由可分组设计构造对称设计

本文提出了由一类可分组设计构造出对称设计的方法.注意到这类可分组设计的关联图对应着5类结合方案的关系图.本文利用该5类结合方案的商结合方案,由这类可分组设计构造对称设计,并举例说明了构造的具体过程.此外,提出了一种利用阵列由对称设计构造可分组设计的方法.在此基础上,证明了两个有对偶性质的可分组设计GDDDP(2,11;5;0,1)和GDDDP(2,16;6;0,1)不存在.     

分奇偶求数列通项问题的类型及策略

某些数列的奇数项与偶数项分别是不同的数列,与此类数列有关的求通项或求和问题,需要分n为奇数或偶数进行讨论.那么满足什么特征的数列,需要分奇偶进行讨论?本文就奇偶数列所呈现的特征进行例析,并对处理策略进行总结.     

介绍书号、刊号的校验码

书号的全称是“中国标准书号”，也称“ISBN号”，它由标识符号ISBN和13位数字（分为5段）组成，在每本书封底的定价旁边或条形码、版权页上，我们都能见到它的身影，它是图书的身份证．例如，笔者的第一本专著《初等数学研究（I）》已由哈尔滨工业大学出版2008年9月正式出版发行（16开本，正文677页，833千字），其书号是ISBN978—7-5603—2733-4．     

组型为$2^u$的Kite-可分组设计的相交数问题

Kite-可分组设计的相交数问题是确定所有可能的元素对$(T,s)$, 使得存在一对具有相同组型 $T$ 的Kite-可分组设计 $(X,{\cal H},{\cal B}_1)$ 和$(X,{\cal H},{\cal B}_2)$ 满足$|{\cal B}_1\cap {\cal B}_2|=s$. 本文研究组型为 $2^u$ 的Kite-可分组设计的相交数问题, 设 $J(u)=\{s:\exists$ 组型为 $2^u$ 的Kite-可分组设计相交于$s$ 个区组\}, $I(u)=\{0,1,\ldots,b_{u}-2,b_{u}\}$,其中 $b_u=u(u-1)/2$ 是组型为$2^u$ 的Kite-可分组设计的区组个数. 我们将给出对任意整数 $u\ge 4$ 都有$J(u)=I(u)$ 且 $J(3)= \{0,3\}$.     

超形变核转动惯量的系统奇偶差与堵塞效应

与正常形变核相似,超形变核的转动惯量存在系统的奇偶差,这是超形变核中对力及堵塞效应存在的无可争辩的证据。随转动频率增高,由于Coriolis反配对效应,奇偶差逐渐变弱,特别是当hω≥0.20MeV后,动力学转动惯量J²的奇偶差变得模糊,在某些情况下,可能出现相邻核的J²值几乎相同的现象。但对于运动学转动惯量J¹,即使在很高的转动频率下,仍在一定程度上呈现奇偶差.     

广义Bethe树上奇偶马尔可夫链场上的若干极限性质

通过构造两个非负鞅证明了一个强极限定理,然后把它应用到本文所定义的广义Bethe树上的奇偶马尔可夫链场上,从而获得了此马氏链场上的一类强极限定理.     

精准设计题目 提升课堂效率——以数列分奇偶项求和的高三复习课为例

数列分奇偶项求和是一个比较难的知识点,在考试中出现的频率比较大.本研究精心选取了一些例题,并对例题进行适当地变式,让学生在课堂教学活动中有自己的思考,提升课堂效率,帮助学生更好地掌握这部分学习内容,给教师们提供一些教学参考.     

关于HSOLSSOM（2^nu^1）的谱

本文讨论型为２＾ｎｕ＾１的有对称正交侣的带洞自正交拉丁方（ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１））的谱。证明当ｎ≤９时,ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１）存在的充分必要条件是ｕ为偶数且ｎ≥３ｕ／２＋１;当ｎ≥２６３时,若ｕ为偶数且ｎ≥２（ｕ－２）,则ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１）存在。     

基于T-S模糊模型的非线性不确定系统奇偶方程鲁棒故障诊断

针对T-S模糊模型描述的具有外部干扰的非线性不确定系统,构造了相应的测量冗余方程和奇偶方程,给出并证明了对特定传感器和执行器故障敏感的最优奇偶向量的存在条件和求解定理.采用奇偶方程故障检测与诊断方法,研究了非线性不确定系统的鲁棒故障检测和诊断.最后,通过仿真示例说明了本文所提出的方法是有效的.     

奇偶项巧讨论，多思维妙拓展——一道数列题的探究

数列中的奇偶项综合问题,以一个数列的场景同时考查数列的多个基本知识,综合性强,创新性高,倍受各方关注.本文以一道数列模拟题为例,借助数列中的奇偶项综合创设,从不同的数学思维视角进行分析与求解,总结规律与应用,合理变式拓展,引领并指导数学教学与复习备考.     

Determination of Sizes of Optimal Three‐Dimensional Optical Orthogonal Codes of Weight Three with the AM‐OPP Restriction

In this paper, we further investigate the constructions on three‐dimensional optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM‐OPP 3D ‐OOCs) by way of the corresponding designs. Several new auxiliary designs such as incomplete holey group divisible designs and incomplete group divisible packings are introduced and therefore new constructions are presented. As a consequence, the exact number of codewords of an optimal AM‐OPP 3D ‐OOC is finally determined for any positive integers and .     

Constant Weight Codes and Group Divisible Designs

The study of a class of optimal constant weight codes over arbitrary alphabets was initiated by Etzion, who showed that such codes are equivalent to special GDDs known as generalized Steiner systems GS(t,k,n,g) Etzion. This paper presents new constructions for these systems in the case t=2, k=3. In particular, these constructions imply that the obvious necessary conditions on the length n of the code for the existence of an optimal weight 3, distance 3 code over an alphabet of arbitrary size are asymptotically sufficient.     

Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes

We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4 ^p —for any prime such that (p–1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for . In this case an explicit construction was given for . Here, such an explicit construction is also realized for .We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime , p>7. The existence is guaranteed for p>(2q ³–3q ²+1)²+3q ² where q is the least prime factor of (p–1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6 ^p for any prime p>5 and the existence of a cyclic (4, 1)-GDD of type 8 ^p for any prime . The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with =1.     

A Sequence of Unique Quaternary Griesmer Codes

This paper establishes that there is no [98,5,72]₄ code. Such a code would meet the Griesmer bound and the weights of its codewords would all be divisible by 4. The proof of nonexistence uses the uniqueness of codes with parameters [n,4,n - 5]₄,14 n 17. The uniqueness of these codes for n 15 had been established geometrically by others; but it is rederived here, along with that of the [14,4,9]₄ code, by exploiting the Hermitian form obtained when the weight function is read modulo 2.     

构作正交空间中的一类Cartesian认证码

利用正交几何构作出一类Cartesian认证码,并且计算了它们的参数.假定信源和编码规则都按等概率分布选取,求出了认证码的成功的模仿攻击概率PI和成功的替换攻击概率PS.本文构作的Cartesian认证码的成功的模仿攻击概率PI均达到了其下界.     

An Introduction to Divisible Codes

This paper presents some basic facts about divisible codes, culminating in a divisible version of the Gleason-Pierce theorem on self-dual codes.     

Existence of directed GDDs with block size five

In this article, we construct directed group divisible designs (DGDDs) with block size five, group-type hⁿ, and index unity. The necessary conditions for the existence of such a DGDD are n ≥ 5, (n − 1)h ≡ 0 (mod 2) and n(n − 1)h² ≡ 0 (mod 10). It is shown that these necessary conditions are also sufficient, except possibly for n = 15 where h ≡ 1 or 5 (mod 6) and h ≢ 0 (mod 5), or (n, h) = (15, 9). © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 389–402, 1998     

Incomplete group divisible designs with block size four and general index

In this paper, we investigate the existence of incomplete group divisible designs (IGDDs) with block size four, group-type (g, h) u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg(u 1) ≡ 0 (mod 3), λ(g h)(u 1) ≡ 0 (mod 3), and λu(u 1)(g 2 h 2 ) ≡ 0 (mod 12). These necessary conditions are shown to be sufficient for all λ≥ 2. The known existence result for λ = 1 is also improved.     

Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint

The study of optical orthogonal codes has been motivated by an application in an optical code‐division multiple access system. From a practical point of view, compared to one‐dimensional optical orthogonal codes, two‐dimensional optical orthogonal codes tend to require smaller code length. On the other hand, in some circumstances only with good cross‐correlation one can deal with both synchronization and user identification. These motivate the study of two‐dimensional optical orthogonal codes with better cross‐correlation than auto‐correlation. This paper focuses on optimal two‐dimensional optical orthogonal codes with the auto‐correlation and the best cross‐correlation 1. By examining the structures of w‐cyclic group divisible designs and semi‐cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two‐dimensional ‐optical orthogonal codes. When and , the exact number of codewords of an optimal two‐dimensional ‐optical orthogonal code is determined for any positive integers n and .     

Resolvable modified group divisible designs with block size three

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. © 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007