Digital Self-Calibration Technique Based on 14-Bit SAR ADC

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.

Evaluation of Total Precipitable Water over East Asia from FY-3A/VIRR Infrared Radiances

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.

Discrete Weighted Hardy Inequalities with Different Kinds of Boundary Conditions

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.

Bilateral Hardy-type Inequalities

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.

Dissipation and Decay Estimates

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.

Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping

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.

Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time

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.