广义Rudin－Shapiro函数及其性质

为获得动力系统的高阶谱数［１２］，Ｑｕｅｆｆｅｌｅｃ引入了广义（ｑ阶ｑ≥３）Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列｛ｒｋ｝，起关键作用的指数和的不等式为：回一１其中常数Ｃ取值为，本文对广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列进行了进一步研究，引入了广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ函数，将以上系数Ｃ改进为，并证明了是Ｒ上一个连续但几乎处处不可微的周期为１的函数，取值于与之间，使得     

Riordan阵与Cauchy多项式

给出了Cauchy多项式c_n~α(z)的定义,并导出它的生成函数.再利用Riordan阵方法得到包含Cauchy多项式的一些恒等式,获得它与广义调和多项式H_n~((r))(z),广义Stirling多项式P_(n,r)(z)的关系式.     

一类广义指派问题的有效解法

提出一类广义指派问题,这类问题研究的是m个人执行n项任务,每个人执行的任务数、执行每项任务的人数以及总的指派人项数均有限制,要求最优指派.对这类广义指派问题建立了数学模型,并找到一种转换方法,将这类问题转换为平衡指派问题,从而用传统方法,如匈牙利法求解.最后用一个箅例来说明这种转换方法的简便和有效性.     

Goedel逻辑系统中的广义重言式理论

本文将王国俊教授在逻辑系统/W，W，Wk中的广义重言式理论进行推广并应用到了Gooedel逻辑系统/G，G，Gn中。主要结果是：在逻辑系统/G，G中，重言式不可能由对非重言式进行有限次升级算法得到；在逻辑系统Gn中，对任一公式最多进行n次升级算法即可得到重言式；利用可达广义重言式概念和α-矛盾式概念分别在/G，G，Gn中给出了F（S）的一个关于→同余的分划。     

广义G-M模型参数估计的相对效率

本文提出了广义Ｇ－Ｍ模型中参数β的ＢＬＵＥβ^*和ＬＳ估计β的一种新的相对效率,对其与其他两种相对效率的关系及其下界进行了研究,并讨论了它与广义相关系数的关系．     

广义Rudin—Shaprio函数及其性质

为获得动力系统的高阶谱数「１２」，Ｑｕｅｆｆｅｌｅｃ引入了广义（ｑ阶，ｑ≥３）Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列｛ｒｋ｝起关键作用的指数和的不等式为：ｍａｘθ│∑ｎ－１ｋ＝０ｒｋｅ＾ｉｋθ│≤Ｃｎ，（ｎ≥１）其中常数Ｃ取值为ｑ＋ｑｑ，本文对广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列进行了进一步研究，引入了广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ函数ψ，将以上系数Ｃ改进为（１＋２）ｑ，并证明了ψ是Ｒ上一个连续但几乎处处不     

关于广义函数赋值问题的完善与积分问题

本文采用非标准分析方法，首先对广义函数的赋值问题进行了完善；接着界定了广义函数的积分；最后讨论了广义函数的广义连续性．     

关于Fuzzy矩阵的广州逆

本文分别给出了Fuzzy矩阵存在广义{1，3}－逆、广义{1，4}－逆以及Mocre-Penrose广义逆Fuzzy矩阵的一些充要条件。又得到求上述广义逆Fuzzy矩阵的一些公式。主要的结果有：1．Fuzzy矩阵A的广义{1，3}－逆A^(1,3)（广义{1，4}－逆A^(1,4)的充要条件是Fuzzy关系方程X。A^T。A＝（A。A^T。Y＝A）有解。2．Fuzzy矩阵A的Mocre-Penrose广义逆A^＋存在的充要条件是Fuzzy关系方程X。A^T。A＝A，A。A^T。Y＝A均有解。3．如果B、C分别的Fuzzy关系方程X。A^T。A＝A，A。A^T。Y＝A的一个解，那么A^ ＝A^T。C。B＝C^T。AB^T＝C^T。B。A^T。     

回归分析中参数估计的一种新方法

本文根据矩阵的广义逆理论，建立了回归分析中进行参数估计的一种新方法，该方法更简单更精确。     

群体决策中方案排序的一种广义α—比较数法

给出了方案比较的新概念－偏爱度，并对偏爱度进行了详细的刻划，提出了多目标群组决策问题的一种广义α－比较数排序法，通过算例说明了该法的实用性和有效性。     

比赛项目排序的模型

本文将2005年“电工杯”B题的最优化问题转化为独立的问题来讨论。解决了在比赛项目排序过程中尽可能使每个运动员不连续参加两项比赛问题。即把运动员参加的项目记作1，把未参加的项目记为0，这样把运动员报名表转化成为一个0-1矩阵。问题转化成为0-1矩阵进行列交换顺序，使得每一行中两个1相邻出现的次数和达到最小。并对模型进行了推广。最后指出了模型的优缺点。     

Complete enumeration of pure‐level and mixed‐level orthogonal arrays

We specify an algorithm to enumerate a minimum complete set of combinatorially non‐isomorphic orthogonal arrays of given strength t, run‐size N, and level‐numbers of the factors. The algorithm is the first one handling general mixed‐level and pure‐level cases. Using an implementation in C, we generate most non‐trivial series for t=2, N≤28, t=3, N≤64, and t=4, N≤168. The exceptions define limiting run‐sizes for which the algorithm returns complete sets in a reasonable amount of time. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 123–140, 2010     

Products of mixed covering arrays of strength two

A covering array CA(N;t,k, v is an N × k array such that every N × t subarray contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple “cut‐and‐paste” construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t = 2 is derived. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 124–138, 2006     

On the state of strength‐three covering arrays

A covering array of size N, strength t, degree k, and order υ is a k × N array on υ symbols in which every t × N subarray contains every possible t × 1 column at least once. We present explicit constructions, constructive upper bounds on the size of various covering arrays, and compare our results with those of a commercial product. Applications of covering arrays include software testing, drug screening, and data compression. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 217–238, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10002     

WIDE SENSE STABILITY OF COMPLEX SYSTEMS OF DIFFERENTIAL EQUATIONS OF ARBITRARY DIMENSION

ＷＩＤＥＳＥＮＳＥＳＴＡＢＩＬＩＴＹＯＦＣＯＭＰＬＥＸＳＹＳＴＥＭＳＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＡＲＢＩＴＲＡＲＹＤＩＭＥＮＳＩＯＮ￥ＺＩＡＤＺＡＨＲＥＤＤＩＮＥＡｂｓｔｒａｃｔ：ＩｔｉｓｓｈｏｗｎｈｏｗｔｈｅｅｘｔｅｎｄｅｄＲ...     

Constructions of augmented orthogonal arrays

Augmented orthogonal arrays (AOAs) were introduced by Stinson, who showed the equivalence between ideal ramp schemes and AOAs (Discrete Math. 341 (2018), 299–307). In this paper, we show that there is an AOA if and only if there is an OA which can be partitioned into subarrays, each being an OA, and that there is a linear AOA if and only if there is a linear maximum distance separable (MDS) code of length and dimension over , which contains a linear MDS subcode of length and dimension over . Some constructions for AOAs and some new infinite classes of AOAs are also given.     

Riordan 矩阵在广义 Motzkin 路计数中的应用

用Riordan矩阵的方法研究了具有4种步型的加权格路(广义Motzkin路)的计数问题,引入了一类新的计数矩阵,即广义Motzkin矩阵.同时给出了这类矩阵的Riordan表示,也得到了广义Motzkin路的计数公式.Catalan矩阵,Schrder矩阵和Motzkin矩阵都是广义Motzkin矩阵的特殊情形.     

The decomposability of simple orthogonal arrays on 3 symbols having t + 1 rows and strength t

It is well‐known that all orthogonal arrays of the form OA(N, t + 1, 2, t) are decomposable into λ orthogonal arrays of strength t and index 1. While the same is not generally true when s = 3, we will show that all simple orthogonal arrays of the form OA(N, t + 1, 3, t) are also decomposable into orthogonal arrays of strength t and index 1. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 442–458, 2000     

A construction of maximal linearly independent array

Let M be a subset of r-dimensional vector space Vτ （F2） over a finite field F2, consisting of n nonzero vectors, such that every t vectors of M are linearly independent over F2. Then M is called （n, t）-linearly independent array of length n over Vτ（F2）. The （n, t）-linearly independent array M that has the maximal number of elements is called the maximal （r, t）-linearly independent array, and the maximal number is denoted by M（r, t）. It is an interesting combinatorial structure, which has many applications in cryptography and coding theory. It can be used to construct orthogonal arrays, strong partial balanced designs. It can also be used to design good linear codes, In this paper, we construct a class of maximal （r, t）-linearly independent arrays of length r ＋ 2, and provide some enumerator theorems.     

Nonlinear dynamics in double square-well potentials

The first example of the coexistence of Josephson oscillations with a self-trapping regime is found in the context of the coherent nonlinear dynamics in a double square-well potential. We prove the simultaneous existence of symmetric, antisymmetric, and asymmetric stationary solutions of the associated Gross-Pitaevskii equation, which explains this macroscopic bistability. We illustrate and confirm the effect with numerical simulations. This property allows suggesting experiments with Bose-Einstein condensates in engineered optical lattices or with weakly coupled optical waveguide arrays. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 292–303, August, 2007.