MATRIX ANALYSIS TO ADDITIVE SCHWARZ METHODS

Matrix analysis on additive Schwarz methods as preconditioners is given in this paper. Both cases of with and without coarse mesh are considered. It is pointed out that an advantage of matrix analysis is to obtain more exact upper hound. Our numerical tests access the estimations.

MATRIX ANALYSIS ON LEADING TERM OF CONDITION NUMBER FOR ADDITIVE SCHWARZ METHODS

It is well known the order of preconditioned matrix by using additive Schwarz methods. In order to estimate the resulted PCG iteration counts, the related leading term brfore the order is given in this paper.

Investigation and Countermeasures of the Development of Chinese Pharmaceutical E-commerce in the B2C Model Based on PEST-SWOT Analysis

Objective To analyze the problems of pharmaceutical e-commerce and provide strategies for its development in the future B2C mode since drug network management has great potential in China.Methods By collecting,identifying,and conducting literature research,PEST-SWOT identification and positioning of pharmaceutical e-commerce in the B2C mode were carried out.Results and Conclusion A PEST-SWOT analysis matrix was established to analyze the status of B2C pharmaceutical e-commerce,and to summarize its advantages,disadvantages,opportunities and threats from four perspectives of politics,economy,society and technology.Suggestions on cultivating compound talents proficient in medicine and e-commerce,exploring online payment methods for medical insurance,integration of upstream and downstream of the industrial chain and data sharing are put forward to promote the healthy and long-term development of pharmaceutical e-commerce under the background of big data.

Histologic analysis and long-term effect of acellular dermal matrix combined with autologous thin split-thickness skin graft

Objective To evaluate the long-term therapeutic effect and histologic result of ADM combined with autologous thin split-thickness skin graft.Methods 23 patients were treated with acellalar dermal matrix(ADM) combined with autoiogous

Exact Tail Asymptotics for a Queueing System with a Retrial Orbit and Batch Service

This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.

Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

Spatial Dislocation Analysis of Tourism Economy and Its Influencing Factors in Jiangsu Province

Taking 13 prefecture-level cities in Jiangsu Province as the research object,based on the theory of spatial dislocation,the gravity model and two-dimensional composite matrix method are used to analyze the spatial dislocation between tourism resources,permanent population and other factors in Jiangsu Province and tourism revenue.The results show that the population center,the center of tourism resources,the center of tourist numbers,the center of economic development,and the center of tourism revenue of Jiangsu Province are all biased toward the southern part of Jiangsu Province.From the analysis of four sets of two-dimensional composite matrixes,13 prefecture-level cities have synchronized coordination and also have positive and negative dislocation types.Southern Jiangsu has the best synchronization and coordination,and northern Jiangsu has a strong negative dislocation trend;the combination of tourist numbers and tourism revenue is the strongest,but the dislocation is weak;population and tourism revenue have a strong positive dislocation trend;there is a strong negative dislocation trend between economic development and tourism revenue;the matrix combination of Nanjing,Wuxi and Suzhou has good synchronization;the city of Xuzhou in northern Jiangsu has a strong negative dislocation.In view of the results of spatial dislocation analysis,suggestions for improvement and optimization are put forward to promote the high-quality development of tourism in Jiangsu Province.

Impact of transparent exopolymer particles on the dynamics of dissolved organic carbon in the Amundsen Sea,Antarctica

The Southern Ocean is an important carbon sink pool and plays a critical role in the global carbon cycling.The Amundsen Sea was reported to be highly productive in inshore area in the Southern Ocean.In order to investigate the influence of transparent exopolymer particles(TEP)on the behavior of dissolved organic carbon(DOC)in this region,a comprehensive study was conducted,encompassing both open water areas and highly productive polynyas.It was found that microbial heterotrophic metabolism is the primary process responsible for the production of humic-like fluorescent components in the open ocean.The relationship between apparent oxygen utilization and the two humic-like components can be accurately described by a power-law function,with a conversion rate consistent with that observed globally.The presence of TEP was found to have little impact on this process.Additionally,the study revealed the accumulation of DOC at the sea surface in the Amundsen Sea Polynya,suggesting that TEP may play a critical role in this phenomenon.These findings contribute to a deeper understanding of the dynamics and surface accumulation of DOC in the Amundsen Sea Polynya,and provide valuable insights into the carbon cycle in this region.

The Application of Sensitivity Analysis on Comprehensive Transportation Evaluation

Comprehensive transportation evaluation objects using multi-objective decision method is a process of choosing the best one from a few objects through calculating, analyzing, and comparing the index system. The result may be different because of the difference of the index weight and index value. Therefore, sensitivity analysis should be one of the necessary parts of the decision-making. It is desired to give the index with higher sensitivity and its varying scope to control the index strictly during the execution process. This paper derives transfer index weight, which changes the rank evaluation order of the projects. Meanwhile, a simple, effective and practical method based on sensitivity district and sensitivity matrix is proposed for the sensitivity analysis of decision-making. As an example, the index sensitivity in decision-making of some provinces comprehensive transportation objects, and their influence on the final decision are discussed.

Modeling mechanism and extension of GM (1,1)

Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM （1,1）, which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM （1,1）. Finally, the paper proposes a generalization grey model GGM （1,1）, which is a extended form of GM （1,1） and also a unified form of model GM （1,1）, model GM （1,1,α）, stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed.

Soft Sensing Modelling Based on Optimal Selection of Secondary Variables and Its Application

The composition of the distillation column is a very important quality value in refineries, unfortunately, few hardware sensors are available on-line to measure the distillation compositions. In this paper, a novel method using sensitivity matrix analysis and kernel ridge regression （KRR） to implement on-line soft sensing of distillation compositions is proposed. In this approach, the sensitivity matrix analysis is presented to select the most suitable secondary variables to be used as the soft sensor＇s input. The KRR is used to build the composition soft sensor. Application to a simulated distillation column demonstrates the effectiveness of the method.

A Revisited Definition of the Three Solute Descriptors Related to the Van der Waals Forces in Solutions

It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present study is limited to those of solutes, and among them the three ones are involved in the Van der Waals forces, whereas the two ones involved in the hydrogen bonding are left aside at this stage. These three studied parameters, which we call δ, ω and ε, respectively reflect the three types of Van der Waals forces: dispersion, orientation or polarity strictly speaking, and induction-polarizability. These parameters have been experimentally obtained in previous studies for 121 Volatile Organic Compounds (VOC) via an original Multiplicative Matrix Analysis (MMA) applied to a superabundant and accurate GLC data set. Then, also in previous studies, attempts have been made to predict these parameters via a Simplified Molecular Topology procedure (SMT). Because these last published results have been somewhat disappointing, a promising new strategy of prediction is developed and detailed in the present article.

Determination of Three-Dimensional Structures of Oridonin in Solution by NOESY Spectrum and Molecular Mechanics Calculation

The phase sensitive NOESY spectrum of oridonin was treated using Full Relaxation Matrix Analysis(FRMA) approach, and the cross relaxation rates of proton pairs were obtained by diagonalizing the NOE matrix of oridonin. The inter proton distances were calculated according to 1/r6 ij ∝σij. The three-dimensional structure of oridonin in solution was calculated by the combination of WUPH, WUPH-S method with molecular mechanics minimization on the basis of NMR experiment.

The Kemeny’s Constant and Spanning Trees of Hexagonal Ring Network

Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology of hepatitis C virus(HCV)infection.On the other hand,Kemeny’s constant(Ω)is a beneficial quantifier characterizing the universal average activities of a Markov chain.This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state si.Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues.Motivated by Levene and Loizou,we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial.Based on the achieved results,entirely results are obtained for the M鯾ius hexagonal ring network.

BALANCE ROUTING TRAFFIC IN GENERALIZED SHUFFLE-EXCHANGE NETWORK

A methodology is proposed to handle problem that under equiproble address of packet traffic at the input port, Generalized Shuffle-Exchange Network (GSEN) routes traffic unevenly because of the unbalanced routing tags. The idea is to use routing tag according to probability, which can be evaluated by using Moore-Penrose inverse in matrix analysis. An instance is used to illustrate the idea, and the simulation is done to show the improvement in performance issues.

On the Mathematical Model of Universal Co-kriging

Due to its complexities in both mathematicM formulations and applications, universal co-kriging （UCK） has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporation of a polynomial variable trend is proposed in this paper. Estimators of the value and expectation of a regionMized vector taken in a point are obtained on the basis of cross-covaxiance and cross-vaxiogram, respectively. The complex expressions of co-kriging with trend are greatly simplified by introducing special matrix operations, such as Kronecker product, into the formulations. This simplification offers a feasible and easier approach for computer coding of the UCK, and helps the practitioners to use the UCK technique conveniently in real cases.

Rejuvenating wood carving industry in Taiwan Sanyi： A perspective of strategic management

This research aimed at providing suggestions to rejuvenate the wood carving industry in Taiwan Sanyi. The authors conducted interviews with representative store keepers and sculptors to gain industrial insights, and applied the strategic matrix analysis developed by Dr. Seetoo to examine industrial conditions and formulate strategic suggestions for wood carving companies. The industry was found lack of market orientation, which was considered as the critical factor of the long term depression. However, a market of tourism for nostalgic and cultural experience started developing in the near area, providing opportunities for Sanyi wood carving industry to recover. The main suggestions the authors made are （1） restructuring the product scope to respond to the market, and （2） branding with resorts in near area.

Research on Tourism Development Strategy of Zhaoqing Seven Star Cave Scenic Area in the Context of Guangdong-Hong Kong-Macao Greater Bay Area

The national strategy of"Guangdong-Hong Kong-Macao Greater Bay Area"has replaced the original Pearl River Delta economic circle.As one of them,the economic development of Zhaoqing City ushered in a historic opportunity.Other cities in Greater Bay Area provide sufficient tourist resources for the development of Zhaoqing’s tourism industry.Under the new situation,Seven Star Cave,the leading scenic spot in Zhaoqing,should firmly grasp the national strategic dividend of the"Guangdong-Hong Kong-Macao Greater Bay Area",accelerate the transformation and upgrading,and enhance the market competitiveness.In this paper,the data are collected by nominal group technique,and are integrated into SWOT matrix for analysis.The development strategy of Zhaoqing Seven Star Cave Scenic Area is obtained by matching internal and external factors.

Parameters Sensitivity Characteristics of Highly Integrated Valve-Controlled Cylinder Force Control System

Nowadays, a highly integrated valve?controlled cylinder(HIVC) is applied to drive the joints of legged robots. Although the adoption of HIVC has resulted in high?performance robot control, the hydraulic force system still has problems, such as strong nonlinearity, and time?varying parameters. This makes HIVC force control very diffcult and complex. How to improve the control performance of the HIVC force control system and find the influence rule of the system parameters on the control performance is very significant. Firstly, the mathematical model of HIVC force control system is established. Then the mathematical expression for parameter sensitivity matrix is obtained by applying matrix sensitivity analysis(PSM). Then, aimed at the sinusoidal response under(three factors and three levels) working conditions, the simulation and the experiment are conducted. While the error between the simulation and experiment can’t be avoided. Therefore, combined with the range analysis, the error in the two performance indexes of sinusoidal response under the whole working condition is analyzed. Besides, the sensitivity variation pattern for each system parameter under the whole working condition is figured out. Then the two sensitivity indexes for the three system parameters, which are supply pressure, proportional gain and initial displacement of piston, are proved experimentally. The proposed method significantly reveals the sensitivity characteristics of HIVC force control system, which can make the contribution to improve the control performance.

Image registration based on matrix perturbation analysis using spectral graph

We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.