The present study had the objectives to apply the splitting technique in feed pellet quality prediction models and validate these models through Herzberg equation.The independent factors(input data)were the particle s...The present study had the objectives to apply the splitting technique in feed pellet quality prediction models and validate these models through Herzberg equation.The independent factors(input data)were the particle size(PS:coarse and medium),heat treatment(HT:expanded-pelleted and pelleted),fat addition levels(FA:15,25,35 and 45 g/kg of feed)and moisture addition levels(MA:0,7,14 and 21 g/kg of feed)which were combined in a full factorial design(2×2×4×4),resulting in 64 different treatments with eight replicates each.The intact pellets amount and pellet durability index(PDI)were considered as the model’s output data.In the splitting technique the whole data set,composed by 512 observations,were splitted in two data set:(1)model construction set(75%of the total data)and(2)model validation set(25%of the total data set,which were selected randomly from the original data set).Both equations,the one obtained by splitting method and the one obtained by whole data set,had good coefficient of determination and similar residues square means.It was concluded that splitting technique can be successfully applied to fit a prediction equation for feed pelleting process and that Herzberg equation consists in a useful tool to validate the coefficient of determination of those models.展开更多
An error correction technique to achieve a 14-bit successive approximation register analog-to-digital converter(SAR ADC) is proposed. A tunable split capacitor is designed to eliminate the mismatches caused by parasit...An error correction technique to achieve a 14-bit successive approximation register analog-to-digital converter(SAR ADC) is proposed. A tunable split capacitor is designed to eliminate the mismatches caused by parasitic capacitors. The linearity error of capacitor array caused by process mismatch is calibrated by a novel calibration capacitor array that can improve the sampling rate. The dual-comparator topology ensures both the speed and precision of the ADC. The simulation results show that the SAR ADC after calibration achieves 83.07 dB SNDR and 13.5 bit ENOB at 500 kilosamples/s.展开更多
Satellite retrieval of atmospheric water vapor is intended to further understand the role played by the energy and water cycle to determine the Earth's weather and climate.The algorithm for operational retrieval o...Satellite retrieval of atmospheric water vapor is intended to further understand the role played by the energy and water cycle to determine the Earth's weather and climate.The algorithm for operational retrieval of total precipitable water (TPW) from the visible and infrared radiometer (VIRR) onboard Fengyun 3A (FY-3A) employs a split window technique for clear sky radiances over land and oceans during both day and night.The retrieved TPW is compared with that from the moderate resolution imaging spectroradiometer (MODIS) onboard the Terra satellite and data from radiosonde observations (RAOB).During the study period,comparisons show that the FY-3A TPW is in general agreement with the gradients and distributions from the Terra TPW.Their zonal mean difference over East Asia is smaller in the daytime than at night,and the main difference occurs in the complex terrain at mid latitude near 30°N.Compared with RAOB,the zonal FY-3A and the Terra TPW have a moist bias at low latitudes and a dry bias at mid and high latitudes;in addition,the FY-3A TPW performs slightly better in zonal mean biases and the diurnal cycle.The temporal variation of the FY-3A and the Terra TPW generally fits the RAOB TPW with the FY-3A more accurate at night while Terra TPW more accurate during the daytime.Comparisons of correlations,root mean square differences and standard deviations indicate that the FY-3A TPW series is more consistent with the RAOB TPW at selected stations.As a result,the FY-3A TPW has some advantages over East Asia in both spatial and temporal dimensions.展开更多
In this paper,we study mainly the long-time behavior of the stochastic plate equations of kirchhoff type with nonlinear damping on unbounded domains.Due to the lack of compactness of Sobolev embeddings on unbounded do...In this paper,we study mainly the long-time behavior of the stochastic plate equations of kirchhoff type with nonlinear damping on unbounded domains.Due to the lack of compactness of Sobolev embeddings on unbounded domains,pullback asymptotic compactness of cocycle associated with the system is proved by the tailestimates method and splitting technique.展开更多
This paper presents three regularized models for the logarithmic Klein-Gordon equation.By using a modified Crank-Nicolson method in time and the Galerkin finite element method(FEM)in space,a fully implicit energy-cons...This paper presents three regularized models for the logarithmic Klein-Gordon equation.By using a modified Crank-Nicolson method in time and the Galerkin finite element method(FEM)in space,a fully implicit energy-conservative numerical scheme is constructed for the local energy regularized model that is regarded as the best one among the three regularized models.Then,the cut-off function technique and the time-space error splitting technique are innovatively combined to rigorously analyze the unconditionally optimal and high-accuracy convergence results of the numerical scheme without any coupling condition between the temporal step size and the spatial mesh width.The theoretical framework is uniform for the other two regularized models.Finally,numerical experiments are provided to verify our theoretical results.The analytical techniques in this work are not limited in the FEM,and can be directly extended into other numerical methods.More importantly,this work closes the gap for the unconditional error/stability analysis of the numerical methods for the logarithmic systems in higher dimensional spaces.展开更多
This study proposes a novel approach that involves applying the flux vector splitting(FVS)technique to discretize and approximate conservative Navier-Stokes equations and thus reconstruct pressure fields from planar v...This study proposes a novel approach that involves applying the flux vector splitting(FVS)technique to discretize and approximate conservative Navier-Stokes equations and thus reconstruct pressure fields from planar velocimetry data in compressible flows,especially for supersonic flows with strong shocks.Data are typically resolved by using the particle image velocimetry(PIV)technique.Two supersonic experiments under Mach 2.9-3.0 conditions were conducted to generate strong shocks and investigate the performance of the FVS method,including oblique shock flow and shock wave/boundary layer interaction(SWBLI)coupled with flow separation.Reconstructed pressure fields were comprehensively evaluated.The shock polar results indicated that FVS method possessed higher accuracy in post-shock regions with a pressure ratio error of less than2%,especially for the areas downstream of the shock-shock intersection point and the shock-boundary intersection point,where the conventional Poisson method was ineffective and larger errors accumulated.Wall pressure in SWBLI flow also had better agreement.Furthermore,the performances of different methods were discussed from the perspective of the physical characteristics in supersonic flows,which explained the superiority of the FVS method because the pressure information was delivered along the characteristic direction of physical waves.展开更多
This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant wi...This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint （ND-case）. Based on the dual method, it can be translated into the case vanishing at left endpoint （DN-case）. Secondly, the condition is the case that the sequences vanish at two endpoints （DD-case）. The third type of condition is the generality of the mean zero condition （NN-case）, which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.展开更多
This paper studies the Hardy-type inequalities on the intervals （may be infinite） with two weights, either vaaishing at two endpoiats of the interval or having mean zero. For the first type of inequalities, in terms...This paper studies the Hardy-type inequalities on the intervals （may be infinite） with two weights, either vaaishing at two endpoiats of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric constants, the factor of upper and lower bounds becomes smaller than the known ones. The second type of the inequalities is motivated from probability theory and is new ia the analytic context. The proofs are now rather elementary. Similar improvements are made for Nash inequality, Sobolev-type inequality, and the logarithmic Sobolev inequality on the intervals.展开更多
We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future probl...We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future problem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied. The main hypotheses are the existence of global solutions of the equations and some growth control of the Fourier transform of the solutions. We establish the optimal rates of decay of the solutions for initial data in different spaces. The main ingredients and technical tools are the Fourier splitting method, the iteration skill and the energy estimates.展开更多
In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is prop...In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is proposed.By the error split technique,the Stokes operator and the H^(-1)-norm estimate,unconditional optimal error estimates for the velocity in the norms L^(∞)(L^(2)) and L^(∞)(H^(1)),and the pressure in the norm L^(∞)(L^(2))are deduced.Finally,two numerical examples are provided to confirm the theoretical analysis.展开更多
In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with varia...In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with variable coefficients in quantum mechanics.The two methods can preserve the intrinsic properties of original problems as much as possible.The splitting technique increases the computational efficiency.Meanwhile,the error estimation and some conservative properties are investigated.It is proved to preserve the charge conservation exactly.The global energy and momentum conservation laws can be preserved under several conditions.Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.展开更多
文摘The present study had the objectives to apply the splitting technique in feed pellet quality prediction models and validate these models through Herzberg equation.The independent factors(input data)were the particle size(PS:coarse and medium),heat treatment(HT:expanded-pelleted and pelleted),fat addition levels(FA:15,25,35 and 45 g/kg of feed)and moisture addition levels(MA:0,7,14 and 21 g/kg of feed)which were combined in a full factorial design(2×2×4×4),resulting in 64 different treatments with eight replicates each.The intact pellets amount and pellet durability index(PDI)were considered as the model’s output data.In the splitting technique the whole data set,composed by 512 observations,were splitted in two data set:(1)model construction set(75%of the total data)and(2)model validation set(25%of the total data set,which were selected randomly from the original data set).Both equations,the one obtained by splitting method and the one obtained by whole data set,had good coefficient of determination and similar residues square means.It was concluded that splitting technique can be successfully applied to fit a prediction equation for feed pelleting process and that Herzberg equation consists in a useful tool to validate the coefficient of determination of those models.
基金Supported by National Science and Technology Major Project of China(No.2012ZX03004008)
文摘An error correction technique to achieve a 14-bit successive approximation register analog-to-digital converter(SAR ADC) is proposed. A tunable split capacitor is designed to eliminate the mismatches caused by parasitic capacitors. The linearity error of capacitor array caused by process mismatch is calibrated by a novel calibration capacitor array that can improve the sampling rate. The dual-comparator topology ensures both the speed and precision of the ADC. The simulation results show that the SAR ADC after calibration achieves 83.07 dB SNDR and 13.5 bit ENOB at 500 kilosamples/s.
基金supported by the National High Technology Research and Development Program of China(Grant No. 2007AA12Z144)the Professional Projects (Grant Nos.GYHY200706005 and GYHY200906036)the China Meteoro-logical Administration New Technology Promotion Project (GrantNo. CMATG2008Z04)
文摘Satellite retrieval of atmospheric water vapor is intended to further understand the role played by the energy and water cycle to determine the Earth's weather and climate.The algorithm for operational retrieval of total precipitable water (TPW) from the visible and infrared radiometer (VIRR) onboard Fengyun 3A (FY-3A) employs a split window technique for clear sky radiances over land and oceans during both day and night.The retrieved TPW is compared with that from the moderate resolution imaging spectroradiometer (MODIS) onboard the Terra satellite and data from radiosonde observations (RAOB).During the study period,comparisons show that the FY-3A TPW is in general agreement with the gradients and distributions from the Terra TPW.Their zonal mean difference over East Asia is smaller in the daytime than at night,and the main difference occurs in the complex terrain at mid latitude near 30°N.Compared with RAOB,the zonal FY-3A and the Terra TPW have a moist bias at low latitudes and a dry bias at mid and high latitudes;in addition,the FY-3A TPW performs slightly better in zonal mean biases and the diurnal cycle.The temporal variation of the FY-3A and the Terra TPW generally fits the RAOB TPW with the FY-3A more accurate at night while Terra TPW more accurate during the daytime.Comparisons of correlations,root mean square differences and standard deviations indicate that the FY-3A TPW series is more consistent with the RAOB TPW at selected stations.As a result,the FY-3A TPW has some advantages over East Asia in both spatial and temporal dimensions.
文摘In this paper,we study mainly the long-time behavior of the stochastic plate equations of kirchhoff type with nonlinear damping on unbounded domains.Due to the lack of compactness of Sobolev embeddings on unbounded domains,pullback asymptotic compactness of cocycle associated with the system is proved by the tailestimates method and splitting technique.
基金supported by the China Postdoctoral Science Foundation(Grant No.2023T160589)by the Cultivation Foundation of Zhengzhou University(Grant No.JC23153003)+4 种基金by the National Natural Science Foundation of China(Grant Nos.11801527,11971416)by the Natural Science Foundation of Henan Province(Grant No.222300420256)by the Training Plan of Young Backbone Teachers in Colleges of Henan Province(Grant No.2020GGJS230)by the Program for Innovative Research Team(in Science and Technology)in University of Henan Province(Grant No.23IRTSTHN018)by the Academic Degrees&Graduate Education Reform Project of Henan Province(Grant No.2021SJGLX224Y).
文摘This paper presents three regularized models for the logarithmic Klein-Gordon equation.By using a modified Crank-Nicolson method in time and the Galerkin finite element method(FEM)in space,a fully implicit energy-conservative numerical scheme is constructed for the local energy regularized model that is regarded as the best one among the three regularized models.Then,the cut-off function technique and the time-space error splitting technique are innovatively combined to rigorously analyze the unconditionally optimal and high-accuracy convergence results of the numerical scheme without any coupling condition between the temporal step size and the spatial mesh width.The theoretical framework is uniform for the other two regularized models.Finally,numerical experiments are provided to verify our theoretical results.The analytical techniques in this work are not limited in the FEM,and can be directly extended into other numerical methods.More importantly,this work closes the gap for the unconditional error/stability analysis of the numerical methods for the logarithmic systems in higher dimensional spaces.
基金supported by the National Natural Science Foundation of China(Grant No.12332018)。
文摘This study proposes a novel approach that involves applying the flux vector splitting(FVS)technique to discretize and approximate conservative Navier-Stokes equations and thus reconstruct pressure fields from planar velocimetry data in compressible flows,especially for supersonic flows with strong shocks.Data are typically resolved by using the particle image velocimetry(PIV)technique.Two supersonic experiments under Mach 2.9-3.0 conditions were conducted to generate strong shocks and investigate the performance of the FVS method,including oblique shock flow and shock wave/boundary layer interaction(SWBLI)coupled with flow separation.Reconstructed pressure fields were comprehensively evaluated.The shock polar results indicated that FVS method possessed higher accuracy in post-shock regions with a pressure ratio error of less than2%,especially for the areas downstream of the shock-shock intersection point and the shock-boundary intersection point,where the conventional Poisson method was ineffective and larger errors accumulated.Wall pressure in SWBLI flow also had better agreement.Furthermore,the performances of different methods were discussed from the perspective of the physical characteristics in supersonic flows,which explained the superiority of the FVS method because the pressure information was delivered along the characteristic direction of physical waves.
基金Supported by NSFC(Grant No.11131003)the “985” project from the Ministry of Education in China
文摘This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint （ND-case）. Based on the dual method, it can be translated into the case vanishing at left endpoint （DN-case）. Secondly, the condition is the case that the sequences vanish at two endpoints （DD-case）. The third type of condition is the generality of the mean zero condition （NN-case）, which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.
基金Supported by NSFC(GrantNo.11131003)the"985"project from the Ministry of Education in China
文摘This paper studies the Hardy-type inequalities on the intervals （may be infinite） with two weights, either vaaishing at two endpoiats of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric constants, the factor of upper and lower bounds becomes smaller than the known ones. The second type of the inequalities is motivated from probability theory and is new ia the analytic context. The proofs are now rather elementary. Similar improvements are made for Nash inequality, Sobolev-type inequality, and the logarithmic Sobolev inequality on the intervals.
文摘We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future problem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied. The main hypotheses are the existence of global solutions of the equations and some growth control of the Fourier transform of the solutions. We establish the optimal rates of decay of the solutions for initial data in different spaces. The main ingredients and technical tools are the Fourier splitting method, the iteration skill and the energy estimates.
基金supported by Fundamental Research Funds for the Henan Provincial Colleges and Universities(No.20A110002).
文摘In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is proposed.By the error split technique,the Stokes operator and the H^(-1)-norm estimate,unconditional optimal error estimates for the velocity in the norms L^(∞)(L^(2)) and L^(∞)(H^(1)),and the pressure in the norm L^(∞)(L^(2))are deduced.Finally,two numerical examples are provided to confirm the theoretical analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.91130013,10971226,and 11001270)Hunan Provincial Innovation Foundation(Grant Nos.CX2011B011,and CX2012B010)+1 种基金the Innovation Fund of NUDT(Grant No.B120205)Chinese Scholarship Council.
文摘In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with variable coefficients in quantum mechanics.The two methods can preserve the intrinsic properties of original problems as much as possible.The splitting technique increases the computational efficiency.Meanwhile,the error estimation and some conservative properties are investigated.It is proved to preserve the charge conservation exactly.The global energy and momentum conservation laws can be preserved under several conditions.Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.
