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.     

Minimum Weight Design for Structural Eigenvalue Problems by Optimal Control Theory*, †

The application of optimal control theory to minimum weight design of continuous one-dimensional structural elements subject to eigenvalue constraints is discussed. If not only the value of an eigenvalue is prescribed but also its position in the sequence of the ordered eigenvalues—for example, the critical buckling load of a column—the corresponding optimal control problem is shown to include necessarily all eigenvalues. Considering the unspecified eigenvalues as free parameters, necessary conditions for minimum weight design are derived. These conditions are compared with those obtained by use of variational methods. Attention is focused on the special case of multimodal solutions.     

一个特殊6点图Q与nK_1,P_n及C_n的联图交叉数

图的交叉数是图的一个重要参数,研究图的交叉数问题是拓扑图论中的前沿难题.确定图的交叉数是NP-难问题,因为其难度,能够确定交叉数的图类很少.通过圆盘画法途径,确定了一个特殊6点图与n个孤立点nK_1,路P_n及圈C_n的联图的交叉数分别是cr(Q+nK_1)=Z(6,n)+2[n/2],cr(Q+P_n)=Z(6,n)+2[n/2]+1及cr(Q+C_n)=Z(6,n)+2[n/2]+3.     

Structure of random 312‐avoiding permutations

We evaluate the probabilities of various events under the uniform distribution on the set of 312‐avoiding permutations of . We derive exact formulas for the probability that the i^th element of a random permutation is a specific value less than i, and for joint probabilities of two such events. In addition, we obtain asymptotic approximations to these probabilities for large N when the elements are not close to the boundaries or to each other. We also evaluate the probability that the graph of a random 312‐avoiding permutation has k specified decreasing points, and we show that for large N the points below the diagonal look like trajectories of a random walk. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 599–631, 2016     

Muscle oxygenation measurement in humans by noninvasive optical spectroscopy and Locally Weighted Regression

We have developed a method to make real-time, continuous, noninvasive measurements of muscle oxygenation (Mox) from the surface of the skin. A key development was measurement in both the visible and near infrared (NIR) regions. Measurement of both oxygenated and deoxygenated myoglobin and hemoglobin resulted in a more accurate measurement of Mox than could be achieved with measurement of only the deoxygenated components, as in traditional near-infrared spectroscopy (NIRS). Using the second derivative with respect to wavelength reduced the effects of scattering on the spectra and also made oxygenated and deoxygenated forms more distinguishable from each other. Selecting spectral bands where oxygenated and deoxygenated forms absorb filtered out noise and spectral features unrelated to Mox. NIR and visible bands were scaled relative to each other in order to correct for errors introduced by normalization. Multivariate Curve Resolution (MCR) was used to estimate Mox from spectra within each data set collected from healthy subjects. A Locally Weighted Regression (LWR) model was built from calibration set spectra and associated Mox values from 20 subjects using 2562 spectra. LWR and Partial Least Squares (PLS) allow accurate measurement of Mox despite variations in skin pigment or fat layer thickness in different subjects. The method estimated Mox in five healthy subjects with an RMSE of 5.4%.     

计算化学在正丁醚制备实验教学中的应用*

正丁醚的制备是重要的大学有机化学实验,为提高学生对该实验所涉及的反应机理和关键操作要点的深入了解,采用Gaussian计算软件对正丁醇在酸催化下和无催化剂下的反应体系进行了研究,重点考察了酸催化下反应的主、副反应方向的反应机理。结果表明无催化剂下,正丁醇在常压液相下几乎不能发生反应;在酸催化下,正丁醇发生取代反应生成醚的反应路径是优势反应通道;酸催化下正丁醇的取代和消除反应速率常数均随温度增加而迅速增大,但消除反应的反应速率随温度增加更快,温度超过420 K消除反应将变得很明显,综合考虑,制备正丁醚的反应温度应控制在130~140 ℃之间较为合适。利用计算化学以图、表和动图等形式直观、动态、量化地解释了正丁醇成醚和成烯反应的竞争,该结果有助于更好地控制该反应体系,可用作实验教材的补充内容。     

Optical constants of organic insulators in the UV range extracted from reflection electron energy loss spectra

Reflection electron energy loss spectroscopy (REELS) spectra were measured for seven insulating organic compounds (DNA, Irganox 1010, Kapton, polyethylene [PE], poly(methyl methacrylate) [PMMA], polystyrene [PS] and polytetrafluoroethylene [PTFE]). Optical constants and energy band gaps were extracted from the measured REELS spectra after elimination of multiple electron scattering via a deconvolution and fitting the normalised single scattering energy loss spectra to Drude and Drude–Lindhard model dielectric functions, constrained by the Kramers–Kronig sum and f-sum rules. Satisfactory agreement is found for those optical constants for which literature data exists. For PTFE, the observed features in the optical data correspond to its electronic structure.     

Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations

We study the focusing mass-critical rough nonlinear Schrödinger equations, where the stochastic integration is taken in the sense of controlled rough path. In both dimensions one and two, the minimal mass blow-up solutions are constructed, which behave asymptotically like the pseudo-conformal blow-up solutions near the blow-up time. Furthermore, the global well-posedness is obtained if the mass of initial data is below that of the ground state. These results yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schrödinger equations with lower order perturbations, particularly in the absence of the standard pseudo-conformal symmetry and the conservation law of energy.