detailed statistical analysis was performed on the data collected to determine any significant differences and deviations in insulin delivery rates that might be due to factors such as: pump type, the set basal flow rate, insulin type, vibration, and possible insulin occlusion due to air bubble formation within the infusion line. Our findings from the Graeco-Latin Square design model show that there are statistical differences due to the devices, and statistical identifiable clusters are used to distinguish the devices. Such hierarchical models used to describe the analyses, include the flow rate, the pump types, and the activity level.

A CASCADING LATIN SCHEME TO TOLERATE DOUBLE DISK FAILURES IN RAID ARCHITECTURES

In recent years,a lot of XOR-based coding schemes have been developed to tolerate double disk failures in Redundant Array of Independent Disks (RAID) architectures,such as EVENODD-code,X-code,B-code and BG-HEDP. Despite those researches,the decades-old strategy of Reed-Solomon (RS) code remains the only popular space-optimal Maximum Distance Separable (MDS) code for all but the smallest storage systems. The reason is that all those XOR-based schemes are too difficult to be implemented,it mainly because the coding-circle of those codes vary with the number of disks. By contrast,the coding-circle of RS code is a constant. In order to solve this problem,we develop a new MDS code named Latin code and a cascading scheme based on Latin code. The cascading Latin scheme is a nearly MDS code (with only one or two more parity disks compared with the MDS ones). Nev-ertheless,it keeps the coding-circle of the basic Latin code (i.e. a constant) and the low encod-ing/decoding complexity similar to other parity array codes.

Latin方阵和二维量子漫步相结合的图像加密

针对数字图像在网络传输过程中容易受到攻击导致信息泄漏的问题,在Arnold置乱变换的基础上引入量子漫步和Latin方阵,设计了一种新型的彩色图像加密方案。首先把彩色图像的三通道分离,用Arnold变换来对图像像素点置乱,量子漫步和Latin方阵被用来处理置乱后图像的像素值,然后对处理之后的图像使用加取模扩散算法进一步改变图像的像素值,最后合并三通道加密图像得到彩色加密图像。量子漫步的作用是为该文的加密算法提供随机序列。该文对加密算法进行了实验仿真,在直方图、相关性、信息熵、噪声攻击、裁剪攻击等多个方面对实验结果进行了性能分析。仿真结果显示:加密图像的直方图均匀分布,像素点之间的相关性趋近于0,信息熵为7.9993,接近于8,说明该算法具有较不错的抵抗统计分析的能力;经过噪声攻击和裁剪攻击之后的加密图像经过解密之后,仍然可以看到原图像信息,表明该算法的鲁棒性是良好的;该加密算法的密钥空间足够大为1060且密钥敏感性良好,NPCR值接近于99.61%,UACI值接近于33.45%,证明该算法拥有抵抗差分攻击的能力。

语义任务与形式任务对二语词汇形义匹配的影响——对加工资源分配模型的验证

本研究采用拉丁方设计,考察任务类型对二语词汇即时学习的影响,并从词汇形义匹配的角度对加工资源分配模型(即TOPRA模型)的适用性进行验证。51名非英语专业一年级大学生分别在语义任务、形式任务和无任务3种条件下学习24个英语单词,之后接受单词自由回忆和单词提示回忆的即时测试。结果发现:在一语自由回忆测试中,任务类型显著影响词汇意义的学习,语义任务对词汇意义的学习有促进作用,而形式任务对词汇意义的学习有抑制作用;在二语自由回忆测试中,任务类型对词汇形式的学习没有影响;在一语和二语提示回忆测试中,任务类型显著影响二语词汇的即时学习效果,语义任务和形式任务都对词汇形义匹配知识的学习有抑制作用。本研究部分验证了TOPRA模型的适用性,希望可以为二语词汇教学提供一定的借鉴和参考。

基于Kriging模型的船舶主机隔离系统抗冲击优化

为了提高系统的抗冲击性能和优化效率,本文以限位隔离系统的刚度阻尼等7个参数为设计变量,以系统冲击响应中的相对位移响应和绝对加速度响最大峰值为响应值建立Kriging代理模型。通过NSGA-II多目标优化算法对构建的代理模型进行多目标优化,优化目标为相对位移响应和绝对加速度响最大峰值两者和的最小值。与初始方案相比,优化后系统相对位移响应降低了27.139%,绝对加速度响应降低了37.846%。结果表明:建立的代理模型对隔离系统的冲击响应有较精确的预报作用,优化后船舶主机隔离系统的抗冲击得到明显提高。

基于正交拉丁方的局部修复码构造

针对目前具有(r,t)局部性的局部修复码码率较低且构造过程中计算复杂度过高的问题,提出基于正交拉丁方的二元局部修复码构造方法.根据正交拉丁方元素与矩阵位置的对应关系构造关联矩阵,得到具有全符号局部性的局部修复码(AS-LRCs),该码的码率和码长渐近边界条件,且最小距离较大.利用关联矩阵级联单位矩阵构造信息位具有(r,t=2)局部性的单校验局部修复码,该码的最小距离和码率均满足最优边界条件,为最优局部修复码.考虑到实际分布式存储系统中存在高故障率节点,利用正交拉丁方完备组构造具有信息位局部性的高可用性单校验局部修复码(IS-LRCs),可以灵活选择可用性t,提高了系统的鲁棒性与灵活性.

基于正交试验的深井泵优化设计

以深井泵叶片数、出口安放角、出口宽度等7个因素,每个因素取3个水平,按L18(37)正交试验方案,设计了18副叶轮。通过CFD技术对叶轮、导叶在内的两级深井泵的全流场进行了设计工况下的三维数值模拟,获得了18组设计方案的效率、扬程值。通过正交试验法探索了各几何参数对效率、扬程的影响规律,并通过极差分析找到了影响这些性能的主要因素和次要因素,根据优选结果结合内部流场测试及样机试验验证对模型泵提出了进一步优化设计方案。本试验结果对采用叶轮极大扬程设计法的深井泵水力设计具有一定的参考价值。

基于移动最小二乘响应面方法的整车轻量化设计优化

汽车轻量化是汽车产业发展方向之一,也是一个汽车厂商和国家技术进步、先进程度的重要标志。优化汽车的结构设计是实现汽车轻量化的有效途径之一,文中采用拉丁方试验设计方法进行样本数据设计,同时,为了提高了计算效率,将基于移动最小二乘拟合的响应面近似模型引入到整车正碰优化设计的复杂系统中,并利用序列响应面优化方法对近似模型进行优化,避免了整车碰撞传统优化设计方法计算量大,且在碰撞非线性系统优化中常常易导致收敛缓慢甚至不收敛的缺点。在满足了CMVDR294安全法规的同时,使汽车车身一些部件的板厚达到合理的配置,从而达到使汽车重量得到一定程度的减轻的目的。

Z_n上的全向置换

本文给出Ｚｎ上全向置换这一概念，讨论全向置换的存在性、函数特性、构造和计数等问题。得到了Ｚｎ上全向置换的存在性定理、不动点特征以及利用正交拉丁方构造全向置换的一种方法，并对全向置换的计数问题进行了研究。

无过载排污泵正交试验研究

用正交试验法研究了各几何参数对无过载排污泵性能的影响,探索了各几何参数对效率、最大轴功率值及其位置的影响规律,并通过方差分析找到了影响这些性能的主要因素和次要因素,验证了无过载排污泵最大轴功率值及其位置公式的正确性,根据试验结果对模型泵提出了进一步设计方案,本试验结果对无过载排污泵水力设计有一定的参考价值。

求解大规模优化问题的可全局收敛蝙蝠算法

为了快速求解大规模优化问题,构造出了可全局收敛的蝙蝠算法。在该算法中,将一个蝙蝠看成是优化问题的一个候选解;采用正交拉丁方原理生成蝙蝠群的初始空间位置,以达到对搜索空间的均衡分散性和整齐可比性覆盖;将蝙蝠的追随、自主、避险和从众行为用于构造每个蝙蝠的空间位置转移策略;利用蝙蝠捕获猎物时的响度和脉冲速率来确保整个蝙蝠群要么保持原状态,要么向好的空间位置转移,但绝不会向差的空间位置转移。在蝙蝠群移动过程中,蝙蝠从一个空间位置转移到另一个空间位置实现了蝙蝠群对优化问题最优解的搜索。结果表明,采用可归约随机矩阵稳定性定理可证明本算法具有全局收敛性。测试案例表明,本算法用于求解大规模优化问题时具有对不同类型优化问题适应性强且收敛速度快的优势。