Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0<p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the ato...Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0<p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the atomic Hardy space Hp,q,γ atb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ∈(μ)via the discrete coefficient K(ρ),p B,S,and prove that the Calder′on-Zygmund operator is bounded from Hp,q,γ,δmb,ρ(μ)(or Hp,q,γatb,ρ(μ))into Lp(μ),and from Hp,q,γ+1atb,ρ(ρ+1)(μ)into H p,q,γ,12(δ-νp+ν)mb,ρ(μ).The boundedness of the generalized fractional integral Tβ(β∈(0,1))from Hp1,q,γ,θmb,ρ(μ)(or Hp1,q,γatb,ρ(μ))into Lp2(μ)with 1/p2=1/p1-β is also established.The authors also introduce theρ-weakly doubling condition,withρ∈(1,∞),of the measure and construct a non-doubling measure satisfying this condition.If isρ-weakly doubling,the authors further introduce the Campanato space Eα,qρ,η,γ(μ)and show that Eα,qρ,η,γ(μ)is independent of the choices ofρ,η,γand q;the authors then introduce the atomic Hardy space Hp,q,γatb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ(μ),which coincide with each other;the authors finally prove that Hp,q,γatb,ρ(μ)is the predual of E1/p-1,1ρ,ρ,1(μ).Moreover,if is doubling,the authors show that Eα,qρ,η,γ(μ)and the Lipschitz space Lipα,q(μ)(q∈[1,∞)),or Hp,q,γatb,ρ(μ)and the atomic Hardy space Hp,q at(μ)(q∈(1,∞])of Coifman and Weiss coincide.Finally,if(X,d,)is an RD-space(reverse doubling space)with(X)=∞,the authors prove that Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ)and Hp,q at(μ)coincide for any q∈(1,2].In particular,when(X,d,):=(RD,||,dx)with dx being the D-dimensional Lebesgue measure,the authors show that spaces Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ),Hp,q,γatb,ρ(μ)and Hp,q,γ,mb,ρ(μ)all coincide with Hp(RD)for any q∈(1,∞).展开更多
The Anderson's model can be applied only to elastic homogeneous deformation and cannot explain complicated phenomena of natural faults, which to a large degree limits the model to practical application. By combing...The Anderson's model can be applied only to elastic homogeneous deformation and cannot explain complicated phenomena of natural faults, which to a large degree limits the model to practical application. By combing the Coulomb-Mohr Criterion with the sandbox modeling and considering non-homogeneous deformation, mechanisms of how basement pre-existing fabrics control fault formation and evolution are analyzed and a mechanical factor, activation-coefficient (faS) of pre-existing fabrics, is proposed. It is determined by the attitude and mechanical properties of pre-existing fabric, and the stress state (the magnitudes and directions of the three principal stresses). The coefficient has taken the heterogeneity of rocks into account and may serve as a criterion for evaluating the activity of a pre-existing fabric. The Mohr-Coulomb Criterion is expanded to non-homogeneous deformation domain in terms of activation-coefficient (faS) of pre-existing fabrics, the general law of the activity of a pre-existing fabric is predicted, the fault complexity real of rift basin is revealed in theory, and the controlling law of basement pre-existing faults to fault formation and evolution is determined, and checked with sandbox modeling. A new way is provided for in-depth study of faulting.展开更多
This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on th...This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.展开更多
Based on Biot's model for fluid-saturated media,which takes the inertial,fluid viscous,mechanical couplings,compressibility of grains and fluid into account,the dispersion equations of plane waves in non-homogeneo...Based on Biot's model for fluid-saturated media,which takes the inertial,fluid viscous,mechanical couplings,compressibility of grains and fluid into account,the dispersion equations of plane waves in non-homogeneously saturated soil are established by using reverberation ray matrix method(RRMM) with the aid of Helmholtz theorem.The non-homogeneity considered is a gradient variation in material properties with depth.The propagation characteristic of elastic waves in non-homogeneously saturated soil is analyzed by numerical example in this paper.The results show that the wave number and dissipation change little for two kinds of compression along the variation direction of the material properties,however,the non-homogeneity has significant effect on the wave number and dissipation of shear wave.展开更多
Software reliability growth models （SRGMs） incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such ...Software reliability growth models （SRGMs） incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.展开更多
The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of subline...The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.展开更多
Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogene...Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogeneity of subsoil condition due to various construction effects.Studies have shown that the damage mechanism of shallow underground structures mainly depends on the inhomogeneity of the subsoil conditions.This would become a considerable factor for the stability of the underground utility tunnel structures.However,this type of research still needs to establish the vulnerable seismic design.In this study,a series of shaking table tests were conducted on non-homogenous soils to investigate the performance of seismic interaction between utility tunnels,surrounding soils and interior pipelines.The dynamic responses measured from the test account for the boundary condition of non-homogeneous soils,the internal forces,displacement of tunnel joints,the dynamic characteristics on interior pipelines and the reasonable spring stiffness with damping in the seismically isolated gas pipeline model inside the tunnel.The vulnerability of underground utility tunnel in non-homogeneous soil zone and the mechanism of the stability of interior facilities are the main topics discussed in this paper.展开更多
The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned...The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned above, is equivalent to the one introduced and studied by HytSnen （2010） in his remarkable framework, i.e., the geometrically doubling metric space with a non-doubling measure satisfying a so-called upper doubling condition. As an application, we obtain the T1 theorem in this more general setting. Moreover, the Gaussian measure is also discussed.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11301534,11171027,11361020 and 11101339)Da Bei Nong Education Fund(Grant No.1101-2413002)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2012LYB26,2012CXQT09,2013YB60 and 2014KJJCA10)
文摘Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0<p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the atomic Hardy space Hp,q,γ atb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ∈(μ)via the discrete coefficient K(ρ),p B,S,and prove that the Calder′on-Zygmund operator is bounded from Hp,q,γ,δmb,ρ(μ)(or Hp,q,γatb,ρ(μ))into Lp(μ),and from Hp,q,γ+1atb,ρ(ρ+1)(μ)into H p,q,γ,12(δ-νp+ν)mb,ρ(μ).The boundedness of the generalized fractional integral Tβ(β∈(0,1))from Hp1,q,γ,θmb,ρ(μ)(or Hp1,q,γatb,ρ(μ))into Lp2(μ)with 1/p2=1/p1-β is also established.The authors also introduce theρ-weakly doubling condition,withρ∈(1,∞),of the measure and construct a non-doubling measure satisfying this condition.If isρ-weakly doubling,the authors further introduce the Campanato space Eα,qρ,η,γ(μ)and show that Eα,qρ,η,γ(μ)is independent of the choices ofρ,η,γand q;the authors then introduce the atomic Hardy space Hp,q,γatb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ(μ),which coincide with each other;the authors finally prove that Hp,q,γatb,ρ(μ)is the predual of E1/p-1,1ρ,ρ,1(μ).Moreover,if is doubling,the authors show that Eα,qρ,η,γ(μ)and the Lipschitz space Lipα,q(μ)(q∈[1,∞)),or Hp,q,γatb,ρ(μ)and the atomic Hardy space Hp,q at(μ)(q∈(1,∞])of Coifman and Weiss coincide.Finally,if(X,d,)is an RD-space(reverse doubling space)with(X)=∞,the authors prove that Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ)and Hp,q at(μ)coincide for any q∈(1,2].In particular,when(X,d,):=(RD,||,dx)with dx being the D-dimensional Lebesgue measure,the authors show that spaces Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ),Hp,q,γatb,ρ(μ)and Hp,q,γ,mb,ρ(μ)all coincide with Hp(RD)for any q∈(1,∞).
基金supported by National Natural Science Foundation of China (Grant No.40772086)Oil and Gas Exploration Projects in Common Ahead of China National Petroleum Corporation (Grant No.07-01C-01-04)
文摘The Anderson's model can be applied only to elastic homogeneous deformation and cannot explain complicated phenomena of natural faults, which to a large degree limits the model to practical application. By combing the Coulomb-Mohr Criterion with the sandbox modeling and considering non-homogeneous deformation, mechanisms of how basement pre-existing fabrics control fault formation and evolution are analyzed and a mechanical factor, activation-coefficient (faS) of pre-existing fabrics, is proposed. It is determined by the attitude and mechanical properties of pre-existing fabric, and the stress state (the magnitudes and directions of the three principal stresses). The coefficient has taken the heterogeneity of rocks into account and may serve as a criterion for evaluating the activity of a pre-existing fabric. The Mohr-Coulomb Criterion is expanded to non-homogeneous deformation domain in terms of activation-coefficient (faS) of pre-existing fabrics, the general law of the activity of a pre-existing fabric is predicted, the fault complexity real of rift basin is revealed in theory, and the controlling law of basement pre-existing faults to fault formation and evolution is determined, and checked with sandbox modeling. A new way is provided for in-depth study of faulting.
基金supported by the National Natural Science Foundation of China(7090104171171113)the Aeronautical Science Foundation of China(2014ZG52077)
文摘This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.
基金supported by the National Natural Science Foundation of China (Grant No. 11162008)the Fund of Education Department of Gansu Province of China for Master's Tutor (1103-07)the Fundamental Research Funds for the Gansu Universities (Grant No. 1104ZTC140)
文摘Based on Biot's model for fluid-saturated media,which takes the inertial,fluid viscous,mechanical couplings,compressibility of grains and fluid into account,the dispersion equations of plane waves in non-homogeneously saturated soil are established by using reverberation ray matrix method(RRMM) with the aid of Helmholtz theorem.The non-homogeneity considered is a gradient variation in material properties with depth.The propagation characteristic of elastic waves in non-homogeneously saturated soil is analyzed by numerical example in this paper.The results show that the wave number and dissipation change little for two kinds of compression along the variation direction of the material properties,however,the non-homogeneity has significant effect on the wave number and dissipation of shear wave.
文摘Software reliability growth models （SRGMs） incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.
基金the North China Electric Power University Youth Foundation(No.200611004)the Renmin University of China Science Research Foundation(No.30206104)
文摘The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.
基金National Key Research and Invention Program of The Thirteenth under Grant Nos.2016YFC0802407,2018YFC0809605。
文摘Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogeneity of subsoil condition due to various construction effects.Studies have shown that the damage mechanism of shallow underground structures mainly depends on the inhomogeneity of the subsoil conditions.This would become a considerable factor for the stability of the underground utility tunnel structures.However,this type of research still needs to establish the vulnerable seismic design.In this study,a series of shaking table tests were conducted on non-homogenous soils to investigate the performance of seismic interaction between utility tunnels,surrounding soils and interior pipelines.The dynamic responses measured from the test account for the boundary condition of non-homogeneous soils,the internal forces,displacement of tunnel joints,the dynamic characteristics on interior pipelines and the reasonable spring stiffness with damping in the seismically isolated gas pipeline model inside the tunnel.The vulnerability of underground utility tunnel in non-homogeneous soil zone and the mechanism of the stability of interior facilities are the main topics discussed in this paper.
基金supported by National Natural Science Foundation of China(Grant No.61203249)
文摘The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned above, is equivalent to the one introduced and studied by HytSnen （2010） in his remarkable framework, i.e., the geometrically doubling metric space with a non-doubling measure satisfying a so-called upper doubling condition. As an application, we obtain the T1 theorem in this more general setting. Moreover, the Gaussian measure is also discussed.
