Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives...Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.展开更多
In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simu...In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simulations were given.展开更多
In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)an...In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.展开更多
Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-roug...Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.展开更多
Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law charac...Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.展开更多
Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough ...Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough sets namely the two law forecast model is proposed, which includes upper law forecast model and lower law forecast model; and its＇ implement algorithm is given. Finally, the validity of the model is demonstrated by the forecast for region economic development of Hainan Province.展开更多
Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of...Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.展开更多
Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function ...Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we est...Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).展开更多
Single-atom catalysts(SACs)have attracted considerable interest in the fields of energy and environmental science due to their adjustable catalytic activity.In this study,we investigated the matching of valence electr...Single-atom catalysts(SACs)have attracted considerable interest in the fields of energy and environmental science due to their adjustable catalytic activity.In this study,we investigated the matching of valence electron numbers between single atoms and adsorbed intermediates(O,N,C,and H)in MXene-anchored SACs(M-Ti_(2)C/M-Ti_(2)CO_(2)).The density functional theory results demonstrated that the sum of the valence electron number(VM)of the interface-doped metal and the valence electron number(VA)of the adsorbed intermediates in M-Ti_(2)C followed the 10-valence electron matching law.Furthermore,based on the 10-valence electron matching law,we deduced that the sum of the valence electron number(k)and VMfor the molecular adsorption intermediate interactions in M-Ti_(2)CO_(2)adhered to the 11-valence electron matching law.Electrostatic repulsion between the interface electrons in M-Ti_(2)CO_(2)and H_(2)O weakened the adsorption of intermediates,Furthermore,we applied the 11-valence electron matching law to guide the design of catalysts for nitrogen reduction reaction,specifically for N_(2)→NNH conversion,in the MTi_(2)CO_(2)structure.The sure independence screening and sparsifying operator algorithm was used to fit a simple three-dimensional descriptor of the adsorbate(R_(2)up to 0.970)for catalyst design.Our study introduced a valence electron matching principle between doped metals(single atoms)and adsorbed intermediates(atomic and molecular)for MXene-based catalysts,providing new insights into the design of high-performance SACs.展开更多
This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking...This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to f...展开更多
基金This project was supported by Natural Science Foundation of Shandong Province of China (Y2004A04), Natural ScienceFoundation of Fujian of China (Z051049) and Education Foundation of Fujian of China (JA04268),.
文摘Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.
基金Project supported by National Natural Science Foundation of China(Grant No .10271072)
文摘In this paper, the Riemann solutions for scalar conservation laws with discontinuous flux function were constructed. The interactions of elementary waves of the conservation laws were concerned, and the numerical simulations were given.
基金Project supported by the National Key Research and Development Program of China(No.2022YFB3207100)Hubei Provincial Strategic Scientist Training Plan(No.2022EJD009)the Fundamental Research Funds for the Central Universities of China(No.2042023kf1041)。
文摘In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.
基金Supported by the Nature Science Foundation of Henan Province(0511012700).
文摘Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.
基金Supported by the Elementary and Advanced Technology Foundation of Henan Province(082300410040, 102300410153)
文摘Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.
基金supported by the National Natural Science Foundation of China (60364001, 70461004)the Hainan Provincial Natural Science Foundation of China (807054)Hainan Provincial Eduction Office Foundation (HJ2008-56).
文摘Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough sets namely the two law forecast model is proposed, which includes upper law forecast model and lower law forecast model; and its＇ implement algorithm is given. Finally, the validity of the model is demonstrated by the forecast for region economic development of Hainan Province.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10372033)
文摘Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.
文摘Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
基金Research supported by National Natural Science Foundation of China.
文摘Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).
基金funded by the National Natural Science Foundation of China(61701288,51706128)the Natural Science Basic Research Program of Shaanxi Province(2021JM-485)+2 种基金the Key Scientific Research Project of Shaanxi Provincial Education Department(20JS019)the High-level Achievement Cultivation Project of Collaborative Innovation Center for Comprehensive Development of Qinba Biological Resources(QBXT-17-8)the Postgraduate Innovation Project of Shaanxi University of Technology(SLGYCX2410).
文摘Single-atom catalysts(SACs)have attracted considerable interest in the fields of energy and environmental science due to their adjustable catalytic activity.In this study,we investigated the matching of valence electron numbers between single atoms and adsorbed intermediates(O,N,C,and H)in MXene-anchored SACs(M-Ti_(2)C/M-Ti_(2)CO_(2)).The density functional theory results demonstrated that the sum of the valence electron number(VM)of the interface-doped metal and the valence electron number(VA)of the adsorbed intermediates in M-Ti_(2)C followed the 10-valence electron matching law.Furthermore,based on the 10-valence electron matching law,we deduced that the sum of the valence electron number(k)and VMfor the molecular adsorption intermediate interactions in M-Ti_(2)CO_(2)adhered to the 11-valence electron matching law.Electrostatic repulsion between the interface electrons in M-Ti_(2)CO_(2)and H_(2)O weakened the adsorption of intermediates,Furthermore,we applied the 11-valence electron matching law to guide the design of catalysts for nitrogen reduction reaction,specifically for N_(2)→NNH conversion,in the MTi_(2)CO_(2)structure.The sure independence screening and sparsifying operator algorithm was used to fit a simple three-dimensional descriptor of the adsorbate(R_(2)up to 0.970)for catalyst design.Our study introduced a valence electron matching principle between doped metals(single atoms)and adsorbed intermediates(atomic and molecular)for MXene-based catalysts,providing new insights into the design of high-performance SACs.
文摘This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to f...
