BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2^n-（n-k） DESIGNS

Clear effects criterion is an important criterion for selecting fractional factorial designs[1].Tang et al.[2]derived upper and lower bounds on the maximum number of clear two-factor interactions（2fi＇s）in 2^n-（n-k）designs of resolution Ⅲ and Ⅳ by constructing 2^n-（n-k）designs.But the method in[2]does not perform well sometimes when the resolution is Ⅲ.This article modifies the construction method for 2^n-（n-k） designs of resolution Ⅲ in[2].The modified method is a great improvement on that used in[2].     

Some results on 4~m2~n designs with clear two-factor interaction components

Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.     

非同构饱和正交设计的最小矩混杂优势准则

为了区分不同构的饱和正交设计, Fang 和 Zhang^[2]提出最小混杂优势准则区分不同构的对称饱和正交设计, 然而该方法不能区分非对称的情况. 为此, 该文考虑最小矩混杂优势准则及其性质并推广文献[2]的结果. 同时, 基于该准则, 给出一个新算法来检测对称或非对称设计的非同构性. 例子显示最小矩混杂优势准则可以有效的区分非同构饱和设计.     

Rigidity Theorem for Hypersurfaces in a Unit Sphere

By investigating hypersurfaces M ⁿ in the unit sphere S ⁿ⁺¹(1) with H _k = 0 and with two distinct principal curvatures, we give a characterization of torus the . We extend recent results of Perdomo [9], Wang [10] and Otsuki [8].     

Bounds on the maximum numbers of clear two-factor interactions for 2~((n1+n2)-(k1+k2)) fractional factorial split-plot designs

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures. There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors, which can form three types of two-factor interactions: WP2fi, WS2fi and SP2fi. This paper considers FFSP designs with resolutionⅢorⅣunder the clear effects criterion. It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs, and gives some methods for constructing the desired FFSP designs. It further examines the performance of the construction methods.     

8×4×2~n设计纯净两因子交互作用成分最大数的界

混水平部分因析设计在各类试验中有广泛应用.纯净效应准则是用于选取最优部分因析设计的重要准则之一.本文考虑含有一个八水平因子、一个四水平因子和若干二水平因子的8×4×2~n混水平设计,给出了分辨度为Ⅲ和Ⅳ的该类混水平设计包含纯净两因子交互作用成分最大数的上界和下界.下界通过构造特定设计而得到.     

方程f~（n）（x）＝Af~（n－k）（（ax＋b）／（cx－a））

本文提出方程ｆ~（ｎ）（ｘ）＝Ａｆ（ｎ－ｋ）（（ａｘ＋ｂ）／（ｃｘ－ａ）），证明它是可积的．所得结论是文献［１］中结论的推广．     

On the optimality of a class of designs with three concurrences

In the present paper we consider a class of unequally replicated designs having concurrence range 2 and spectrum of the form μ₁(μ₂)^v−3μ₃. Now, Jacroux’s [Some sufficient conditions for the type I optimality of block designs, J. Statist. Plann. Inference 11 (1985) 385-396] Proposition 2.4 says that a design with spectrum of the above form, if satisfies some further conditions, is type 1 optimal. Unfortunately, this proposition does not apply to our designs since they have a poor status regarding E-optimality. Yet we are able to prove the A-optimality (in the general class) of these designs using majorisation technique. A method of construction of an infinite series of our A-optimal designs has also been given.The first and only known infinite series of examples of designs satisfying Jacroux’s conditions appears to be the first one in Section 4.1 of Morgan and Srivastav [On the Type-1 optimality of nearly balanced incomplete block designs with small concurrence range, Statist. Sinica 10 (2000) 1091-1116] - hitherto referred to as [MS]. In this paper, we use majorisation technique to prove stronger optimality properties of the above mentioned designs of [MS] as well as to present simpler proof of another optimality result in [MS].     

Topology optimization methods for guided flow – comparison of optimality criteria vs. phase-field method

Optimization of guided flow problems is an important task for industrial applications especially those with high Reynolds numbers. There exist several optimization methods to increase the energy efficiency of these problems. Different optimization methods are shown bei Klimetzek [1], Hinterberger [2] and Pingen [3]. In recent years the phase-field method has been shown to be an applicable method for different kinds of topology optimization [4, 5]. We present results of topology optimization methods with optimality criterion and by using a phase-field model in the area of guided fluid flow problems. The two methods aim on the same main target reducing the pressure drop between the inlet and outlet of the flow domain. The first method is based on local optimality criterion, preventing the backflow in the flow domain [1, 6, 7]. The second method is based on a phase field model, which describes a minimization problem and uses a specially constructed driving force to minimize the total energy of the system [4, 5]. We investigate the capabilities and limits of both methods and present examples of different resulting geometries. The initial configurations are prepared in a way that the same optimization problem is solved with both methods. We discuss these results regarding the shape of the improved flow geometry. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

泛函梯度数值计算的一种新方法—正交试验法

本文研究并揭示了L_(2~a)(2~(2~a-1))型正交表行(列)间的递推规律,提出了一种泛函梯度数值计算的新方法——正交试验法,该方法在计算速度和精度上优于直接梯度法;在通用性及节省内存方面优于伴随算子法。     

求解线性规划问题的一种全搜索方法

在[1]基础上提出一个全搜索方法,它通常只需迭代一、二次,即可得到一个基可行解,之后依据最优性条件进行的寻优迭代,也较[2]的搜索方位更多,从而总体上效果更好。     

Fixpunkte in homogenen Räumen

This note contains a criterion for the existence of fixed points under the operation of a real Lie group on a symmetric space of non-compact type. This generalizes results of [2] and [4] and gives a shorter proof for the special case considered in [2] and [4].     

Rigidity Theorem for Hypersurfaces in a Unit Sphere

By investigating hypersurfaces M ⁿ in the unit sphere S ⁿ⁺¹(1) with H _k = 0 and with two distinct principal curvatures, we give a characterization of torus the S¹(?{k/n})×S^n-1(?{(n-k)/n})S^1(\sqrt{k/n})\times S^{n-1}(\sqrt{(n-k)/n}) . We extend recent results of Perdomo [9], Wang [10] and Otsuki [8].     

奇异(k,n-k)多点边值问题的正解

应用不动点指数理论,在与相应线性算子本征值有关的条件下,得到了高阶(k, n-k)多点边值问题(-1)n-kφ(n)(x)=h(x)f(φ(x)),0相似文献   

A Fixed Point Approach to Almost Double Derivations and Lie *-Double Derivations

Using the fixed point method, we prove the Hyers–Ulam stability of double derivations associated with the following additive mapping: $$\begin{array}{ll}{\sum\limits^{n}_{k=2}\left(\sum\limits^{k}_{i_{1}=2} \sum\limits^{k+1}_{i_{2}=i_{1}+1}\dots \sum\limits^{n}_{i_{n-k+1}=i_{n-k}+1}\right)}\\ {\quad \times f\left( \sum\limits^{n}_{i=1, i\neq i_{1},\dots,i_{n-k+1} } x_{i}\right.\left.-\sum\limits^{n-k+1}_{ r=1}x_{i_{r}}\right)+f\left(\sum\limits^{n}_{ i=1} x_{i}\right) =2^{n-1} f(x_{1})}\end{array}$$ for a fixed positive integer n with n ≥ 2.     

Über Picardmengen ganzer Funktionen

Following Lehto we call a set E in the complex plane a Picard set for integral functions, if every non-rational integral function omits at most one finite value in the complement (with respect to the plane) of E. The existence of non-trivial Picard sets was proved by Lehto [3]. The aim of this paper is to give a new criterion for denumberable point sets E to be Picard sets for integral functions. In some way the criterion given by theorem 1 is an extension of the result on Picard sets for integral functions given by Toppila [5] and improves the criterion given by the author in [6].     

On the Ascending Subgraph Decomposition Problem

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｐａｐｅｒ［１］,Ａｌａｖｉａｎｄｏｔｈｅｒｓｄｅｆｉｎｅｄｔｈｅｃｏｎｃｅｐｔｏｆａｓｃｅｎｄｉｎｇｓｕｂｇｒａｐｈｄｅｃｏｍｐｏｓｉｔｉｏｎ：Ｄｅｆｉｎｉｔｉｏｎ　ＬｅｔＧｂｅａｇｒａｐｈｏｆｐｏｓｉｔｉｖｅｓｉｚｅｑ,ａｎｄｌｅｔｎｂｅｔｈａｔｐｏｓｉｔｉｖｅｉｎｔｅｇｅｒｆｏｒｗｈｉｃｈｎ＋１２ｑ＜ｎ＋２２．ＴｈｅｎＧｉｓｓａｉｄｔｏｈａｖｅａｎａｓｃｅｎｄｉｎｇｓｕｂｇｒａｐｈｄｅｃｏｍｐｏｓｉｔｉｏｎ（ＡＳＤ）ｉｆＧｃａｎｂｅｄｅｃｏｍｐｏｓｅｄ…     

NORM SUMMABILITY OF N(O)RLUND LOGARITHMIC MEANS ON UNBOUNDED VILENKIN GROUPS

The (N(o)rlund)logarithmic means of the Fburier series is:tnf=1/ln∑n-1k=1Skf/n-k,where ln=∑n-1k=11/k.In general,the Fejér(C,1)means have better propeaies than the logarithmic ones.We compare them and show that in the case of some unbounded Vilenkin systems the situation changes.     

On 2-dimensional insertion-deletion Reed-Solomon codes with optimal asymptotic error-correcting capability

Reed-Solomon codes have gained a lot of interest due to its encoding simplicity, well structuredness and list-decoding capability [6] in the classical setting. This interest also translates to other metric setting, including the insertion and deletion (insdel for short) setting which is used to model synchronization errors caused by positional information loss in communication systems. Such interest is supported by the construction of a deletion correcting algorithm of insdel Reed-Solomon code in [22] which is based on the Guruswami-Sudan decoding algorithm [6]. Nevertheless, there have been few studies [3] on the insdel error-correcting capability of Reed-Solomon codes.In this paper, we discuss a criterion for a 2-dimensional insdel Reed-Solomon codes to have optimal asymptotic error-correcting capabilities, which are up to their respective lengths. Then we provide explicit constructions of 2-dimensional insdel Reed-Solomon codes that satisfy the established criteria. The family of such constructed codes can then be shown to extend the family of codes with asymptotic error-correcting capability reaching their respective lengths provided in [3, Theorem 2] which provide larger error-correcting capability compared to those defined in [25].     

Asynchronous multisplitting iteration with different weighting schemes

The multisplitting iteration method was presented by O’Leary and White [5] for solving large sparse linear systems on parallel multiprocessor system. In this paper, we further set up an asynchronous variant for the multisplitting iteration method with different weighting schemes studied by White [8]. Moreover, we establish a general convergence criterion for asynchronous iteration framework, and then prove the convergence of the new asynchronous multisplitting iteration method with different weighting schemes by making use of this general criterion.