In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the ...In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.展开更多
Precipitation and associated cloud hydrometeors have large temporal and spatial variability, which makes accurate quantitative precipitation forecasting difficult. Thus, dependence of accurate precipitation and associ...Precipitation and associated cloud hydrometeors have large temporal and spatial variability, which makes accurate quantitative precipitation forecasting difficult. Thus, dependence of accurate precipitation and associated cloud simulation on temporal and spatial scales becomes an important issue. We report a cloud- resolving modeling analysis on this issue by comparing the control experiment with experiments perturbed by initial temperature, water vapor, and cloud conditions. The simulation is considered to be accurate only if the root-mean-squared difference between the perturbation experiments and the control experiment is smaller than the standard deviation. The analysis may suggest that accurate precipitation and cloud simulations cannot be obtained on both fine temporal and spatial scales simultaneously, which limits quanti- tative precipitation forecasting. The accurate simulation of water vapor convergence could lead to accurate precipitation and cloud simulations on daily time scales, but it may not be beneficial to precipitation and cloud simulations on hourly time scales due to the dominance of cloud processes.展开更多
Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmande...Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.展开更多
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
The study investigated the concentration of Lead, Cadmium, Nickels and Chromium in sediment and seagrass tissues at six selected sites along the Sudanese Red Sea coast. The findings of the study added some important a...The study investigated the concentration of Lead, Cadmium, Nickels and Chromium in sediment and seagrass tissues at six selected sites along the Sudanese Red Sea coast. The findings of the study added some important and necessary information about the status and condition of the coastal environment in the Sudanese Red Sea coast in terms of the extent of pollution with heavy metals. The study sites included: Marsa Bashayer, Marsa Dama Dama, Green Area, Shipyard, Marsa Halout and Dungonab Bay. The Atomic Absorption Spectrophotometer was used to measure Lead, Cadmium and Nickels. The colorimetric detection method was used for Chromium using the Spectrophotometer. Marsa Dama Dama site revealed high levels concentration of heavy metals in sediment for Lead (60.5) μg/g, Cadmium (0.22) μg/g and Chromium (146.65) μg/g. Marsa Halout showed the highest mean concentration of Nickel in sediment at 14 μg/g. The variation of concentration of metals in sediment between the sites was not significant. The mean concentration of metals in seagrass species tissues ranged from 3.9 to 26.25 μg/g for Lead, 0.1 to 0.90 μg/g for Cadmium, 0.38 to 5.96 μg/g for Nickel and 0.15 to 0.495 μg/g for Chromium. The differences of concentration of heavy metals in seagrass tissues among the sites were significant for Lead and not significant for Cadmium;Nickel and Chromium.展开更多
The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qu...The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Frechet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-Kuhn- Tucker （KKT） conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP.展开更多
This paper is devoted to investigating the weighted LP-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish th...This paper is devoted to investigating the weighted LP-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type （p, p） estimates for 1 〈 p 〈 ∞ and the weighted weak type （1, 1） estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain HSrmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini＇s conditions as model examples. Meanwhile, we also obtain the weighted LP-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO（Rd）-functions.展开更多
This paper mainly designs artificial boundary conditions for 'vortex in cell' method in solving two-dimensional incompressible inviscid fluid under two conditions: one is with periodical initial value in one d...This paper mainly designs artificial boundary conditions for 'vortex in cell' method in solving two-dimensional incompressible inviscid fluid under two conditions: one is with periodical initial value in one direction and the other with compact supported initial value. To mimic the vortex motion, Euler equation is transformed into vorticity-stream function and the technique of vortex in cell is applied incorporating with the artificial boundary conditions.展开更多
文摘In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.
基金supported from the National Key Basic Research and Development Projectof China(2009CB421505)the National Natural Sciences Foundation of China(40775031)the Project(No.2008LASW-A01)
文摘Precipitation and associated cloud hydrometeors have large temporal and spatial variability, which makes accurate quantitative precipitation forecasting difficult. Thus, dependence of accurate precipitation and associated cloud simulation on temporal and spatial scales becomes an important issue. We report a cloud- resolving modeling analysis on this issue by comparing the control experiment with experiments perturbed by initial temperature, water vapor, and cloud conditions. The simulation is considered to be accurate only if the root-mean-squared difference between the perturbation experiments and the control experiment is smaller than the standard deviation. The analysis may suggest that accurate precipitation and cloud simulations cannot be obtained on both fine temporal and spatial scales simultaneously, which limits quanti- tative precipitation forecasting. The accurate simulation of water vapor convergence could lead to accurate precipitation and cloud simulations on daily time scales, but it may not be beneficial to precipitation and cloud simulations on hourly time scales due to the dominance of cloud processes.
基金partially supported by the NSFC(11631011,11626251)
文摘Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
文摘The study investigated the concentration of Lead, Cadmium, Nickels and Chromium in sediment and seagrass tissues at six selected sites along the Sudanese Red Sea coast. The findings of the study added some important and necessary information about the status and condition of the coastal environment in the Sudanese Red Sea coast in terms of the extent of pollution with heavy metals. The study sites included: Marsa Bashayer, Marsa Dama Dama, Green Area, Shipyard, Marsa Halout and Dungonab Bay. The Atomic Absorption Spectrophotometer was used to measure Lead, Cadmium and Nickels. The colorimetric detection method was used for Chromium using the Spectrophotometer. Marsa Dama Dama site revealed high levels concentration of heavy metals in sediment for Lead (60.5) μg/g, Cadmium (0.22) μg/g and Chromium (146.65) μg/g. Marsa Halout showed the highest mean concentration of Nickel in sediment at 14 μg/g. The variation of concentration of metals in sediment between the sites was not significant. The mean concentration of metals in seagrass species tissues ranged from 3.9 to 26.25 μg/g for Lead, 0.1 to 0.90 μg/g for Cadmium, 0.38 to 5.96 μg/g for Nickel and 0.15 to 0.495 μg/g for Chromium. The differences of concentration of heavy metals in seagrass tissues among the sites were significant for Lead and not significant for Cadmium;Nickel and Chromium.
基金supported by National Natural Science Foundation of China(Grant No.11431002)Shandong Province Natural Science Foundation(Grant No.ZR2016AM07)
文摘The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Frechet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-Kuhn- Tucker （KKT） conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP.
基金Supported by the NNSF of China(Grant Nos.11371295 and 11471041)the NSF of Fujian Province of China(Grant No.2015J01025)Foundation for Doctors of Yili Normal College(Grant No.2017YSBS09)
文摘This paper is devoted to investigating the weighted LP-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type （p, p） estimates for 1 〈 p 〈 ∞ and the weighted weak type （1, 1） estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain HSrmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini＇s conditions as model examples. Meanwhile, we also obtain the weighted LP-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO（Rd）-functions.
基金This work is supported by the Special Funds for Major State Basic Research Projects.
文摘This paper mainly designs artificial boundary conditions for 'vortex in cell' method in solving two-dimensional incompressible inviscid fluid under two conditions: one is with periodical initial value in one direction and the other with compact supported initial value. To mimic the vortex motion, Euler equation is transformed into vorticity-stream function and the technique of vortex in cell is applied incorporating with the artificial boundary conditions.
