摘要：
The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.
摘要：
当前的服务选择方法大都假设所有服务的QoS(Quality of Service)属性值必须均为确定的实数,并未考虑QoS属性的模糊性。这个假设在实际应用需求中具有一定的局限性,还会丢失大量的数据信息。为增强QoS表达能力,将QoS属性值描述成精确数值型、区间数值型、模糊数值型。同时,用序关系向量表示用户对不同QoS属性的需求偏好,将其转换成用户对QoS属性的主观权重,并采用熵权法计算QoS属性的客观权重。在此基础上,采用相对优势度算法给出混合QoS属性的服务选择过程。最后通过模拟和实验验证,证明相对优势度算法的有效性与合理性。
作者机构：
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079;College of Science, China Three Gorges University, Yichang, 443002;[刘敏] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079;[刘红美] College of Science, China Three Gorges University, Yichang, 443002
作者机构：
[Qin Hong] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Wang Zhenghong] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.;[Chatterjee, Kashinath] Visva Bharati Univ, Dept Stat, Santini Ketan, W Bengal, India.
通讯机构：
[Qin Hong] C;[Wang Zhenghong] S;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.
关键词：
Lower bound;minimum projection uniformity;orthogonality;projection Lee discrepancy;uniformity pattern
摘要：
The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials. On the basis of Lee discrepancy, the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection designs. Moreover, the concepts of uniformity pattern and minimum projection uniformity criterion are proposed, which can be used to assess and compare two and three mixed levels factorials. Statistical justification of uniformity pattern is also investigated.
摘要：
The author studies the properties and applications of quasi-Killing spinors and quasi-twistor spinors and obtains some vanishing theorems. In particular, the author classifies all the types of quasi-twistor spinors on closed Riemannian spin manifolds. As a consequence, it is known that on a locally decomposable closed spin manifold with nonzero Ricci curvature, the space of twistor spinors is trivial. Some integrability condition for twistor spinors is also obtained.
摘要：
We study the differential uniformity of a class of permutations over F_(2n) with n even. These permutations are different from the inverse function as the values x–1 are modified to be (γx)~(–1) on some cosets of a fixed subgroup <γ> of F_(2n)~*. We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent (CCZ-equivalent) classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.
摘要：
Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E(G), define d(e) = d(u) + d(v). Let F denote the set of all simple 2-edge-connected graphs on n ≥ 4 vertices such that G ∈ F if and only if d(e) + d(e')≥ 2n for every pair of independent edges e, e' of G. We prove in this paper that for each G ∈ F,G is not Z_3-connected if and only if G is one of K_(2,n-2), K_(3.n-3)~+ or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 2010, 310: 3390—3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308: 6233-6240].
作者机构：
[李畅] Hubei Province Key Laboratory for Geographical Process Analysing &, Modelling, Central China Normal University, Wuhan, 430079, China;[董才林] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China;[马浩] School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, 430079, China;[李畅] College of Urban and Environmental Science, Central China Normal University, Wuhan, 430079, China
通讯机构：
School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, China
摘要：
We consider the quasilinear Schrodinger equations of the form where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C~1(R) is an odd function with subcritical growth and V (x) is a positive Holder continuous function which is bounded from below, away from zero, and inf_Λ V (x) < inf_(?Λ) V (x) for some open bounded subset Λ of R~N. We prove that there is an ε0 > 0 such that for all ε ∈ (0, ε0], the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V (x) as ε → 0+.
作者机构：
[Ou Zujun] Jishou Univ, Coll Math & Stat, Jishou 416000, Peoples R China.;[Qin Hong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Ou Zujun; Cai Xu] Cent China Normal Univ, Sch Phys Sci & Technol, Wuhan 430079, Peoples R China.
通讯机构：
[Qin Hong] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
three-level factorials;wrap around L2-discrepancy;combined design;foldover plan;lower bound
摘要：
The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L_2-discrepancy to assess the optimal foldover plans for three-level designs. For three-level fractional factorials as the original designs, the general foldover plan and combined design under a foldover plan are defined, some theoretical properties of the defined foldover plans are obtained, a tight lower bound of the wrap-around L_2-discrepancy of combined designs under a general foldover plan is also obtained, which can be used as a benchmark for searching optimal foldover plans. For illustration of the usage of our theoretical results, a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated, where 2 ≤ s ≤ 11.
作者机构：
[Qin, Hong; Wang, Zhenghong] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Zhenghong] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.
通讯机构：
[Wang, Zhenghong] S;South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.
摘要：
We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all the Hamming distances of any two distinct runs are the same, and the uniformity pattern proposed by H. Qin, Z. Wang, and K. Chatterjee [J. Statist. Plann. Inference, 2012, 142: 1170–1177] comes from discrete discrepancy for q-level designs. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity rule to assess and compare q-level factorials.
作者机构：
[Li, Gong-bao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gong-bao] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
In this paper, we study the existence of multiple solutions to the following nonlinear elliptic boundary value problem of p-Laplacian type: {-Delta(p)u = f(x,u), x is an element of Omega, u = 0, x is an element of partial derivative Omega, where 1 < p < infinity, Omega subset of R-N is a bounded smooth domain, Delta(p)u = div (vertical bar Du vertical bar(p-2)Du) is the p-Laplacian of u and f: Omega x R -> R satisfies lim(vertical bar t vertical bar ->infinity) f(x, t)/vertical bar t vertical bar(p-2)t = l uniformly with respect to x is an element of Omega, and l is not an eigenvalue of -Delta(p) in W-0(1,p)(Omega) but f(x, t) dose not satisfy the Ambrosetti-Rabinowitz condition. Under suitable assumptions on f (x, t), we have proved that (*) has at least four nontrivitial solutions in W-0(1,p) (Omega) by using Nonsmooth Mountain-Pass Theorem under (C)(c) condition. Our main result generalizes a result by N. S. Papageorgiou, E. M. Rocha and V. Staicu in 2008 (Calculus of Variations and Partial Differential Equations, 33: 199-230(2008)) and a result by G. B. Li and H. S. Zhou in 2002 (Journal of the London Mathematical Society, 65: 123-138(2002)).
