On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.     

Multiple response optimization: a global criterion‐based method

Processes and products have by nature many quality characteristics that must be in some sense optimized simultaneously. With this aim, a method which can be used easily and efficiently by practitioners for optimizing multi‐response problems is proposed. Implementation steps and considerations, in addition to optimization measures to assess method's solutions and guide the analyst in finding an effective compromise solution, are also presented. Three classical examples from the literature are used to assess the performance of several prominent methods in the response surface methodology (RSM) framework and help practitioners make a better‐informed choice among them. Copyright © 2010 John Wiley & Sons, Ltd.     

A diagonal measure and a local distance matrix to display relations between objects and variables

Proper permutation of data matrix rows and columns may result in plots showing striking information on the objects and variables under investigation. To control the permutation first, a diagonal matrix measure D was defined expressing the size relations of the matrix elements. D is essentially the absolute norm of a matrix where the matrix elements are weighted by their distance to the matrix diagonal. Changing the order of rows and columns increases or decreases D. Monte Carlo technique was used to achieve maximum D in the case of the object distance matrix or even minimal D in the case of the variable correlation matrix to get similar objects or variables close together. Secondly, a local distance matrix was defined, where an element reflects the distances of neighboring objects in a limited subspace of the variables. Due to the maximization of D in the local distance matrix by row and column changes of the original data matrix, the similar objects were arranged close to each other and simultaneously the variables responsible for their similarity were collected close to the diagonal part defined by these objects. This combination of the diagonal measure and the local distance matrix seems to be an efficient tool in the exploration of hidden similarities of a data matrix. Copyright © 2009 John Wiley & Sons, Ltd.     

A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers’ demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically.     

平环和的Heegaard亏格的一个下界

Let Mi, i = 1,2, be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of OMi. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper, we give a lower bound for the genus of the annulus sum M in the condition of the Heegaard distances of the submanifolds M1 and M2     

Long distance laser ultrasonic propagation imaging system for damage visualization

Wind turbine blade failure is the most prominent and common type of damage occurring in operating wind turbine systems. Conventional nondestructive testing systems are not available for in situ wind turbine blades. We propose a portable long distance ultrasonic propagation imaging (LUPI) system that uses a laser beam targeting and scanning system to excite, from a long distance, acoustic emission sensors installed in the blade. An examination of the beam collimation effect using geometric parameters of a commercial 2 MW wind turbine provided Lamb wave amplitude increases of 41.5 and 23.1 dB at a distance of 40 m for symmetrical and asymmetrical modes, respectively, in a 2 mm-thick stainless steel plate. With this improvement in signal-to-noise ratio, a feasibility study of damage detection was conducted with a 5 mm-thick composite leading edge specimen. To develop a reliable damage evaluation system, the excitation/sensing technology and the associated damage visualization algorithm are equally important. Hence, our results provide a new platform based on anomalous wave propagation imaging (AWPI) methods with adjacent wave subtraction, reference wave subtraction, reference image subtraction, and the variable time window amplitude mapping method. The advantages and disadvantages of AWPI algorithms are reported in terms of reference data requirements, signal-to-noise ratios, and damage evaluation accuracy. The compactness and portability of the proposed UPI system are also important for in-field applications at wind farms.     

大口径合成孔径激光成像雷达演示样机及其实验室验证

合成孔径激光成像雷达(SAIL)的主要技术指标如光学足趾尺寸和成像分辨率等都必须在所设计的远距离传输后实现.提出了一种在实验室空间近距离实现SAIL全系统贯通验证的方法,即在SAIL中附加光学装置使得其在近距离产生发射光束的准几何投影和足够大的外差接收视场,从而产生近距离二维SAIL成像必需的并且适当的光学足趾和方位向...     

Spectral studies of Co substituted Ni-Zn ferrites

The spinel ferrites Zn_0.35Ni_0.65−xCo_xFe₂O₄, 0≤x≤1, have been prepared using the standard ceramic technique. Room temperature Mössbauer, X-ray and infrared IR spectra were used for carrying out this study. X-ray patterns reveal that all the samples have single-phase cubic spinel structure. The Mössbauer spectra of the samples show a paramagnetic phase for x=0 and a six-line magnetic pattern and a central paramagnetic phase for x≥0.1. They are analyzed and attributed to two magnetic subpatterns and two quadrupole doublets due to Fe³⁺ ions at the tetrahedral A-sites and octahedral B-sites. Four absorption bands are observed in IR spectra. They confirm the spinel structure of the samples and existence of Fe³⁺ ions in the sample sublattices. The deduced hyperfine interactions, lattice parameters, absorption band positions and intensities and force constant are found to be dependent on the substitution factor x, where the cation distribution is estimated. The hyperfine magnetic fields, magnetization and lattice resonant frequency are found to be dependent on the interionic distance.     

光速在相对论中的核心地位

介绍了关于真空中光速的假定的重要作用,它不仅是相对论理论的基础,而且使人们能够定义同时性并测量空间距离.     

Locating a single facility and a high-speed line

In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time from the clients to the facility, using the _L1$L_1$ or Manhattan metric. The rapid transit line is given by a segment with any length and orientation, and is an alternative transportation line that can be used by the clients to reduce their travel time to the facility. We study the variant of the problem in which clients can enter and exit the highway at any point. We provide an O(n³)$O(n^3)$-time algorithm that solves this variant, where n is the number of clients. We also present a detailed characterization of the solutions, which depends on the speed given along the highway.