A fuzzy shortest path with the highest reliability

This paper concentrates on a shortest path problem on a network where arc lengths (costs) are not deterministic numbers, but imprecise ones. Here, costs of the shortest path problem are fuzzy intervals with increasing membership functions, whereas the membership function of the total cost of the shortest path is a fuzzy interval with a decreasing linear membership function. By the max–min criterion suggested in [R.E. Bellman, L.A. Zade, Decision-making in a fuzzy environment, Management Science 17B (1970) 141–164], the fuzzy shortest path problem can be treated as a mixed integer nonlinear programming problem. We show that this problem can be simplified into a bi-level programming problem that is very solvable. Here, we propose an efficient algorithm, based on the parametric shortest path problem for solving the bi-level programming problem. An illustrative example is given to demonstrate our proposed algorithm.     

An extension of labeling techniques for finding shortest path trees

Label setting techniques are all based on Dijkstra’s condition of always scanning the node with the minimum label, which guarantees that each node will be scanned exactly once; while this condition is sufficient it is not necessary. In this paper, we discuss less restrictive conditions that allow the scanning of a node that does not have the minimum label, yet still maintaining sufficiency in scanning each node exactly once; various potential shortest path schemes are discussed, based on these conditions. Two approaches, a label setting and a flexible hybrid one are designed and implemented. The performance of the algorithms is assessed both theoretically and computationally. For comparative analysis purposes, three additional shortest path algorithms – the commonly cited in the literature – are coded and tested. The results indicate that the approaches that rely on the less restrictive optimality conditions perform substantially better for a wide range of network topologies.     

Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation

In this paper, symmetries and group invariant solutions to the Gardner-KP equation are obtained by using the direct symmetry method. At the same time, we find the corresponding Lie algebra, optimal system, classification and the similarity reductions to the equation, respectively. Our exact solutions generalize the corresponding results obtained by Wazwaz. In addition, the conservation laws of Gardner-KP equation are also given.     

Application of Rouche’s theorem for MP filter design

The method for the minimum-phase (MP) finite impulse response (FIR) filter design, based on Rouche’s theorem from complex analysis is presented here. The filter is designed directly from a given specification. The method uses the cosine filters and the sharpening technique resulting in a multiplierless filter.     

Algebras of fuzzy sets

In this paper we investigate two kinds of algebras of fuzzy sets, which are obtained by using Zadeh's extension principle. We give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets. We prove that if the structure of truth values is a complete residuated lattice, the induced algebra of a subalgebra of an algebra can be embedded into the induced algebra of fuzzy sets of . For direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product. In the case of homomorphisms and direct products, the two kinds of algebras of fuzzy sets behave in different ways.     

Correlation Inequalities and Applications to Vector-Valued Gaussian Random Variables and Fractional Brownian Motion

In this paper we extend certain correlation inequalities for vector-valued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correlation assumption, we prove a Borel-Cantelli lemma, maximal inequalities and several laws of large numbers. This extends results of Be?ka and Ciesielski and of Hytönen and the author. In the second part of the paper we consider a certain class of vector-valued Gaussian processes which are α-Hölder continuous in p-th moment. For these processes we obtain Besov regularity of the paths of order α. We also obtain estimates for the moments in the Besov norm. In particular, the results are applied to vector-valued fractional Brownian motions. These results extend earlier work of Ciesielski, Kerkyacharian and Roynette and of Hytönen and the author.     

构成型顾客满意模型的偏最小二乘路径建模及其应用

本文研究了偏最小二乘路径建模在顾客满意模型中的应用,特别是引入了构成型关系的模型。本文首先比较了构成型模型和反映型模型的区别,并详尽阐述了构成型模型的偏最小二乘建模原理,接着构建了电信企业顾客满意度指数模型,并考虑了如何在指数模型中引入构成型外部关系.利用该电信企业的数据,比较分析了构成型模型(顾客期望和质量感知潜变量调整为构成型关系)和反映型模型(所有潜变量均为反映型关系)的实证结果,研究表明在为企业提供改善顾客满意水平的信息上两种模型具有较好的相似性,但是构成型模型能够提供更加稳定的结果,从而验证了顾客满意模型中引入构成型模型的可行性.     

The Geodesic Problem in Quasimetric Spaces

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality d(x,y)≤σ(d(x,z)+d(z,y)) for some constant σ≥1, rather than the usual triangle inequality. Such a space is called a quasimetric space. We show that many well-known results in metric spaces (e.g. Ascoli-Arzelà theorem) still hold in quasimetric spaces. Moreover, we explore conditions under which a quasimetric will induce an intrinsic metric. As an example, we introduce a family of quasimetrics on the space of atomic probability measures. The associated intrinsic metrics induced by these quasimetrics coincide with the d _α metric studied early in the study of branching structures arisen in ramified optimal transportation. An optimal transport path between two atomic probability measures typically has a “tree shaped” branching structure. Here, we show that these optimal transport paths turn out to be geodesics in these intrinsic metric spaces. This work is supported by an NSF grant DMS-0710714.     

$W_m$与$P_n$ 的笛卡儿积图的交叉数

Most results on crossing numbers of graphs focus on some special graphs, such as the Cartesian products of small graphs with path, star and cycle. In this paper, we obtain the crossing number formula of Cartesian products of wheel Wm with path Pn, for arbitrary m ≥ 3 and n≥ 1.     

Electronic micropipettor: a versatile fluid propulsion and injection device for micro-flow analysis

The shortage of ready to use small sized liquid propulsion and switching devices for microfluidic cells (μ-cell) is a bottleneck in the dissemination of micro-flow analysis (μ-FA), now that microfluidic electrochemical cells can be designed and assembled in any laboratory by thermal transfer of laser printed masks and CD-Rs. Microprocessor-controlled electronic pipettors, commercially available with minimum capacity of 10 μL, represent a compromise solution between oversized peristaltic pumps and tiny “on a chip” micropumps and valves. The versatility of the electronic pipette coupled with the μ-cell (13-μm deep longitudinal channel) was demonstrated in three operation modes: SIA like, FIA like and direct injection analysis (DIA). Injections of 100 nL K₄Fe(CN)₆ (0.1 mol L⁻¹ KCl) define a linear analytical curve (r = 0.999) in the range of 5 × 10⁻⁷ to 1.0 × 10⁻³ mol L⁻¹ for flow amperometry at a gold electrode potentiostated at 0.4 V versus Ag/AgCl. Methods for the amperometric μ-flow determination of promethazine (FIA like), dipyrone (SIA like) and chlorpromazine (DIA) in pharmaceutical formulations were developed and applied to real samples. Excellent linearity of analytical curves and high repeatability (R.S.D. < 3.0%) at the low picomole range was obtained and all results for real samples were in agreement with reference methods. The results reflect the stability and the reliability of the setups envisioned for the electronic pipette coupled with amperometric μ-cell and the validity of the μ-FA methods.