RELATIVE ASYMPTOTICS FOR ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A PERTURBED MATRIX MEASURE ON THE UNIT CIRCLE

Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.

Relation Matrix of Water Exchange for Sea Bays and Its Application

Water exchange is an important hydrodynamic character of sea bays, and it is the basis for the study of the environmental capacity of sea bays. In this paper, a relation matrix is set up to describe the interaction among different areas of a sea bay, and to predict the water quality of those areas. The relation matrix is calculated based on the numerical results from a water quality model. This method is applied to the study of water exchange and the prediction of water quality of the Bohai Sea. The Bohai Sea is divided into five areas, and the effect of seasonal wind is taken into consideration. The results show a） the relation matrix can be used to study the water exchange among different areas and predict water quality of different areas at the respective characteristic time, b） the reduction of pollutant is dependent on both water exchange and initial distribution of the pollutant, and c） the half-life time of the pollutant is longer than the half-exchange time of the sea water.

Effect of sintering on the relative density of Cr-coated diamond/Cu composites prepared by spark plasma sintering

Cr-coated diamond/Cu composites were prepared by spark plasma sintering. The effects of sintering pressure, sintering temperature, sintering duration, and Cu powder particle size on the relative density and thermal conductivity of the composites were investigated in this paper. The influence of these parameters on the properties and microstructures of the composites was also discussed. The results show that the relative density of Cr-coated diamond/Cu reaches ~100% when the composite is gradually compressed to 30 MPa during the heating process. The densification temperature increases from 880 to 915℃ when the diamond content is increased from 45vol% to 60vol%. The densification temperature does not increase further when the content reaches 65vol%. Cu powder particles in larger size are beneficial for increasing the relative density of the composite.

Attribute Reduction in Decision Systems Based on Relation Matrix

This paper proposes,from the viewpoint of relation matrix,a new algorithm of attribute reduction for decision systems.Two new and relative reasonable indices are first defined to measure significance of the attributes in decision systems and then a heuristic algorithm of attribute reduction is formulated.Moreover,the time complexity of the algorithm is analyzed and it is proved to be complete.Some numerical experiments are also conducted to access the performance of the presented algorithm and the results demonstrate that it is not only effective but also efficient.

Fuzzy Optimum Model of Semi-Structural Decision for Lectotype Optimization of Offshore Platforms

In the process of concept design of offshore platforms, it is necessary to select the best from feasible alternatives through comparison and filter. The criterion set, used to evaluate and select the satisfying alternative, consists of many qualitative and quantitative factors. Therefore, the selection is a problem of multicriteria and semi-structural decision-making. Different from traditional methods in semi-structural decision-making, a new framework and methodology is presented in this paper for evaluation of offshore platform alternatives, First, the criterion set is established for the evaluation of alternatives. Next, the approach is studied to construct the relative membership degree matrix, in which both qualitative and quantitative factors are consistent with the uniform calculating standard. And then a new weight-assessing method is developed for calculation of the weights based on the relative membership degree matrix. Finally, a multi-hierarchy fuzzy optimum model is adopted to select the satisfying offshore platform alternative. A case study shows that the new framework and methodology are scientific, reasonable and easy to use in practice.

PDRK:A General Kinetic Dispersion Relation Solver for Magnetized Plasma

A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.

On the correspondence between three nodes W states in quantum network theory and the oriented links in knot theory

The GHZ states and W states are two fundamental types of three qubits quantum entangled states. For finding the knotted pictures of three nodes W states, on the one side, we empty any one node, thus obtaining three degenerated twonode W states, then we find the nonzero submatrix of the corresponding covariance correlation tensor in quantum network theory. On the other side, excepting the linkage 41 corresponding to Bell bases, we conjecture that the another one possible oriented link （which is composed of two-component knots entangled with each other and has four crossings） would be the required knotted pictures of the two nodes W states, thence obtain the nonzero submatrix of the Alexander relation matrix in the theory of knot crystals for these knotted pictures. The equality of the two nonzero submatfices of different kinds thus verify the exactness of our conjecture. The superposition of three knotted pictures of two-node W states from different choices of the emptied node gives the knotted pictures of three-node W states, thus shows the correspondence between three-node W states in quantum network theory and the oriented links in knot theory. Finally we point out that there is an intimate and simple relationship between the knotted pictures of GHZ states and W states.

Correspondence Between Bell Bases and Oriented Links in Knot Theory

From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage in knot theory.

An Improved Direction Relation Detection Model for Spatial Objects

Direction is a common spatial concept that is used in our daily life. It is frequently used as a selection condition in spatial queries. As a result, it is important for spatial databases to provide a mechanism for modeling and processing direction queries and reasoning. Depending on the direction relation matrix, an inverted direction relation matrix and the concept of direction pre- dominance are proposed to improve the detection of direction relation between objects. Direction predicates of spatial systems are also extended. These techniques can improve the veracity of direction queries and reasoning. Experiments show excellent efficiency and performance in view of direction queries.

The application of fuzzy equivalence relation based on the quotient space in cluster analysis

A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.

A New Method of Global Path Planning for AGV

Path planning is important in the research of a mobile robot （MR）. Methods for it have been used in different applications. An automated guided vehicle（ AGV） , which is a kind of MR, is used in a flexible manufacturing system （FMS）. Path planning for it is essential to improve the efficiency of FMS. A new method was proposed with known obstacle space FMS in this paper. FMS is described by the Augmented Pos Matrix of a Machine （ APMM ） and Relative Pos Matrix of Machines （ RPMM）, which is smaller. The optimum path can be obtained according to the probability of the path and the maximal probability path. The suggested algorithm of path planning was good performance through simulation result： simplicity, saving time and reliability.

Research and Implementation of Task Management Model in Product Development Process Management

The implementation of product development process management (PDPM) is an effective means of developing products with higher quality in shorter lead time. It is argued in this paper that product, data, person and activity are basic factors in PDPM With detailed analysis of these basic factors and their relations in product developmed process, all product development activities are considered as tasks and the management of product development process is regarded as the management of task execution A task decomposition based product development model is proposed with methods of constructing task relation matrix from layer model and constraint model resulted from task decomposition. An algorithm for constructing directed task graph is given and is used in the management of tasks. Finally, the usage and limitation of the proposed PDPM model is given with further work proposed.

Scientific articles recommendation with topic regression and relational matrix factorization

In this paper we study the problem of recommending scientific articles to users in an online community with a new perspective of considering topic regression modeling and articles relational structure analysis simultaneously. First, we present a novel topic regression model, the topic regression matrix factorization （tr-MF）, to solve the problem. The main idea of tr-MF lies in extending the matrix factorization with a probabilistic topic modeling. In particular, tr-MF introduces a regression model to regularize user factors through probabilistic topic modeling under the basic hypothesis that users share similar preferences if they rate similar sets of items. Consequently, tr-MF provides interpretable latent factors for users and items, and makes accurate predictions for community users. To incorporate the relational structure into the framework of tr-MF, we introduce relational matrix factorization. Through combining tr-MF with the relational matrix femtorization, we propose the topic regression collective matrix factorization （tr-CMF） model. In addition, we also present the collaborative topic regression model with relational matrix factorization （CTR-RMF） model, which combines the existing collaborative topic regression （CTR） model and relational matrix factorization （RMF）. From this point of view, CTR-RMF can be considered as an appropriate baseline for tr-CMF. Further, we demonstrate the efficacy of the proposed models on a large subset of the data from CiteULike, a bibliography sharing service dataset. The proposed models outperform the state-of-the-art matrix factorization models with a significant margin. Specifically, the proposed models are effective in making predictions for users with only few ratings or even no ratings, and support tasks that are specific to a certain field, neither of which has been addressed in the existing literature.

A Relation Matrix Approach to Labelling Temporal Relations in Scheduling

In this paper,we present a relation matrix description of temporal relations.Based on this modela new algorithm for labelling temporal relations is proposed.Under certain conditions the algorithm iscompleted and has a polynomial complexity.In general cases it is still an efficient algorithm comparedto some known algorithms.

Precedent Order on Economic Sectors of Qingchuan County

In this model. the method of crass-influential analysis in multiobjective comprehensive appraisment is made to arrange economic sectors of Qingchuan county in precedent order of development. We established the system on appreciatory index. and obtained the related distribution by contributing mains and related matrix. Using different programs. we arranged alphabetically the sectors of Qingchuan county in the precedent orders of development and a comprehensive analysis was given. The result is satisfactory. It provides scientific basis for making up developmental plan of Qingchuan’s economy.