The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay prop...The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.展开更多
We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the...The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the threat of secondary disasters,the small baseline subsets(SBAS)technology is applied to process 59 synthetic aperture radar(SAR)images captured from Sentinel-1A satellite.Firstly,the time series deformation of the Zhongbao landslide along the radar line of sight(LOS)direction is calculated by SBAS technology.Then,the projection transformation is conducted to determine the slope displacement.Furthermore,the Hurst exponent of the surface deformation along the two directions is calculated to quantify the hidden deformation development trend and identify the unstable deformation areas.Given the suddenness of the Zhongbao landslide failure,the multi-temporal interferometric synthetic aperture radar(InSAR)technology is the ideal tool to obtain the surface deformation history without any monitoring equipment.The obtained deformation process indicates that the Zhongbao landslide is generally stable with slow creep deformation before failure.Moreover,the Hurst exponent distribution on the landslide surface in different time stages reveals more deformation evolution information of the Zhongbao landslide,with partially unstable areas detected before the failure.Two potential unstable areas after the Zhongbao landslide disaster are revealed by the Hurst exponent distribution and verified by the GNSS monitoring results and deformation mechanism discussion.The method combining SBASInSAR and Hurst exponent proposed in this study could help prevent and control secondary landslide disasters.展开更多
In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The eff...In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.展开更多
Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it canno...Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.展开更多
In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exp...In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exponent from the Schrödinger cocycle in[24]to a Szegö cocycle.展开更多
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ...Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.展开更多
Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition sy...Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition system, and noise interference, seismic attributes for seismic data interpretation have uncertainties. Especially, the antinoise ability of seismic attributes directly affects the reliability of seismic interpretations. Gray system theory is used in time series to minimize data randomness and increase data regularity. Detrended fluctuation analysis （DFA） can effectively reduce extrinsic data tendencies. In this study, by combining gray system theory and DFA, we propose a new method called gray detrended fluctuation analysis （GDFA） for calculating the fractal scaling exponent. We consider nonlinear time series generated by the Weierstrass function and add random noise to actual seismic data. Moreover, we discuss the antinoise ability of the fractal scaling exponent based on GDFA. The results suggest that the fractal scaling exponent calculated using the proposed method has good antinoise ability. We apply the proposed method to 3D poststack migration seismic data from southern China and compare fractal scaling exponents calculated using DFA and GDFA. The results suggest that the use of the GDFA-calculated fractal scaling exponent as a seismic attribute can match the known distribution of sedimentary facies.展开更多
In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions ...In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.展开更多
The emphasis of this exploration was to examine the workability and work hardening performance of Mg(Magnesium)specimen and Mg-B_(4)C composites created via the powder metallurgy technique.The pure Mg and Mg-B_(4)C co...The emphasis of this exploration was to examine the workability and work hardening performance of Mg(Magnesium)specimen and Mg-B_(4)C composites created via the powder metallurgy technique.The pure Mg and Mg-B_(4)C composites are made with distinct weight percentages(Mg-5%B_(4)C,Mg-10%B_(4)C,and Mg-15%B_(4)C)at the unit aspect ratio.The powders and composites characterization are executed by SEM(Scanning Electron Microscope),EDS(Energy Dispersive Spectrum)with an elemental map,and XRD(X-ray Diffraction)examination.It displays that,the B_(4)C particles were dispersed consistently with the Mg matrix.The workability and work hardening examination was conducted in triaxial stress conditions using the cold deformation process.The consequence of workability stress exponent factor(β_(σ)),distinct stress proportion factors(σ_(m)/σ_(eff)and σ_(θ)/σ_(eff)),instantaneous work hardening exponent(n_(1)),work hardening exponent(n),coefficient of strength(k)and instantaneous coefficient of strength(k_(1))are recognized.The outcome displays that Mg-15%B_(4)C specimen has greater workability and work hardening parameter,initial relative density,and triaxial stresses compared with the Mg specimen and Mg-(5–10%)B_(4)C composites.展开更多
For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is t...For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.展开更多
The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this t...The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.展开更多
In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal di...In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal dimension of the global attractors of this problem is finite.展开更多
The variational cumulant expansion developed in recent years has been extended to treat the Ising model in statistical physics.In this paper,a detailed calculation of the critical temperature T c (L) and criti...The variational cumulant expansion developed in recent years has been extended to treat the Ising model in statistical physics.In this paper,a detailed calculation of the critical temperature T c (L) and critical exponent β(L) for the magnetic film of L layers are presented by means of the variational cumulant expansion.For L >1,the results of our theoretical calculations are in approximate coincidence with the experimental ones made before,and for the special case of L =1 (2 D),the results of the calculation are identical to the data from other reports.展开更多
In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with ...In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively.展开更多
A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical syste...A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.展开更多
In this paper,we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball.We are interested in the critical global expon...In this paper,we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball.We are interested in the critical global exponent q_o and the critical Fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case.展开更多
The question of the power-law exponent of exponential growth networks is studied here.In a discrete case,the degree distribution is defined as the probability distribution of the discrete variable.Based on this,the de...The question of the power-law exponent of exponential growth networks is studied here.In a discrete case,the degree distribution is defined as the probability distribution of the discrete variable.Based on this,the degree distribution of the pseudofractal scale-free web,an exponential growth network,is obtained.The power-law exponent ln3/ln2 is analyzed according to the maximum likelihood principle.It satisfies consistency and is good for small generations of the network.For many exponential growth networks,their power-law exponent needs to be tested.The work provides a new view on the power-law exponent of an exponential growth network.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
基金supported by the Natural Science Research Project of Anhui Educational Committee(2023AH040155)Zhisu Liu's research was supported by the Guangdong Basic and Applied Basic Research Foundation(2023A1515011679+2 种基金2024A1515012704)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(CUG2106211CUGST2).
文摘The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
基金support from the National Key R&D Program of China(Grant No.2021YFB3901403)Project supported by graduate research and innovation foundation of Chongqing,China(Grant No.CYS23115)Special project for performance incentive and guidance of scientific research institutions in Chongqing(Grant No.cstc2021jxjl120011)are greatly appreciated。
文摘The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the threat of secondary disasters,the small baseline subsets(SBAS)technology is applied to process 59 synthetic aperture radar(SAR)images captured from Sentinel-1A satellite.Firstly,the time series deformation of the Zhongbao landslide along the radar line of sight(LOS)direction is calculated by SBAS technology.Then,the projection transformation is conducted to determine the slope displacement.Furthermore,the Hurst exponent of the surface deformation along the two directions is calculated to quantify the hidden deformation development trend and identify the unstable deformation areas.Given the suddenness of the Zhongbao landslide failure,the multi-temporal interferometric synthetic aperture radar(InSAR)technology is the ideal tool to obtain the surface deformation history without any monitoring equipment.The obtained deformation process indicates that the Zhongbao landslide is generally stable with slow creep deformation before failure.Moreover,the Hurst exponent distribution on the landslide surface in different time stages reveals more deformation evolution information of the Zhongbao landslide,with partially unstable areas detected before the failure.Two potential unstable areas after the Zhongbao landslide disaster are revealed by the Hurst exponent distribution and verified by the GNSS monitoring results and deformation mechanism discussion.The method combining SBASInSAR and Hurst exponent proposed in this study could help prevent and control secondary landslide disasters.
基金supported by the National Natural Science Foundation of China(Grant Nos.42225501 and 42105059)the National Key Scientific and Tech-nological Infrastructure project“Earth System Numerical Simula-tion Facility”(EarthLab).
文摘In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.
基金supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20200737)the Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant No.NY223109)+1 种基金the Innovation Research Project of Jiangsu Province(Grant No.JSSCBS20210521)the China Postdoctoral Science Foundation(Grant No.2022M721693)。
文摘Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.
文摘In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exponent from the Schrödinger cocycle in[24]to a Szegö cocycle.
文摘Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2012QNA62)the Natural Science Foundation of Jiangsu Province(Grant No.BK20130201)+1 种基金the Chinese Postdoctoral Science Foundation(Grant No.2014M551703)the National Natural Science Foundation of China(Grant No.41374140)
文摘Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition system, and noise interference, seismic attributes for seismic data interpretation have uncertainties. Especially, the antinoise ability of seismic attributes directly affects the reliability of seismic interpretations. Gray system theory is used in time series to minimize data randomness and increase data regularity. Detrended fluctuation analysis （DFA） can effectively reduce extrinsic data tendencies. In this study, by combining gray system theory and DFA, we propose a new method called gray detrended fluctuation analysis （GDFA） for calculating the fractal scaling exponent. We consider nonlinear time series generated by the Weierstrass function and add random noise to actual seismic data. Moreover, we discuss the antinoise ability of the fractal scaling exponent based on GDFA. The results suggest that the fractal scaling exponent calculated using the proposed method has good antinoise ability. We apply the proposed method to 3D poststack migration seismic data from southern China and compare fractal scaling exponents calculated using DFA and GDFA. The results suggest that the use of the GDFA-calculated fractal scaling exponent as a seismic attribute can match the known distribution of sedimentary facies.
文摘In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.
文摘The emphasis of this exploration was to examine the workability and work hardening performance of Mg(Magnesium)specimen and Mg-B_(4)C composites created via the powder metallurgy technique.The pure Mg and Mg-B_(4)C composites are made with distinct weight percentages(Mg-5%B_(4)C,Mg-10%B_(4)C,and Mg-15%B_(4)C)at the unit aspect ratio.The powders and composites characterization are executed by SEM(Scanning Electron Microscope),EDS(Energy Dispersive Spectrum)with an elemental map,and XRD(X-ray Diffraction)examination.It displays that,the B_(4)C particles were dispersed consistently with the Mg matrix.The workability and work hardening examination was conducted in triaxial stress conditions using the cold deformation process.The consequence of workability stress exponent factor(β_(σ)),distinct stress proportion factors(σ_(m)/σ_(eff)and σ_(θ)/σ_(eff)),instantaneous work hardening exponent(n_(1)),work hardening exponent(n),coefficient of strength(k)and instantaneous coefficient of strength(k_(1))are recognized.The outcome displays that Mg-15%B_(4)C specimen has greater workability and work hardening parameter,initial relative density,and triaxial stresses compared with the Mg specimen and Mg-(5–10%)B_(4)C composites.
基金supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 41522502)the National Program on Global Change and Air–Sea Interaction (Grant No. GASI-IPOVAI06)the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2015BAC03B07)
文摘For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.
基金Supported by the National Natural Science Foundation of China (11071065, 10771110, 10471069)sponsored by the 151 Talent Fund of Zhejiang Province
文摘The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
文摘In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal dimension of the global attractors of this problem is finite.
文摘The variational cumulant expansion developed in recent years has been extended to treat the Ising model in statistical physics.In this paper,a detailed calculation of the critical temperature T c (L) and critical exponent β(L) for the magnetic film of L layers are presented by means of the variational cumulant expansion.For L >1,the results of our theoretical calculations are in approximate coincidence with the experimental ones made before,and for the special case of L =1 (2 D),the results of the calculation are identical to the data from other reports.
文摘In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively.
文摘A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
基金The Fundamental Research Funds for the Central Universities and the NSF(11071100) of China
文摘In this paper,we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball.We are interested in the critical global exponent q_o and the critical Fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case.
基金Supported by the National Natural Science Foundation of China under Grant No 10774035the Foundation of Inner Mongolia University of Technology under Grant No X200937.
文摘The question of the power-law exponent of exponential growth networks is studied here.In a discrete case,the degree distribution is defined as the probability distribution of the discrete variable.Based on this,the degree distribution of the pseudofractal scale-free web,an exponential growth network,is obtained.The power-law exponent ln3/ln2 is analyzed according to the maximum likelihood principle.It satisfies consistency and is good for small generations of the network.For many exponential growth networks,their power-law exponent needs to be tested.The work provides a new view on the power-law exponent of an exponential growth network.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
