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Operation optimization strategy of existing residential building energy-saving renovation market:From the perspective of subject behavior
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作者 GUO Han-ding LI Rui-jiao +1 位作者 QIN Guang-lei ZHANG Yin-xian 《Ecological Economy》 2024年第3期290-300,共11页
The energy-saving renovation of existing residential buildings is a crucial measure to achieve the strategic goal of energy conservation and emission reduction in China and build ecologically livable cities.This artic... The energy-saving renovation of existing residential buildings is a crucial measure to achieve the strategic goal of energy conservation and emission reduction in China and build ecologically livable cities.This article focuses on the perspective of subject behavior,starting from analyzing the current situation and difficulties of the operation of the energy-saving renovation market for existing residential buildings in China,drawing on the practical experience of the operation of the existing residential building energy-saving renovation market abroad.Based on principles such as systematicity,humanization,feasibility,and sustainability,the article constructs an operation optimization system of the existing residential building energy-saving renovation market from the perspective of subject behavior.In order to provide a reference for the healthy and orderly operation of the existing residential building energy-saving renovation market,this paper proposes implementation strategies for optimizing the operation of the existing residential building energy-saving renovation market.Suggestions are proposed from four aspects:optimizing the market environment,innovating the financing model,building the information sharing platform,and utilizing the synergies of the main subjects. 展开更多
关键词 the existing residential buildings energy-saving renovation market operation optimization strategy perspective of subject behavior
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Observation of the Effect of Video Assessment Method on the Operation Skills of Individual Nurses
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作者 Jianhua Qin Xiaolu Wan Nannan Ma 《Journal of Clinical and Nursing Research》 2024年第8期122-128,共7页
Objective:To explore the application effect of video assessment method in clinical nurses’nursing operation skills.Method:To select 58 nurses who participated in the individual soldier standard in the children’s hos... Objective:To explore the application effect of video assessment method in clinical nurses’nursing operation skills.Method:To select 58 nurses who participated in the individual soldier standard in the children’s hospital in 2019 and 2020 as the research objects,among which the nurses who participated in the individual soldier standard in 2019 were the nurses who participated in the individual soldier standard in 2019 and 2020.A total of 29 people in the first batch were set as the control group,using traditional assessment methods.In 2020,the second batch of 29 nurses who participated in the individual soldier standard reached the experimental group.Using the video assessment method,there was no significant difference in general information between the two groups(P>0.05).After the assessment,the scores,coping with work pressure,and proactiveness of the two groups of research subjects were compared.Results:The experimental group’s nursing operation assessment scores,coping with work pressure,and proactiveness were significantly better than those of the control group,the difference was statistically significant(P<0.05).Conclusion:The application of the video assessment method improves the passing rate of nurses’operational skills examination,enhances nurses’initiative in learning,reduces examination pressure,and can be accurately,timely,and safely applied to clinical nursing work,which is worthy of study and promotion. 展开更多
关键词 Video assessment method NURSE operation skills Effect observation
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Research and Practice of the Blended Teaching Model of BOPPPS Teaching Method Under the Background of Digital Education: Taking Operations Research Course as an Example
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作者 Yan Wu 《Journal of Contemporary Educational Research》 2024年第6期155-160,共6页
The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participat... The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participatory learning,Post-assessment,Summary)teaching method in the development of a blended teaching model for the Operations Research course under the background of digital education.In response to the characteristics of the course and the needs of the student group,the teaching design is reconstructed with a student-centered approach,increasing practical teaching links,improving the assessment and evaluation system,and effectively implementing it in conjunction with digital educational technology.This teaching model has shown significant effectiveness in the context of digital education,providing valuable experience and insights for the innovation of the Operations Research course. 展开更多
关键词 Digital education BOPPPS teaching method Blended teaching model operations research
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Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Kunfeng Liang Zhijun Liu Xinru Bao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期3033-3049,共17页
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna... Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed. 展开更多
关键词 Population balance equation CRYSTALLIZATION peridynamic differential operator Euler’s first-order explicit method
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From Knowledge Transfer to Capability Development:The Future of PBL+CBL Teaching Method in Operating Room Nursing Education
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作者 Kun Zhu Jiao Zhou +3 位作者 Yaqing Cui Zhengyan Shi Juntao Li Jia Li 《Journal of Contemporary Educational Research》 2024年第10期185-191,共7页
Concomitant with the advancement of contemporary medical technology,the significance of perioperative nursing has been increasingly accentuated,necessitating elevated standards for the pedagogy of perioperative nursin... Concomitant with the advancement of contemporary medical technology,the significance of perioperative nursing has been increasingly accentuated,necessitating elevated standards for the pedagogy of perioperative nursing.Presently,the PBL(problem-based learning)pedagogical approach,when integrated with CBL(case-based learning),has garnered considerable interest.An extensive literature review has been conducted to analyze the application of the PBL-CBL fusion in the education of perioperative nursing.Findings indicate that this integrative teaching methodology not only enhances students’theoretical knowledge,practical competencies,and collaborative skills but also contributes to the elevation of teaching quality.In conclusion,the PBL-CBL teaching approach holds immense potential for broader application in perioperative nursing education.Nevertheless,it is imperative to continually refine this combined pedagogical strategy to further enhance the caliber of perioperative nursing instruction and to cultivate a greater number of exceptional nursing professionals in the operating room setting. 展开更多
关键词 Knowledge transfer Capability development PBL+CBL teaching method operating room nursing EDUCATION
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Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method
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作者 Mohammad Kamrul Hasan Abeda Sultana Nirmal Kanti Mitra 《American Journal of Computational Mathematics》 2023年第1期99-121,共23页
In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis... In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique. 展开更多
关键词 Picture Fuzzy Set Generalized Trapezoidal Picture Fuzzy Number γ β)-Cut Arithmetic operations Vertex method
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EFFECT OF DIFFERENT OPERATION METHODS ON METHANE HYDRATE FORMATION 被引量:3
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作者 HAO Wenfeng~(1,2), FAN Shuanshi~2 and WANG Jinqu~1 (~1 Institute of Adsorption and Inorganic Membrane, Dalian University of Technology, Dalian 116012, Liaoning, China ~2 Guangzhou Institute of Energy Canversion, The Chinese Academy of Sciences, Guangzhou 510070, Guangdong, China) 《化工学报》 EI CAS CSCD 北大核心 2003年第z1期33-36,共4页
Three experiments of static state storage method, low-temperature and constant-pressure storage method and low-temperature and constant-pressure storage method were carried out to investigate which method was best in ... Three experiments of static state storage method, low-temperature and constant-pressure storage method and low-temperature and constant-pressure storage method were carried out to investigate which method was best in gas hydrate. The relationships of hydrate rate, capacity and liquid temperature versus time were derived and three results were contrasted. The experimental results show lowtemperature and constant-pressure method is better than the other two methods because it's operation period is shorter and storage capacity is larger than the other two. Low-temperature and constant-pressure method is the best method. So new method will be new research objective. 展开更多
关键词 effect operation method methane hydrate FORMATION
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Operational Methods for Ships in Waves From Perspectives of Structure Health and Maneuvering Convenience
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作者 ZHOU Feng ZHOU Junwei +1 位作者 CHEN Yuli WANG Deling 《Journal of Shipping and Ocean Engineering》 2017年第3期100-107,共8页
Based on the stress-strain data collected by a CSSMAS (container ship structure monitoring and analyzing system) onboard a container vessel, stress-strain responses of the ship's structure in high wave were analyze... Based on the stress-strain data collected by a CSSMAS (container ship structure monitoring and analyzing system) onboard a container vessel, stress-strain responses of the ship's structure in high wave were analyzed and illustrated for the identification of reasonable safe course sections. Besides the ship's structure safety, the maneuvering convenience is also deemed as a main concern which influences the safety of vessels in heavy waves. In order to develop a comprehensive guidance in adverse weather condition, the basic requirements on maneuvering convenience for vessels in storm were further discussed. In combination of the two requirements, namely structure health and maneuvering convenience, a proposed operational method was thus developed, which was an amendment to the traditional navigational method for ship in extreme weather. At the end of this paper, an example of optimal course planning in bad weather was illustrated by using the operational method proposed. 展开更多
关键词 Structural health maneuvering convenience extreme weather operational method
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Incentive operation characteristics and influence feedback of existing building energy-saving renovation market development
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作者 WANG Feng-hui GUO Han-ding WANG Xing 《Ecological Economy》 2021年第3期186-207,共22页
The quality of the existing building energy-saving renovation market determines the inherent inevitability of incentive,while unique requirements for the incentive should be satisfied by stage characteristics and indi... The quality of the existing building energy-saving renovation market determines the inherent inevitability of incentive,while unique requirements for the incentive should be satisfied by stage characteristics and individualization of the three entities of the existing building energy-saving renovation market development.Firstly,the analysis of internal and external factors’composition and system influencing the existing construction market development incentive structure was performed.Then,system dynamics was implemented to build the feedback model of incentive effects of market development of existing buildings energy-saving reconstruction.Discussions on the realization path of the incentive for the development of the existing energy-saving building market were also pointed out.Finally,this paper conducted the analysis of the dynamic feedback characteristics and key incentive factors of the incentive for the development of the existing building energy-saving renovation market.Based on the analyses and discussions above,this paper provides methodological guidance and implementation approach for the incentive path selection and policy-making of the existing building energy-saving transformation market,trying to help improve the incentive effectiveness of the market,and also promote healthy and sustainable development of the existing building energy-saving renovation market. 展开更多
关键词 existing building energy-saving renovation market development incentive operation influencing factor dynamic feedback
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ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Ioannis K.ARGYROS Santhosh GEORGE 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1318-1324,共7页
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is... In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping. 展开更多
关键词 nonlinear ill-posed equations iterative regularization m-accretive operator Newton type method
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Comparative Analysis of Pythagorean MCDM Methods for the Risk Assessment of Childhood Cancer
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作者 Shaista Habib Muhammad Akram MMAli Al-Shamiri 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2585-2615,共31页
According to the World Health Organization(WHO),cancer is the leading cause of death for children in low and middle-income countries.Around 400,000 kids get diagnosed with this illness each year,and their survival rat... According to the World Health Organization(WHO),cancer is the leading cause of death for children in low and middle-income countries.Around 400,000 kids get diagnosed with this illness each year,and their survival rate depends on the country in which they live.In this article,we present a Pythagorean fuzzy model that may help doctors identify the most likely type of cancer in children at an early stage by taking into account the symptoms of different types of cancer.The Pythagorean fuzzy decision-making techniques that we utilize are Pythagorean Fuzzy TOPSIS,Pythagorean Fuzzy Entropy(PF-Entropy),and Pythagorean Fuzzy PowerWeighted Geometric(PFPWG).Ourmodel is fed with nineteen symptoms and it diagnoses the risk of eight types of cancers in children.We develop an algorithm for each method and calculate its complexity.Additionally,we consider an example to make a clear understanding of our model.We also compare the final results of various tests that prove the authenticity of this study. 展开更多
关键词 Risk assessment Pythagorean fuzzy sets TOPSIS method ENTROPY power weighted geometric operators
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GALERKIN-PETROV METHODS OF TOEPLITZ OPERATORS ON DIRICHLET SPACE 被引量:1
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作者 王晓峰 曹广福 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期308-316,共9页
The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that s... The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry. 展开更多
关键词 Galerkin-Petrov methods polynomial collocation analytic element collocation Toeplitz operators Dirichlet space
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Multilevel Iteration Methods for Solving Linear Operator Equations of the First Kind 被引量:2
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作者 罗兴钧 《Northeastern Mathematical Journal》 CSCD 2008年第1期1-9,共9页
In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen... In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework. 展开更多
关键词 operator equations of the first kind ill-posed problem multilevel iteration method Tikhonov regularization
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Regularization Methods to Approximate Solutions of Variational Inequalities
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作者 Nguyen Van Kinh 《Open Journal of Optimization》 2023年第2期34-60,共27页
In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul... In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data  satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones. 展开更多
关键词 Ill-Posed Problem Variational Inequality Regularization method Monotone operator Hemi-Continuous operator Lower Semi-Continuous Function
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Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications
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作者 Tahir Mahmood Zeeshan Ali Muhammad Naeem 《CAAI Transactions on Intelligence Technology》 SCIE EI 2023年第1期40-63,共24页
Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and pu... Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis. 展开更多
关键词 averaging/geometric aggregation operators complex q-rung orthopair normal fuzzy information confidence levels strategic decision-making methods
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Satellite remote sensing of sea-ice and its operational monitoring method along the coast of China 被引量:3
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作者 Gong Jialong National Marine Environment Forecasting Center, SOA, Beijing. China 《Acta Oceanologica Sinica》 SCIE CAS CSCD 1989年第3期379-390,共12页
Sea-ice is an important operational item for real timely monitoring and forecasting marine environment of China. This paper introduces an operational method of satellite remote sensing to monitor sea- ice using quanti... Sea-ice is an important operational item for real timely monitoring and forecasting marine environment of China. This paper introduces an operational method of satellite remote sensing to monitor sea- ice using quantitative data of NOAA, and its contents include computer processing of AVHRR sounding data of NOAA and its program design, imagery processing of sea-ice imagery from satellite and their thematic analysis. The sea-ice satellite colour imageries processed via this software system are able to interpret sea-ice pattern, characterizing it by thickness, maximum position of ice boundary, floe concentration and dynamic process of ice changing. At the same time, analyses of the ice condition of the Bohai Sea for the two-year period (1986-1988) as monitored by satellite have been summarized. 展开更多
关键词 In Satellite remote sensing of sea-ice and its operational monitoring method along the coast of China
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A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem onImplicit Surfaces
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作者 Young Kyu Lee Shingyu Leung 《Communications on Applied Mathematics and Computation》 EI 2024年第2期1189-1216,共28页
We propose a simple embedding method for computing the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on implicit surfaces.The approach follows an embedding approach for solving the surface eikonal eq... We propose a simple embedding method for computing the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on implicit surfaces.The approach follows an embedding approach for solving the surface eikonal equation.We replace the differential operator on the interface with a typical Cartesian differential operator in the surface neighborhood.Our proposed algorithm is easy to implement and efficient.We will give some two-and three-dimensional numerical examples to demonstrate the effectiveness of our proposed approach. 展开更多
关键词 Laplace-Beltrami operator Level set method Implicit representation EIGENVALUES Numerical PDEs
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Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Zeyue Zhang Boyu Chen Zhijun Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2707-2728,共22页
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t... Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions. 展开更多
关键词 Peridynamic differential operator finite difference method STABILITY transient heat conduction problem
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Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method
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作者 Yanan Wang Lin Chen +3 位作者 Junjiang Liu Baijie Qiao Weifeng He Xuefeng Chen 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2024年第3期170-188,共19页
In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although ... In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration. 展开更多
关键词 Impact force identification Non-convex sparse regularization Alternating direction method of multipliers Proximal operators
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INCOMPLETE SEMI-ITERATIVE METHODS FOR SOLVING SINGULAR LINEAR OPERATOR EQUATIONS IN BANACH SPACE WITH APPLICATIONS IN MARKOV CHAIN MODELING
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作者 Wei Yimin(魏益民) +1 位作者 Wu Hebing(吴和兵) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2001年第2期129-144,共16页
We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent h... We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high. 展开更多
关键词 SINGULAR linear operator equation index DRAZIN inverse semi-iterative method incomplete semi-iterative method Markov chain.
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