This paper has two aims. The first one is to investigate the existence of chaotic structures in the oil prices, expectations of investors and stock returns by combining the Lyapunov exponent and Kolmogorov entropy, an...This paper has two aims. The first one is to investigate the existence of chaotic structures in the oil prices, expectations of investors and stock returns by combining the Lyapunov exponent and Kolmogorov entropy, and the second one is to analyze the dependence behavior of oil prices, expectations of investors and stock returns from January 02, 1990, to June 06, 2017. Lyapunov exponents and Kolmogorov entropy determined that the oil price and the stock return series exhibited chaotic behavior. TAR-TR-GARCH and TAR-TR-TGARCH copula methods were applied to study the co-movement among the selected variables. The results showed significant evidence of nonlinear tail dependence between the volatility of the oil prices, the expectations of investors and the stock returns. Further, upper and lower tail dependence and comovement between the analyzed series could not be rejected. Moreover, the TAR-TR-GARCH and TAR-TR-TGARCH copula methods revealed that the volatility of oil price had crucial effects on the stock returns and on the expectations of investors in the long run.展开更多
Light-absorbing carbonaceous aerosols including black carbon(BC) and brown carbon(BrC)play significant roles in atmospheric radiative properties. One-year measurements of aerosol light absorption at multi-wavelength w...Light-absorbing carbonaceous aerosols including black carbon(BC) and brown carbon(BrC)play significant roles in atmospheric radiative properties. One-year measurements of aerosol light absorption at multi-wavelength were continuously conducted in Xiamen,southeast of China in 2014 to determine the light absorption properties including absorption coefficients(σabs) and absorption ?ngstr?m exponent(AAE) in the coastal city.Light absorptions of BC and BrC with their contributions to total light absorption were further quantified. Mean σabsat 370 nm and 880 nm were 56.6 ± 34.3 and 16.5 ± 11.2 Mm-1,respectively. σabspresented a double-peaks diurnal pattern with the maximum in the morning and the minimum in the afternoon. σabswas low in warm seasons and high in cold seasons. AAE ranged from 0.26 to 2.58 with the annual mean of 1.46, implying that both fossil fuel combustion and biomass burning influenced aerosol optical properties. σabsof BrC at 370 nm was 24.0 ± 5.7 Mm-1, contributing 42% to the total absorption. The highest AAE(1.52 ± 0.02) and largest BrC contributions(47% ± 4%) in winter suggested the significant influence of biomass burning on aerosol light absorption. Long-distance air masses passing through North China Plain and the Yangtze River Delta led to high AAE and BrC contributions. High AAE value of 1.46 in July indicated that long-range transport of the air pollutants from intense biomass burning in Southeast Asia would affect aerosol light absorption in Southeast China. The study will improve the understanding of light absorption properties of aerosols and the optical impacts of BrC in China.展开更多
We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least ...We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived;in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results.展开更多
Based on observational data obtained from 1961 to 2011 in the Tarim River Basin,China,we investigated the chaotic dynamics of temperature,precipitation,relative humidity,and evaporation.The main findings are as follow...Based on observational data obtained from 1961 to 2011 in the Tarim River Basin,China,we investigated the chaotic dynamics of temperature,precipitation,relative humidity,and evaporation.The main findings are as follow:(1)The four data series have significant chaotic and fractal behaviors,which are the result of the evolution of a nonlinear chaotic dynamic system.The climatic process in the Tarim River Basin also has deterministic and stochastic characteristics.(2)To describe the temperature,precipitation,relative humidity,and evaporation dynamics,at least three independent variables at daily scale are required;in terms of complexity,their order is evaporation>temperature>precipitation>relative humidity.(3)Their respective largest Lyapunov exponentλ1 shows the order of their degree of complexity is relative humidity>temperature>precipitation≈evaporation;the maximum time scales for which the four systems can be predicted are 17 days,17 days,16 days,and 16 days,if calculated separately.(4)The Kolmogorov entropy K illustrates that the complexity of the nonlinear precipitation system is much greater than that of the other three systems.Both temperature and evaporation systems exhibit weaker chaotic behavior,their predictability is better,and the degree of complexity is less than that of the other two factors.展开更多
Recent research about reconstruction methods mainly used the interpolation reconstruction of the fluctuating wind pressure field on the surface.However,to investigate wind pressure at the edge of the building,the work...Recent research about reconstruction methods mainly used the interpolation reconstruction of the fluctuating wind pressure field on the surface.However,to investigate wind pressure at the edge of the building,the work presented in this paper focuses on the extrapolation reconstruction of wind pressure fields.Here,we propose an improved proper orthogonal decomposition(POD)and Kriging method with a von Karman correlation function to resolve this issue.The studies show that it works well for not only interpolation reconstruction but also extrapolation reconstruction.The proposed method does require determination of the Hurst exponent and other parameters analysed from the original data.Hence,the fluctuating wind fields have been characterized by the von Karman correlation function,as an a priori function.Compared with the cubic spline method and different variogram,preliminary results suggest less time consumption and high efficiency in extrapolation reconstruction at the edge.展开更多
This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model.With the flow...This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model.With the flow field driven by alternate inflows predicted by a shallow water model,particle trajectories are traced out using a particle tracking model.The horizontal fluid mixing dynamics are then interpreted using dynamics system analysis approaches including finite-time Lyapunov exponent(FTLE)and Lagrangian coherent structure(LCS).From the simulation results,it is confirmed that periodic inflows are able to create a weak dynamic system in an idealised circular lake,with the particle dynamics controlled by a single dimensionless parameter associated with the inflow duration.The mixing and transport property of the lake changes from regular to chaotic as the value of the dimensionless parameter increases until global chaotic particle dynamics is achieved.By further analysing the advection of particles injected continuously to the inflows(freshwater),the fate of“freshwater”particles in a“polluted”lake is tracked and revealed.The results provide useful guidance for engineering applications,i.e.,transferring freshwater from rivers to improve the water quality in polluted water bodies such as lakes.The presented approach will be able to facilitate the design of‘optimised’schemes for such engineering implementation.展开更多
In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bound...In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases:(i) Both q and r are subcritical;(ii) r is critical and q is subcritical;(iii) r is subcritical and q is critical;(iv) Both q and r are critical.展开更多
In this paper,we prove that the supremum sup{∫B∫B|u(y)|^p(|y|)|u(x)|^p(|x|)/|x-y|^u dxdy:u∈H^10,rad(B),‖▽u‖L^2(B)=1}is attained,where B denotes the unit ball in R^N(N≥3),μ∈(0,N),p(r)=2^xμ+r^t,t∈(0,min{N/2-...In this paper,we prove that the supremum sup{∫B∫B|u(y)|^p(|y|)|u(x)|^p(|x|)/|x-y|^u dxdy:u∈H^10,rad(B),‖▽u‖L^2(B)=1}is attained,where B denotes the unit ball in R^N(N≥3),μ∈(0,N),p(r)=2^xμ+r^t,t∈(0,min{N/2-μ/4,N-2})and 2^xμ=(2N-μ)/(N-2)is the critical exponent for the Hardy-Littlewood-Sobolev inequality.展开更多
In this work, two types of predictability are proposed-forward and backward predictability-and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estim...In this work, two types of predictability are proposed-forward and backward predictability-and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.展开更多
This study presents detailed analysis of spatiotemporal variations and trend of dust optical properties i.e., Aerosol Optical Depth (AOD) and Angstrom component over Asian desert regions using thirteen years of data (...This study presents detailed analysis of spatiotemporal variations and trend of dust optical properties i.e., Aerosol Optical Depth (AOD) and Angstrom component over Asian desert regions using thirteen years of data (i.e., 2001–2013) retrieved from Aerosol Robotic Network (AERONET), Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR). These regions include Solar Village, Dunhuang and Dalangzadgad and are considered as origin of desert aerosols in Asia. Mann–Kendall trend test was used to show the trend of AOD. The relationship of AOD with weather parameters and general AOD trend over different wavelengths has also been shown. AOD's trend has been observed significant throughout the year in Solar Village, while in Dunhuang and Dalanzadgad the significant trend has been found only in peak period (March–June). Analysis show high values of AOD and low values of angstrom in Solar Village during peak period. In Chinese desert regions, high values of AOD have been found during peak period and low values in pre-peak period. Significant relationship has been observed between AOD and average temperature in Solar Village and Dalanzadgad whereas rainfall and wind speed showed no significant impact on AOD in all desert regions.展开更多
In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also...In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.展开更多
Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Little...Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function,we obtain several equivalent characterizations of Hp(·)(Rn) in terms of wavelets,which extend the wavelet characterizations of the classical Hardy spaces.The main ingredients are that,we overcome the difficulties of the quasi-norms of Hp(·)(Rn) by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on Lp(·)(Rn),and also overcome the difficulty of the failure of q =2 in the atomic decomposition of Hp(·) (Rn) by a known idea.展开更多
Since 2005,dozens of geographical observational stations have been established in the Heihe River Basin(HRB),and by now a large amount of meteorological,hydrological,and ecological observations as well as data pertain...Since 2005,dozens of geographical observational stations have been established in the Heihe River Basin(HRB),and by now a large amount of meteorological,hydrological,and ecological observations as well as data pertaining to water resources,soil and vegetation have been collected.To adequately analyze these available data and data to be further collected in future,we present a perspective from complexity theory.The concrete materials covered include a presentation of adaptive multiscale filter,which can readily determine arbitrary trends,maximally reduce noise,and reliably perform fractal and multifractal analysis,and a presentation of scale-dependent Lyapunov exponent(SDLE),which can reliably distinguish deterministic chaos from random processes,determine the error doubling time for prediction,and obtain the defining parameters of the process examined.The adaptive filter is illustrated by applying it to obtain the global warming trend and the Atlantic multidecadal oscillation from sea surface temperature data,and by applying it to some variables collected at the HRB to determine diurnal cycle and fractal properties.The SDLE is illustrated to determine intermittent chaos from river flow data.展开更多
In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parame...In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R~3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean’s monotonicity trick and the concentration-compactness principle due to Lions(1984).展开更多
We establish a new characterization of the Musielak-Orlicz-Sobolev space on ?n, which includes the classical Orlicz-Sobolev space, the weighted Sobolev space, and the variable exponent Sobolev space as special cases, ...We establish a new characterization of the Musielak-Orlicz-Sobolev space on ?n, which includes the classical Orlicz-Sobolev space, the weighted Sobolev space, and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. H?st? and A. M. Ribeiro [Commun. Contemp. Math., 2017, 19: 1650022] via weakening the assumption f ∈ L^1(R^n) into f ∈ L^1loc(R^n), which was conjectured to be true by Hosto and Ribeiro in the aforementioned same article.展开更多
Accurate wind and turbulence information are essential to wind energy research and utilization, among which wind shear and turbulence intensity/scale have seldom been investigated. In this paper, the observational dat...Accurate wind and turbulence information are essential to wind energy research and utilization, among which wind shear and turbulence intensity/scale have seldom been investigated. In this paper, the observational data from the100-m high wind towers in Xilinhot in Inner Mongolia(2009–10;grassland region), Huanghua in Hebei Province(2009–10;coastal flat region), and Xingzi County in Jiangxi Province(2010–11;mountain–lake region) are used to study the variations in near surface winds and turbulence characteristics related to the development of local wind energy over different underlying surfaces. The results indicate that(1) the percentage of the observed wind shear exponents exceeding 0.3 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10%for the mountain–lake region. In other words, if the wind speed at 10 m is 10 ms–1, the percentage of the wind speed at 100 m exceeding 20 ms–1 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10% for the mountain–lake region.(2) In terms of the turbulent intensity in the zonal, meridional, and vertical directions(Iu, Iv, and Iw, respectively), the frequencies of Iv/Iu < 0.8 in the grassland, coastal flat, and mountain–lake regions are 23%–29%, 32%–38%, and 30%–37%, respectively. Additionally, the frequencies of Iw/Iu < 0.5 in the grassland, coastal flat, and mountain–lake regions are 45%–75%, 52%–70%, and 43%–53%, respectively. The frequencies of Iv/Iu < 0.8 and Iw/Iu < 0.5 in each region mean that Iu is large and the air flow is unstable and fluctuating,which will damage the wind turbines. Therefore, these conditions do not meet the wind turbine design requirements,which must be considered separately.(3) At 50-and 70-m heights, the value of the turbulence scale parameter Λ in the grassland region is greater than that in the coastal flat region, and the latter is greater than that in the mountain–lake region. Therefore, under the same conditions, some paramet展开更多
Basing upon the recent development of the Patterson–Sullivan measures with a H¨older continuous nonzero potential function,we use tools of both dynamics of geodesic flows and geometric properties of negatively c...Basing upon the recent development of the Patterson–Sullivan measures with a H¨older continuous nonzero potential function,we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson–Sullivan measures with a H¨older continuous potential function and the corresponding critical exponent.展开更多
To increase dynamic stability of the quadrotor unmanned aerial vehicles in varying mechanical structure.The qualitative analysis is considered the main methods for analyzing the dynamic stability,while the index of qu...To increase dynamic stability of the quadrotor unmanned aerial vehicles in varying mechanical structure.The qualitative analysis is considered the main methods for analyzing the dynamic stability,while the index of qualitative analysis of the structural stability and the dynamic stability are still hard to establish.Therefore,the process during rolling or pitching is selected for investigating in the present papers,the method of Lyapunov exponent is adopted for establishing the quantification relationship of between structural parameters of quadrotor unmanned aerial vehicles and dynamic stability,and its dynamic stability for guiding the design of the vehicle′s mechanical structure and the optimization of its stability control by using the relationship.As compared to its counterpart of Lyapunov′s second method,the main advantage of the concept of Lyapunov exponents is that the methods for calculating the exponent process are constructive which makes the stability analysis of complex nonlinear systems possible.展开更多
文摘This paper has two aims. The first one is to investigate the existence of chaotic structures in the oil prices, expectations of investors and stock returns by combining the Lyapunov exponent and Kolmogorov entropy, and the second one is to analyze the dependence behavior of oil prices, expectations of investors and stock returns from January 02, 1990, to June 06, 2017. Lyapunov exponents and Kolmogorov entropy determined that the oil price and the stock return series exhibited chaotic behavior. TAR-TR-GARCH and TAR-TR-TGARCH copula methods were applied to study the co-movement among the selected variables. The results showed significant evidence of nonlinear tail dependence between the volatility of the oil prices, the expectations of investors and the stock returns. Further, upper and lower tail dependence and comovement between the analyzed series could not be rejected. Moreover, the TAR-TR-GARCH and TAR-TR-TGARCH copula methods revealed that the volatility of oil price had crucial effects on the stock returns and on the expectations of investors in the long run.
基金supported by the National Natural Science Foundation of China(Nos.21607148,U1405235,41575146,21507127)the National Key R&D Program of China(No.2016YFC0200500)+2 种基金the Fujian Natural Science Foundation(2017J01082)Youth Innovation Promotion Association CAS(No.2016279)the Chinese Academy of Sciences Interdisciplinary Innovation Team Project.
文摘Light-absorbing carbonaceous aerosols including black carbon(BC) and brown carbon(BrC)play significant roles in atmospheric radiative properties. One-year measurements of aerosol light absorption at multi-wavelength were continuously conducted in Xiamen,southeast of China in 2014 to determine the light absorption properties including absorption coefficients(σabs) and absorption ?ngstr?m exponent(AAE) in the coastal city.Light absorptions of BC and BrC with their contributions to total light absorption were further quantified. Mean σabsat 370 nm and 880 nm were 56.6 ± 34.3 and 16.5 ± 11.2 Mm-1,respectively. σabspresented a double-peaks diurnal pattern with the maximum in the morning and the minimum in the afternoon. σabswas low in warm seasons and high in cold seasons. AAE ranged from 0.26 to 2.58 with the annual mean of 1.46, implying that both fossil fuel combustion and biomass burning influenced aerosol optical properties. σabsof BrC at 370 nm was 24.0 ± 5.7 Mm-1, contributing 42% to the total absorption. The highest AAE(1.52 ± 0.02) and largest BrC contributions(47% ± 4%) in winter suggested the significant influence of biomass burning on aerosol light absorption. Long-distance air masses passing through North China Plain and the Yangtze River Delta led to high AAE and BrC contributions. High AAE value of 1.46 in July indicated that long-range transport of the air pollutants from intense biomass burning in Southeast Asia would affect aerosol light absorption in Southeast China. The study will improve the understanding of light absorption properties of aerosols and the optical impacts of BrC in China.
基金supported in part by a University of Tennessee at Chattanooga SimCenter-Center of Excellence in Applied Computational Science and Engineering (CEACSE) grant.
文摘We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived;in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results.
基金This work is supported by the China Postdoctoral Science Foundation(2016M600515)Postdoctoral Preferred Fund of Jiangxi Province(2017KY48)+5 种基金the Jiangxi Postdoctoral Daily Fund Project(2016RC25)the Opening Fund of Key Laboratory of Poyang Lake Wetland and Watershed Research(Jiangxi Normal University)Ministry of Education(PK2017002)the Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing(2016WICSIP012)the National Natural Science Foundation of China(61703199)and the Science and Technology Research Project of Jiangxi Provincial Education Department(GJJ180926).
文摘Based on observational data obtained from 1961 to 2011 in the Tarim River Basin,China,we investigated the chaotic dynamics of temperature,precipitation,relative humidity,and evaporation.The main findings are as follow:(1)The four data series have significant chaotic and fractal behaviors,which are the result of the evolution of a nonlinear chaotic dynamic system.The climatic process in the Tarim River Basin also has deterministic and stochastic characteristics.(2)To describe the temperature,precipitation,relative humidity,and evaporation dynamics,at least three independent variables at daily scale are required;in terms of complexity,their order is evaporation>temperature>precipitation>relative humidity.(3)Their respective largest Lyapunov exponentλ1 shows the order of their degree of complexity is relative humidity>temperature>precipitation≈evaporation;the maximum time scales for which the four systems can be predicted are 17 days,17 days,16 days,and 16 days,if calculated separately.(4)The Kolmogorov entropy K illustrates that the complexity of the nonlinear precipitation system is much greater than that of the other three systems.Both temperature and evaporation systems exhibit weaker chaotic behavior,their predictability is better,and the degree of complexity is less than that of the other two factors.
基金the National Natural Science Fundation of China(Grant No.51469016).
文摘Recent research about reconstruction methods mainly used the interpolation reconstruction of the fluctuating wind pressure field on the surface.However,to investigate wind pressure at the edge of the building,the work presented in this paper focuses on the extrapolation reconstruction of wind pressure fields.Here,we propose an improved proper orthogonal decomposition(POD)and Kriging method with a von Karman correlation function to resolve this issue.The studies show that it works well for not only interpolation reconstruction but also extrapolation reconstruction.The proposed method does require determination of the Hurst exponent and other parameters analysed from the original data.Hence,the fluctuating wind fields have been characterized by the von Karman correlation function,as an a priori function.Compared with the cubic spline method and different variogram,preliminary results suggest less time consumption and high efficiency in extrapolation reconstruction at the edge.
基金Project supported by the National Natural Science Foundation of China(Grant No.11371117).
文摘This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model.With the flow field driven by alternate inflows predicted by a shallow water model,particle trajectories are traced out using a particle tracking model.The horizontal fluid mixing dynamics are then interpreted using dynamics system analysis approaches including finite-time Lyapunov exponent(FTLE)and Lagrangian coherent structure(LCS).From the simulation results,it is confirmed that periodic inflows are able to create a weak dynamic system in an idealised circular lake,with the particle dynamics controlled by a single dimensionless parameter associated with the inflow duration.The mixing and transport property of the lake changes from regular to chaotic as the value of the dimensionless parameter increases until global chaotic particle dynamics is achieved.By further analysing the advection of particles injected continuously to the inflows(freshwater),the fate of“freshwater”particles in a“polluted”lake is tracked and revealed.The results provide useful guidance for engineering applications,i.e.,transferring freshwater from rivers to improve the water quality in polluted water bodies such as lakes.The presented approach will be able to facilitate the design of‘optimised’schemes for such engineering implementation.
基金Supported by NSFC(Grant Nos.11771300 and 11726634).
文摘In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases:(i) Both q and r are subcritical;(ii) r is critical and q is subcritical;(iii) r is subcritical and q is critical;(iv) Both q and r are critical.
文摘In this paper,we prove that the supremum sup{∫B∫B|u(y)|^p(|y|)|u(x)|^p(|x|)/|x-y|^u dxdy:u∈H^10,rad(B),‖▽u‖L^2(B)=1}is attained,where B denotes the unit ball in R^N(N≥3),μ∈(0,N),p(r)=2^xμ+r^t,t∈(0,min{N/2-μ/4,N-2})and 2^xμ=(2N-μ)/(N-2)is the critical exponent for the Hardy-Littlewood-Sobolev inequality.
基金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 Nos. GASI-IPOVAI- 06 and GASI-IPOVAI-03)the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2015BAC03B07).
文摘In this work, two types of predictability are proposed-forward and backward predictability-and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.
基金National Natural Science Foundations of China (Nos.41475136and 41590871)International Science & Technology Cooperation Program of China (No.2013DFG22820).
文摘This study presents detailed analysis of spatiotemporal variations and trend of dust optical properties i.e., Aerosol Optical Depth (AOD) and Angstrom component over Asian desert regions using thirteen years of data (i.e., 2001–2013) retrieved from Aerosol Robotic Network (AERONET), Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR). These regions include Solar Village, Dunhuang and Dalangzadgad and are considered as origin of desert aerosols in Asia. Mann–Kendall trend test was used to show the trend of AOD. The relationship of AOD with weather parameters and general AOD trend over different wavelengths has also been shown. AOD's trend has been observed significant throughout the year in Solar Village, while in Dunhuang and Dalanzadgad the significant trend has been found only in peak period (March–June). Analysis show high values of AOD and low values of angstrom in Solar Village during peak period. In Chinese desert regions, high values of AOD have been found during peak period and low values in pre-peak period. Significant relationship has been observed between AOD and average temperature in Solar Village and Dalanzadgad whereas rainfall and wind speed showed no significant impact on AOD in all desert regions.
基金supported by Spanish Government Grant(Grant No. MTM2016-79436-P)supported by Nazarbayev University Social Policy Grant.
文摘In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.
基金The author would like to express his deep thanks to the anonymous referees for their several enlightening comments on this article, which do improve the presen tat ion of this article. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11701160, 11871100).
文摘Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function,we obtain several equivalent characterizations of Hp(·)(Rn) in terms of wavelets,which extend the wavelet characterizations of the classical Hardy spaces.The main ingredients are that,we overcome the difficulties of the quasi-norms of Hp(·)(Rn) by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on Lp(·)(Rn),and also overcome the difficulty of the failure of q =2 in the atomic decomposition of Hp(·) (Rn) by a known idea.
基金National Natural Science Foundation of China,No.71661002,No.41671532National Key R&D Program of China,No.2017YFB0504102The Fundamental Research Funds for the Central Universities.
文摘Since 2005,dozens of geographical observational stations have been established in the Heihe River Basin(HRB),and by now a large amount of meteorological,hydrological,and ecological observations as well as data pertaining to water resources,soil and vegetation have been collected.To adequately analyze these available data and data to be further collected in future,we present a perspective from complexity theory.The concrete materials covered include a presentation of adaptive multiscale filter,which can readily determine arbitrary trends,maximally reduce noise,and reliably perform fractal and multifractal analysis,and a presentation of scale-dependent Lyapunov exponent(SDLE),which can reliably distinguish deterministic chaos from random processes,determine the error doubling time for prediction,and obtain the defining parameters of the process examined.The adaptive filter is illustrated by applying it to obtain the global warming trend and the Atlantic multidecadal oscillation from sea surface temperature data,and by applying it to some variables collected at the HRB to determine diurnal cycle and fractal properties.The SDLE is illustrated to determine intermittent chaos from river flow data.
基金supported by National Natural Science Foundation of China(Grant Nos.11771468 and 11271386)supported by National Natural Science Foundation of China(Grant Nos.11771234 and 11371212).
文摘In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R~3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean’s monotonicity trick and the concentration-compactness principle due to Lions(1984).
基金National Natural Science Foundation of China (Grant Nos. 11871254, 11571289. 11571039, 11761131002, 11671185. 11871100)Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2018-111).
文摘We establish a new characterization of the Musielak-Orlicz-Sobolev space on ?n, which includes the classical Orlicz-Sobolev space, the weighted Sobolev space, and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. H?st? and A. M. Ribeiro [Commun. Contemp. Math., 2017, 19: 1650022] via weakening the assumption f ∈ L^1(R^n) into f ∈ L^1loc(R^n), which was conjectured to be true by Hosto and Ribeiro in the aforementioned same article.
基金Supported by the China Meteorological Administration Special Public Welfare Research Fund (GYHY20120626).
文摘Accurate wind and turbulence information are essential to wind energy research and utilization, among which wind shear and turbulence intensity/scale have seldom been investigated. In this paper, the observational data from the100-m high wind towers in Xilinhot in Inner Mongolia(2009–10;grassland region), Huanghua in Hebei Province(2009–10;coastal flat region), and Xingzi County in Jiangxi Province(2010–11;mountain–lake region) are used to study the variations in near surface winds and turbulence characteristics related to the development of local wind energy over different underlying surfaces. The results indicate that(1) the percentage of the observed wind shear exponents exceeding 0.3 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10%for the mountain–lake region. In other words, if the wind speed at 10 m is 10 ms–1, the percentage of the wind speed at 100 m exceeding 20 ms–1 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10% for the mountain–lake region.(2) In terms of the turbulent intensity in the zonal, meridional, and vertical directions(Iu, Iv, and Iw, respectively), the frequencies of Iv/Iu < 0.8 in the grassland, coastal flat, and mountain–lake regions are 23%–29%, 32%–38%, and 30%–37%, respectively. Additionally, the frequencies of Iw/Iu < 0.5 in the grassland, coastal flat, and mountain–lake regions are 45%–75%, 52%–70%, and 43%–53%, respectively. The frequencies of Iv/Iu < 0.8 and Iw/Iu < 0.5 in each region mean that Iu is large and the air flow is unstable and fluctuating,which will damage the wind turbines. Therefore, these conditions do not meet the wind turbine design requirements,which must be considered separately.(3) At 50-and 70-m heights, the value of the turbulence scale parameter Λ in the grassland region is greater than that in the coastal flat region, and the latter is greater than that in the mountain–lake region. Therefore, under the same conditions, some paramet
基金The second author is partially supported by NSFC(Grant Nos.11571207 and 11871045)the third author is partially supported by NSFC(Grant No.11871045)by the State Scholarship Fund from China Scholarship Council(CSC)。
文摘Basing upon the recent development of the Patterson–Sullivan measures with a H¨older continuous nonzero potential function,we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson–Sullivan measures with a H¨older continuous potential function and the corresponding critical exponent.
基金supported by the Basic ScientificResearch Operation Expenses of Central Public Welfare Research Institutes(Y917006,Y917008).
文摘To increase dynamic stability of the quadrotor unmanned aerial vehicles in varying mechanical structure.The qualitative analysis is considered the main methods for analyzing the dynamic stability,while the index of qualitative analysis of the structural stability and the dynamic stability are still hard to establish.Therefore,the process during rolling or pitching is selected for investigating in the present papers,the method of Lyapunov exponent is adopted for establishing the quantification relationship of between structural parameters of quadrotor unmanned aerial vehicles and dynamic stability,and its dynamic stability for guiding the design of the vehicle′s mechanical structure and the optimization of its stability control by using the relationship.As compared to its counterpart of Lyapunov′s second method,the main advantage of the concept of Lyapunov exponents is that the methods for calculating the exponent process are constructive which makes the stability analysis of complex nonlinear systems possible.