In the era of big data,data-driven technologies are increasingly leveraged by industry to facilitate autonomous learning and intelligent decision-making.However,the challenge of“small samples in big data”emerges whe...In the era of big data,data-driven technologies are increasingly leveraged by industry to facilitate autonomous learning and intelligent decision-making.However,the challenge of“small samples in big data”emerges when datasets lack the comprehensive information necessary for addressing complex scenarios,which hampers adaptability.Thus,enhancing data completeness is essential.Knowledge-guided virtual sample generation transforms domain knowledge into extensive virtual datasets,thereby reducing dependence on limited real samples and enabling zero-sample fault diagnosis.This study used building air conditioning systems as a case study.We innovatively used the large language model(LLM)to acquire domain knowledge for sample generation,significantly lowering knowledge acquisition costs and establishing a generalized framework for knowledge acquisition in engineering applications.This acquired knowledge guided the design of diffusion boundaries in mega-trend diffusion(MTD),while the Monte Carlo method was used to sample within the diffusion function to create information-rich virtual samples.Additionally,a noise-adding technique was introduced to enhance the information entropy of these samples,thereby improving the robustness of neural networks trained with them.Experimental results showed that training the diagnostic model exclusively with virtual samples achieved an accuracy of 72.80%,significantly surpassing traditional small-sample supervised learning in terms of generalization.This underscores the quality and completeness of the generated virtual samples.展开更多
At present,although knowledge graphs have been widely used in various fields such as recommendation systems,question and answer systems,and intelligent search,there are always quality problems such as knowledge omissi...At present,although knowledge graphs have been widely used in various fields such as recommendation systems,question and answer systems,and intelligent search,there are always quality problems such as knowledge omissions and errors.Quality assessment and control,as an important means to ensure the quality of knowledge,can make the applications based on knowledge graphs more complete and more accurate by reasonably assessing the knowledge graphs and fixing and improving the quality problems at the same time.Therefore,as an indispensable part of the knowledge graph construction process,the results of quality assessment and control determine the usefulness of the knowledge graph.Among them,the assessment and enhancement of completeness,as an important part of the assessment and control phase,determine whether the knowledge graph can fully reflect objective phenomena and reveal potential connections among entities.In this paper,we review specific techniques of completeness assessment and classify completeness assessment techniques in terms of closed world assumptions,open world assumptions,and partial completeness assumptions.The purpose of this paper is to further promote the development of knowledge graph quality control and to lay the foundation for subsequent research on the completeness assessment of knowledge graphs by reviewing and classifying completeness assessment techniques.展开更多
In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge grap...In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge graphs, quality assessment is particularly important. As an important thing of quality assessment, completeness assessment generally refers to the ratio of the current data volume to the total data volume.When evaluating the completeness of a knowledge graph, it is often necessary to refine the completeness dimension by setting different completeness metrics to produce more complete and understandable evaluation results for the knowledge graph.However, lack of awareness of requirements is the most problematic quality issue. In the actual evaluation process, the existing completeness metrics need to consider the actual application. Therefore, to accurately recommend suitable knowledge graphs to many users, it is particularly important to develop relevant measurement metrics and formulate measurement schemes for completeness. In this paper, we will first clarify the concept of completeness, establish each metric of completeness, and finally design a measurement proposal for the completeness of knowledge graphs.展开更多
This paper applies Gödel’s Incompleteness Theorems to the evolution and development of human social systems.Although Gödel’s Incompleteness Theorems originated in the field of mathematics,their influence h...This paper applies Gödel’s Incompleteness Theorems to the evolution and development of human social systems.Although Gödel’s Incompleteness Theorems originated in the field of mathematics,their influence has long extended beyond mathematics,making an impact on philosophy,systems science,and the humanities and social sciences.The paper analyzes the autonomy and completeness of human social systems,arguing that evolving human societies are generally self-consistent.However,if the completeness of a human social system is compromised,the system either maintains self-consistency,ceases to evolve forward,enters a death spiral,and eventually decays and disintegrates.Or the system addresses the completeness issue,enters a state of non-self-consistency,introduces new axioms,becomes self-governing again,and enters a new form.From the sociological perspective,this is articulated as social revolution-the system continues to evolve forward;the absence of social revolution-the system does not evolve forward(Jin,1988).展开更多
The assessment of the completeness of earthquake catalogs is a prerequisite for studying the patterns of seismic activity.In traditional approaches,the minimum magnitude of completeness(MC)is employed to evaluate cata...The assessment of the completeness of earthquake catalogs is a prerequisite for studying the patterns of seismic activity.In traditional approaches,the minimum magnitude of completeness(MC)is employed to evaluate catalog completeness,with events below MC being discarded,leading to the underutilization of the data.Detection probability is a more detailed measure of the catalog's completeness than MC;its use results in better model compatibility with data in seismic activity modeling and allows for more comprehensive utilization of seismic observation data across temporal,spatial,and magnitude dimensions.Using the magnitude-rank method and Maximum Curvature(MAXC)methods,we analyzed temporal variations in earthquake catalog completeness,finding that MC stabilized after 2010,which closely coincides with improvements in monitoring capabilities and the densification of seismic networks.Employing the probability-based magnitude of completeness(PMC)and entire magnitude range(EMR)methods,grounded in distinct foundational assumptions and computational principles,we analyzed the 2010-2023 earthquake catalog for the northern margin of the Ordos Block,aiming to assess the detection probability of earthquakes and the completeness of the earthquake catalog.The PMC method yielded the detection probability distribution for 76 stations in the distance-magnitude space.A scoring metric was designed based on station detection capabilities for small earthquakes in the near field.From the detection probabilities of stations,we inferred detection probabilities of the network for diff erent magnitude ranges and mapped the spatial distribution of the probability-based completeness magnitude.In the EMR method,we employed a segmented model fitted to the observed data to determine the detection probability and completeness magnitude for every grid point in the study region.We discussed the sample dependency and low-magnitude failure phenomena of the PMC method,noting the potential overestimation of detection probabilities for lower magnitudes and the underestimation of MC in areas with weaker monitoring capabilities.The results obtained via the two methods support these hypotheses.The assessment results indicate better monitoring capabilities on the eastern side of the study area but worse on the northwest side.The spatial distribution of network monitoring capabilities is uneven,correlating with the distribution of stations and showing significant diff erences in detection capabilities among diff erent stations.The truncation eff ects of data and station selection aff ected the evaluation results at the edges of the study area.Overall,both methods yielded detailed descriptions of the earthquake catalog,but careful selection of calculation parameters or adjustments based on the strengths of diff erent methods is necessary to correct potential biases.展开更多
The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and it...The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.展开更多
For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi...For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.展开更多
This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block ...This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.展开更多
The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified...The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.展开更多
In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the...In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded to L-2[0,1] X L-2[0,1], but ZH not equal L-2[0,1] X L-1[0,1].展开更多
The smart grid is an evolving critical infrastructure,which combines renewable energy and the most advanced information and communication technologies to provide more economic and secure power supply services.To cope ...The smart grid is an evolving critical infrastructure,which combines renewable energy and the most advanced information and communication technologies to provide more economic and secure power supply services.To cope with the intermittency of ever-increasing renewable energy and ensure the security of the smart grid,state estimation,which serves as a basic tool for understanding the true states of a smart grid,should be performed with high frequency.More complete system state data are needed to support high-frequency state estimation.The data completeness problem for smart grid state estimation is therefore studied in this paper.The problem of improving data completeness by recovering highfrequency data from low-frequency data is formulated as a super resolution perception(SRP)problem in this paper.A novel machine-learning-based SRP approach is thereafter proposed.The proposed method,namely the Super Resolution Perception Net for State Estimation(SRPNSE),consists of three steps:feature extraction,information completion,and data reconstruction.Case studies have demonstrated the effectiveness and value of the proposed SRPNSE approach in recovering high-frequency data from low-frequency data for the state estimation.展开更多
Based on the concrete conditions of earthquake data in the west of China, East China and SOuth China, we studied the completeness of data in these regions by suitable methods to local conditions. Otherwise, we roughly...Based on the concrete conditions of earthquake data in the west of China, East China and SOuth China, we studied the completeness of data in these regions by suitable methods to local conditions. Otherwise, we roughly estimated monitoring capability of local networks in China since 1970 and some outlying regions where the data is lack. Finally, we gave the regional distribution of the beginning years since which the data for different magnitude intervals are largely complete in the Chinese mainland.展开更多
In order to solve the parallel algorithm of Petri net system with concurrent function, so as to achieve the parallel control and simulation operation of this system, this paper proposes the function partition complete...In order to solve the parallel algorithm of Petri net system with concurrent function, so as to achieve the parallel control and simulation operation of this system, this paper proposes the function partition completeness theory and algorithms of Petri net parallelization, thereby providing the theoretical support for the realization of Petri parallel algorithms. Firstly, according to the concurrent characteristics of Petri net model, we analyze the parallelism of Petri net system; then, by giving the solving process of place invariants and the function partitioning of Petri net, we propose the function partitioning conditions and determination theorem of Petri net parallelization, and conduct its theoretical proof and practical verification. On this basis, we conduct the theoretical study and analysis on the situation that Petri net system has several kinds of parallel function partitioning, propose the completeness theorem of parallelism function partitioning in Petri net system, and verify it. Finally, we give the algorithms, application examples and simulation experiment results of parallel function partitioning of Petri net systems based on place invariant. The theoretical proof and experimental results show that the function partitioning conditions and completeness theory of Petri net parallelization based on place invariant are correct, and the parallel algorithms under such theoretical basis are also correct and effective.展开更多
In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenva...In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.展开更多
This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Fur...This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.展开更多
This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the d...This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.展开更多
The historical earthquake catalogue of China has lasted more than 3000 years,and most of its data are inferred from historical records.The earthquake catalogue in earlier times is not complete owing to various reasons...The historical earthquake catalogue of China has lasted more than 3000 years,and most of its data are inferred from historical records.The earthquake catalogue in earlier times is not complete owing to various reasons,so some events are lost.This paper estimates the loss rate of earthquakes with various magnitudes in the historical earthquake catalogue for different time intervals quantitatively by using the Gutenberg-Richter formula and modern instrumental records,which will provide the references for statistic research in seismicity.展开更多
This paper is the continuation of the paper [13]. Namely, in [13], the scope of the structural completeness in the class of all over-systems of the classical predicate calculus, has been established. In this paper we ...This paper is the continuation of the paper [13]. Namely, in [13], the scope of the structural completeness in the class of all over-systems of the classical predicate calculus, has been established. In this paper we establish the scope of the structural completeness in the class of all over-systems of the classical functional calculus with identity.展开更多
Observations of living organisms by citizen scientists that are reported to online portals are a valuable source of information.They are also a special kind of volunteered geographic information(VGI).VGI data have iss...Observations of living organisms by citizen scientists that are reported to online portals are a valuable source of information.They are also a special kind of volunteered geographic information(VGI).VGI data have issues of completeness,which arise from biases caused by the opportunistic nature of the data collection process.We examined the completeness of bird species represented in citizen science observation data from eBird and iNaturalist in US National Parks(NPs).We used approaches for completeness estimation which were developed for data from OpenStreetMap,a crowdsourced map of the world.First,we used an extrinsic approach,comparing species lists from citizen science data with National Park Service lists.Second,we examined two intrinsic approaches using total observation numbers in NPs and the development of the number of new species being added to the data-set over time.Results from the extrinsic approach provided appropriate completeness estimations to evaluate the intrinsic approaches.We found that total observation numbers are a good estimator of species completeness of citizen science data from US NPs.There is also a close relationship between species completeness and the ratio of new species added to observation data vs.observation numbers in a given year.展开更多
A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, whi...A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.展开更多
基金supported by the National Natural Science Foundation of China(No.62306281)the Natural Science Foundation of Zhejiang Province(Nos.LQ23E060006 and LTGG24E050005)the Key Research Plan of Jiaxing City(No.2024BZ20016).
文摘In the era of big data,data-driven technologies are increasingly leveraged by industry to facilitate autonomous learning and intelligent decision-making.However,the challenge of“small samples in big data”emerges when datasets lack the comprehensive information necessary for addressing complex scenarios,which hampers adaptability.Thus,enhancing data completeness is essential.Knowledge-guided virtual sample generation transforms domain knowledge into extensive virtual datasets,thereby reducing dependence on limited real samples and enabling zero-sample fault diagnosis.This study used building air conditioning systems as a case study.We innovatively used the large language model(LLM)to acquire domain knowledge for sample generation,significantly lowering knowledge acquisition costs and establishing a generalized framework for knowledge acquisition in engineering applications.This acquired knowledge guided the design of diffusion boundaries in mega-trend diffusion(MTD),while the Monte Carlo method was used to sample within the diffusion function to create information-rich virtual samples.Additionally,a noise-adding technique was introduced to enhance the information entropy of these samples,thereby improving the robustness of neural networks trained with them.Experimental results showed that training the diagnostic model exclusively with virtual samples achieved an accuracy of 72.80%,significantly surpassing traditional small-sample supervised learning in terms of generalization.This underscores the quality and completeness of the generated virtual samples.
基金supported by the National Key Laboratory for Complex Systems Simulation Foundation(6142006190301)。
文摘At present,although knowledge graphs have been widely used in various fields such as recommendation systems,question and answer systems,and intelligent search,there are always quality problems such as knowledge omissions and errors.Quality assessment and control,as an important means to ensure the quality of knowledge,can make the applications based on knowledge graphs more complete and more accurate by reasonably assessing the knowledge graphs and fixing and improving the quality problems at the same time.Therefore,as an indispensable part of the knowledge graph construction process,the results of quality assessment and control determine the usefulness of the knowledge graph.Among them,the assessment and enhancement of completeness,as an important part of the assessment and control phase,determine whether the knowledge graph can fully reflect objective phenomena and reveal potential connections among entities.In this paper,we review specific techniques of completeness assessment and classify completeness assessment techniques in terms of closed world assumptions,open world assumptions,and partial completeness assumptions.The purpose of this paper is to further promote the development of knowledge graph quality control and to lay the foundation for subsequent research on the completeness assessment of knowledge graphs by reviewing and classifying completeness assessment techniques.
基金supported by the National Key Laboratory for Comp lex Systems Simulation Foundation (6142006190301)。
文摘In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge graphs, quality assessment is particularly important. As an important thing of quality assessment, completeness assessment generally refers to the ratio of the current data volume to the total data volume.When evaluating the completeness of a knowledge graph, it is often necessary to refine the completeness dimension by setting different completeness metrics to produce more complete and understandable evaluation results for the knowledge graph.However, lack of awareness of requirements is the most problematic quality issue. In the actual evaluation process, the existing completeness metrics need to consider the actual application. Therefore, to accurately recommend suitable knowledge graphs to many users, it is particularly important to develop relevant measurement metrics and formulate measurement schemes for completeness. In this paper, we will first clarify the concept of completeness, establish each metric of completeness, and finally design a measurement proposal for the completeness of knowledge graphs.
文摘This paper applies Gödel’s Incompleteness Theorems to the evolution and development of human social systems.Although Gödel’s Incompleteness Theorems originated in the field of mathematics,their influence has long extended beyond mathematics,making an impact on philosophy,systems science,and the humanities and social sciences.The paper analyzes the autonomy and completeness of human social systems,arguing that evolving human societies are generally self-consistent.However,if the completeness of a human social system is compromised,the system either maintains self-consistency,ceases to evolve forward,enters a death spiral,and eventually decays and disintegrates.Or the system addresses the completeness issue,enters a state of non-self-consistency,introduces new axioms,becomes self-governing again,and enters a new form.From the sociological perspective,this is articulated as social revolution-the system continues to evolve forward;the absence of social revolution-the system does not evolve forward(Jin,1988).
基金funded by Director Fund of the Inner Mongolia Autonomous Region Seismological Bureau(No.2023GG02,2023MS05)the Inner Mongolia Natural Science Foundation(No.2024MS04021)。
文摘The assessment of the completeness of earthquake catalogs is a prerequisite for studying the patterns of seismic activity.In traditional approaches,the minimum magnitude of completeness(MC)is employed to evaluate catalog completeness,with events below MC being discarded,leading to the underutilization of the data.Detection probability is a more detailed measure of the catalog's completeness than MC;its use results in better model compatibility with data in seismic activity modeling and allows for more comprehensive utilization of seismic observation data across temporal,spatial,and magnitude dimensions.Using the magnitude-rank method and Maximum Curvature(MAXC)methods,we analyzed temporal variations in earthquake catalog completeness,finding that MC stabilized after 2010,which closely coincides with improvements in monitoring capabilities and the densification of seismic networks.Employing the probability-based magnitude of completeness(PMC)and entire magnitude range(EMR)methods,grounded in distinct foundational assumptions and computational principles,we analyzed the 2010-2023 earthquake catalog for the northern margin of the Ordos Block,aiming to assess the detection probability of earthquakes and the completeness of the earthquake catalog.The PMC method yielded the detection probability distribution for 76 stations in the distance-magnitude space.A scoring metric was designed based on station detection capabilities for small earthquakes in the near field.From the detection probabilities of stations,we inferred detection probabilities of the network for diff erent magnitude ranges and mapped the spatial distribution of the probability-based completeness magnitude.In the EMR method,we employed a segmented model fitted to the observed data to determine the detection probability and completeness magnitude for every grid point in the study region.We discussed the sample dependency and low-magnitude failure phenomena of the PMC method,noting the potential overestimation of detection probabilities for lower magnitudes and the underestimation of MC in areas with weaker monitoring capabilities.The results obtained via the two methods support these hypotheses.The assessment results indicate better monitoring capabilities on the eastern side of the study area but worse on the northwest side.The spatial distribution of network monitoring capabilities is uneven,correlating with the distribution of stations and showing significant diff erences in detection capabilities among diff erent stations.The truncation eff ects of data and station selection aff ected the evaluation results at the edges of the study area.Overall,both methods yielded detailed descriptions of the earthquake catalog,but careful selection of calculation parameters or adjustments based on the strengths of diff erent methods is necessary to correct potential biases.
文摘The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No. 20080404MS0104the Research Foundation for Talented Scholars of Inner Mongolia University under Grant No. 207066
文摘For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004 and 11061019)the Doctoral Foundation of Inner Mongolia(Grant Nos.2009BS0101 and 2010MS0110)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Chunhui Program of the Ministry of Education of China(Grant No.Z2009-1-01010)
文摘This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.
基金supported by the National Natural Science Foundation of China (Grant No. 10962004)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS0104)
文摘The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.
文摘In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded to L-2[0,1] X L-2[0,1], but ZH not equal L-2[0,1] X L-1[0,1].
基金the Training Program of the Major Research Plan of the National Natural Science Foundation of China(91746118)the Shenzhen Municipal Science and Technology Innovation Committee Basic Research project(JCYJ20170410172224515)。
文摘The smart grid is an evolving critical infrastructure,which combines renewable energy and the most advanced information and communication technologies to provide more economic and secure power supply services.To cope with the intermittency of ever-increasing renewable energy and ensure the security of the smart grid,state estimation,which serves as a basic tool for understanding the true states of a smart grid,should be performed with high frequency.More complete system state data are needed to support high-frequency state estimation.The data completeness problem for smart grid state estimation is therefore studied in this paper.The problem of improving data completeness by recovering highfrequency data from low-frequency data is formulated as a super resolution perception(SRP)problem in this paper.A novel machine-learning-based SRP approach is thereafter proposed.The proposed method,namely the Super Resolution Perception Net for State Estimation(SRPNSE),consists of three steps:feature extraction,information completion,and data reconstruction.Case studies have demonstrated the effectiveness and value of the proposed SRPNSE approach in recovering high-frequency data from low-frequency data for the state estimation.
文摘Based on the concrete conditions of earthquake data in the west of China, East China and SOuth China, we studied the completeness of data in these regions by suitable methods to local conditions. Otherwise, we roughly estimated monitoring capability of local networks in China since 1970 and some outlying regions where the data is lack. Finally, we gave the regional distribution of the beginning years since which the data for different magnitude intervals are largely complete in the Chinese mainland.
基金Supported by the National Natural Science Foundation of China(61866006,61741203)the Natural Science Foundation of Guangxi Province(2016GXNSFAA380243)+1 种基金the Guangxi Innovation-Driven Development of Special Funds Project(Gui Ke AA17204091)the Guangxi Nanning Science and Technology Development Planning Project(2018015-5)
文摘In order to solve the parallel algorithm of Petri net system with concurrent function, so as to achieve the parallel control and simulation operation of this system, this paper proposes the function partition completeness theory and algorithms of Petri net parallelization, thereby providing the theoretical support for the realization of Petri parallel algorithms. Firstly, according to the concurrent characteristics of Petri net model, we analyze the parallelism of Petri net system; then, by giving the solving process of place invariants and the function partitioning of Petri net, we propose the function partitioning conditions and determination theorem of Petri net parallelization, and conduct its theoretical proof and practical verification. On this basis, we conduct the theoretical study and analysis on the situation that Petri net system has several kinds of parallel function partitioning, propose the completeness theorem of parallelism function partitioning in Petri net system, and verify it. Finally, we give the algorithms, application examples and simulation experiment results of parallel function partitioning of Petri net systems based on place invariant. The theoretical proof and experimental results show that the function partitioning conditions and completeness theory of Petri net parallelization based on place invariant are correct, and the parallel algorithms under such theoretical basis are also correct and effective.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11061019 and 10962004)the Chunhui Program of Ministry of Education of China (Grant No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia, China(Grant Nos. 2010MS0110 and 2009BS0101)the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University
文摘In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.
基金supported by the National Natural Science Foundation of China (Nos. 11061019,10962004,11101200,and 11026175)the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia of China (No. 2010MS0110)the Cultivation of Innovative Talent of "211 Project" of Inner Mongolia University
文摘This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.
基金Supported by the National Key Basic Research Program of China(No.2013CB834204)
文摘This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.
文摘The historical earthquake catalogue of China has lasted more than 3000 years,and most of its data are inferred from historical records.The earthquake catalogue in earlier times is not complete owing to various reasons,so some events are lost.This paper estimates the loss rate of earthquakes with various magnitudes in the historical earthquake catalogue for different time intervals quantitatively by using the Gutenberg-Richter formula and modern instrumental records,which will provide the references for statistic research in seismicity.
文摘This paper is the continuation of the paper [13]. Namely, in [13], the scope of the structural completeness in the class of all over-systems of the classical predicate calculus, has been established. In this paper we establish the scope of the structural completeness in the class of all over-systems of the classical functional calculus with identity.
文摘Observations of living organisms by citizen scientists that are reported to online portals are a valuable source of information.They are also a special kind of volunteered geographic information(VGI).VGI data have issues of completeness,which arise from biases caused by the opportunistic nature of the data collection process.We examined the completeness of bird species represented in citizen science observation data from eBird and iNaturalist in US National Parks(NPs).We used approaches for completeness estimation which were developed for data from OpenStreetMap,a crowdsourced map of the world.First,we used an extrinsic approach,comparing species lists from citizen science data with National Park Service lists.Second,we examined two intrinsic approaches using total observation numbers in NPs and the development of the number of new species being added to the data-set over time.Results from the extrinsic approach provided appropriate completeness estimations to evaluate the intrinsic approaches.We found that total observation numbers are a good estimator of species completeness of citizen science data from US NPs.There is also a close relationship between species completeness and the ratio of new species added to observation data vs.observation numbers in a given year.
基金The research was supported by the National Natural Science Foundation of China(10361008) Natural Science Foundation of Yunnan Province(2003A002M)
文摘A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.
