U∧＊均匀设计的均匀性研究

本文以均匀设计在几何和物理意义下的均匀性等价准则为基础,研究了U∧*均匀设计的均匀性,利用本文结果,构造U∧*均匀设计使用表的运算量可减少为原来的s/2∧2-1（这里s为因素数）,而且,当因素数为1/2ψ（n 1)或1/2ψ（n 1）-1时,不必进行任何均匀度评价也可直接给出其使用表,本文还从几何的角度说明了U∧*均匀设计最多只能安排1/2ψ（n 1）个因素。     

基于计算机试验的均匀设计

本文在计算机试验的基础上，提出了最小相关准则和最小距离离差准则，并将信息论中的Hamming距离和Lee距离引入到计算机试验中，证明了均匀设计在Hamming距离下的最优性和部分好格子点均匀设计在Lee距离下的最优性．基于偏差的考虑，给出了一类新的好格子点均匀设计和一个学习算法，利用这个学习算法，给出了基于Lee距离的最小距离离差准则的均匀设计表的构造方法．通过与已有的好格子点均匀设计和循环拉丁方均匀设计作比较，证明了文中的均匀设计在距离和偏差意义下有更好的均匀性．     

均匀设计及其应用（Ⅲ）

均匀设计及其应用（Ⅲ）方开泰第三章均匀设计表的构造本章介绍均匀设计表的构造和使用表的来源，其中涉及到均匀度的度量。在理解了表的构造原理冬我们就能比较灵活地运用均匀设计，故本章也介绍均匀设计这方面的知识。§１均匀设计表的构造定义１：每一个均匀设计表是一...     

含有定性因素的均匀设计

本文讨论如何用均匀设计来安排含有定性因素的试验,以及如何进行数据分析     

均匀性度量的势函数模型

分析了均匀性度量应满足的基本条件，根据物理学的势和力的模型，提出了均匀性度量的势函数模型，该模型较好地解决了均匀性度量的可计算性、布点的均匀性调整方法等问题；而且具有均匀性度量所应该具有的所有优良性质，如旋转对称性、平移对称性、中心对称性等。最后给出了应用实例，并就低维投影的均匀性问题和势函数模型的改进作了讨论。      

投影均匀分片拉丁超立方体设计

空间填充设计是有效的计算机试验设计,比如均匀设计、最大最小距离拉丁超立方体设计等.虽然这些设计在整个试验空间中有较好的均匀性,但其低维投影均匀性可能并不理想.对于因子是定量的计算机试验,已有文献构造了诸如最大投影设计、均匀投影设计等相适应的设计;而对于同时含有定性因子和定量因子的计算机试验,尚未有投影均匀设计的相关文献.文章提出了综合投影均匀准则,利用门限接受算法构造了投影均匀的分片拉丁超立方体设计.在新构造设计中,整体设计与每一片设计均具有良好的投影均匀性.模拟结果显示,与随机分片拉丁超立方体设计相比,利用新构造设计进行试验而拟合的高斯过程模型具有更小的均方根预测误差.     

正交设计的最新发展和应用(Ⅱ)-均匀正交设计

方开泰等．正交设计的最新发展和应用（Ⅱ）—均匀正交设计．令Ｌ（ｎ;ｑｓ）为一切正交表Ｌｎ（ｑｓ）之集合,Ｍ为试验点分布于试验区域的均匀性测度。给定（ｎ,ｑ,ｓ）,在Ｌ（ｎ;ｑｓ）上具有最好均匀性（在测度ＭＦ）的设计称为无匀正交设计,并表为ＵＬｎ（ｑｓ）。本讲座以ＵＬ９（３４）为例说明均匀正交设计在估计和混杂方面的优良性质。在附录中列出了七个均匀正交表,它们都是最近获得的     

正交设计的最新发展和应用(Ⅱ)—均匀正交设计

方开泰等．正交设计的最新发展和应用（Ⅱ）—均匀正交设计．令Ｌ（ｎ;ｑｓ）为一切正交表Ｌｎ（ｑｓ）之集合,Ｍ为试验点分布于试验区域的均匀性测度。给定（ｎ,ｑ,ｓ）,在Ｌ（ｎ;ｑｓ）上具有最好均匀性（在测度ＭＦ）的设计称为无匀正交设计,并表为ＵＬｎ（ｑｓ）。本讲座以ＵＬ９（３４）为例说明均匀正交设计在估计和混杂方面的优良性质。在附录中列出了七个均匀正交表,它们都是最近获得的     

均匀试验设计的理论、方法和应用——历史回顾

本文回顾计算机仿真试验设计的主要两种方法:拉丁超立体抽样和均匀设计,在过去二十五年的发展,特别是均匀设计的发展,包括均匀设计的优良性研究、新的均匀性测度、均匀设计表的构造,以及均匀性在因子设计中的应用。     

任意凸多面体上布点均匀性的度量

均匀性度量是构作均匀设计的基础,本文从距离概念出发,通过对称的方法,得到一种新的距离函数-势函数,并将势函数作为衡量任意凸多面体上布点均匀性好坏的准则.数值例子和多变量Kendall 协和系数检验表明,当试验区域限制在单位立方体上时,势函数与目前常用的两种偏差-中心化L_2-偏差和可卷L_2.偏差在度量布点均匀性方面结论一致.     

A Shannon-McMillan theorem for motley names

The Shannon-McMillan theorem tells us the number of “typical” outcomes of an experiment in which one observes some discrete-valued function of an ergodic dynamical system for many time-steps; it also tells us that most such outcomes are roughly equally likely. Here it is shown that the same uniformity holds when several different measurements are made on the system over the course of time, provided that each sort of measurement is made many times in direct succession.     

Investigations of c-differential uniformity of permutations with Carlitz rank 3

The c-differential uniformity is recently proposed to reflect resistance against some variants of differential attack. Finding functions with low c-differential uniformity is attracting attention from many researchers. For even characteristic, it is known that permutations of low Carlitz rank have good cryptographic parameters, for example, low differential uniformity, high nonlinearity, etc. In this paper we show that permutations with low Carlitz rank have low c-differential uniformity. We also investigate c-differential uniformity of permutations with Carlitz rank 3 in detail.     

CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL

When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small (≤50). In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L2-discrepancy (CD, for short) and wrap-around L2-discrepancy (WD, for short), are employed.     

A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

Latin hypercube design is a good choice for computer experiments. In this paper, we construct a new class of Latin hypercube designs with some high-dimensional hidden projective uniformity. The construction is based on a new class of orthogonal arrays of strength two which contain higher strength orthogonal arrays after their levels are collapsed. As a result, the obtained Latin hypercube designs achieve higher-dimensional uniformity when projected onto the columns corresponding to higher strength orthogonal arrays, as well as twodimensional projective uniformity. Simulation study shows that the constructed Latin hypercube designs are significantly superior to the currently used designs in terms of the times of correctly identifying the significant effects.     

Kato class measures of symmetric Markov processes under heat kernel estimates

We establish the coincidence of two classes of Kato class measures in the framework of symmetric Markov processes admitting upper and lower estimates of heat kernel under mild conditions. One class of Kato class measures is defined by way of the heat kernel, another is defined in terms of the Green kernel depending on some exponents related to the heat kernel estimates. We also prove that pth integrable functions on balls with radius 1 having a uniformity of its norm with respect to centers are of Kato class if p is greater than a constant related to the estimate under the same conditions. These are complete extensions of some results for the Brownian motion on Euclidean space by Aizenman and Simon. Our result can be applicable to many examples, for instance, symmetric (relativistic) stable processes, jump processes on d-sets, Brownian motions on Riemannian manifolds, diffusions on fractals and so on.     

变测度的积分-水平集确定性算法

提出了一个求总极值的变测度确定性算法,对不同的箱子采用不同的测度,结合确定性数论方法选取一致分布佳点集来代替Monte-Carlo随机投点,使水平值充分地下降,更快地到达全局最小,从而提高算法的计算效率.在文中给出了算法的收敛性证明,并通过数值算例验证了它的有效性.     

混水平均匀设计的构造

我们用离散偏差来度量部分因子设计的均匀性,本文的目的在于寻找一些构造混水平均匀设计的方法,这些方法比文献中已有的方法更简单且计算成本更低.我们得到了离散偏差的一个下界,如果一个U 型设计的离散偏差值达到这个下界,那么该设计是—个均匀设计.我们建立了均匀设计与组合设计理论中一致可分解设计之间的联系.通过一致可分解设计,我们提出了一些构造均匀设计的新方法,同时也给出了许多均匀设计存在的无穷类.     

On the concept of possibility-probability consistency

Both probability and possibility may be seen as information about an experiment. It is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once. In this paper some aspects of the concept of possibility-probability consistency are studied. The consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information. We analyse several measures of the degree of consistency and introduce an axiomatic to characterize them.     

Asymptotic expansions of integrals: The term-by-term integration method

The classical term-by-term integration technique used for obtaining asymptotic expansions of integrals requires the integrand to have an uniform asymptotic expansion in the integration variable. A modification of this method is presented in which the uniformity requirement is substituted by a much weaker condition. As we show in some examples, the relaxation of the uniformity condition provides the term-by-term integration technique a large range of applicability. As a consequence of this generality, Watson's lemma and the integration by parts technique applied to Laplace's and a special family of Fourier's transforms become corollaries of the term-by-term integration method.     

Power functions with low uniformity on odd characteristic finite fields

In this paper, we give some new low differential uniformity of some power functions defined on finite fields with odd characteristic. As corollaries of the uniformity, we obtain two families of almost perfect nonlinear functions in GF(3 ⁿ ) and GF(5 ⁿ ) separately. Our results can be used to prove the Dobbertin et al.’s conjecture.