THE PARALLEL MULTISPLITTING METHOD FOR CONSISTENT SYMMETRIC POSITIVE(SEMI-)DEFINITE SYSTEMS

Main resultsTheorem 1 Let A be an n×n symmetric positive semidefinite matrix and let

Estimation of Aqueous Solubility (-lgS_w) of All Polychlorinated Biphenyl (PCB) Congeners by Density Functional Theory and Position of Cl Substitution (NPCS) Method

Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some structural parameters. Consequently, Cl substitution positions were taken as theoretical descriptors to establish a novel QSPR model for predicting –lgSw of all PCB congeners. The model achieved in this work contains four variables, of which r^2 = 0.9527, q^2 = 0.9490 and SD = 0.25 with large t values. In addition, the variation inflation factors （VIFs） of variables in this model are all less than 5.0, suggesting high accuracy of the –lgSw predicting model. And the results of cross-validation test and method validation also show that the model exhibits optimum stability and better predictive capability than that from the AM1 method.

DFT and Position of Cl Substitution (PCS) Methods Studies on n-Octanol/water Partition Coefficients (lgK_(ow)) and Aqueous Solubility (–lgS_w) of All PCDD Congeners

Optimized calculations of 75 PCDDs and their parent DD were carded out at the B3LYP/6-31G＊ level by density functional theory （DFT） method. The structural parameters were obtained and significant correlation between the C1 substitution position and some structural parameters was found. Consequently, the number of C1 substitution positions was taken as theoretical descriptors to establish two novel QSPR models for predicting lgKow and -lgSw of all PCDD congeners. The two models achieved in this work contain two variables （Na and Nβ）, of which r = 0.9312, 0.9965 and SD = 0.27, 0.12 respectively, and t values are all large. The variation inflation factors （VIF） of variables in the two models herein are both less than 5.0, suggesting high accuracy of the lgKow and -lgSw predicting models, and the results of cross-validation test also show that the two models exhibit optimum stability and good predictive power. By comparison, the correlation and predictive ability of the present work are more advantageous than those obtained using semi-empirical AM1 and GC-RI methods.

A new modification of false position method based on homotopy analysis method

A new modification of false position method for solving nonlinear equations is presented by applying homotopy analysis method （HAM）. Some numerical illustrations are given to show the efficiency of algorithm.

A rigorous real-time acoustic positioning method for ocean bottom seismic exploration

The conventional technique for positioning seafloor geophones in ocean bottom seismic exploration encounters several challenges,including the significant impact of outliers on positioning results,underutilization of high-precision observations,and low efficiency in real-time data processing.These issues inevitably affect the quality of seismic exploration outcomes.To address these challenges and enhance the accuracy of geophone positioning,this paper proposes a rigorous real-time acoustic positioning method for geophones based on sequential adjustment and Baarda's outlier detection approach.The proposed method comprises three key steps:grouping the original acoustic observations,constructing the intra-group acoustic positioning model,and synthesizing the positioning results across the different groups.The validity and practicality of this approach are confirmed through a simulation experiment as well as the field experiment conducted in the Bohai Sea,China.The results demonstrate that the proposed method effectively eliminates outliers in the original observations and maximizes the utilization of high-quality observations.Compared to traditional acoustic positioning methods,it significantly reduces positioning errors from meters to decimeters,and in some cases can achieve centimeter-level precision.When the sound velocity profile in the operating sea area is measured,the method can attain the posterior standard deviation at the millimeter level and positioning errors within 10 cm.When the sound velocity profile is unknown,the method can achieve the posterior standard deviation at centimeter-level and positioning errors of approximately 20 cm.

Superconvergence Analysis of Splitting Positive Definite Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equations

In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.

DFT Study on the Thermodynamic Properties of Poly-bromine Carbazole

The molecular structures of 135 poly-bromine carbazole （PBCZs） compounds were fully optimized at the B3LYP/6-31G＊ level, and their thermodynamic properties at 98.15 K, 1.013 ×105 Pa were consequently obtained. Based on our isodesmic reaction, standard formation heat （ΔfHθ） and standard formation free energy （ΔfGθ） of PBCZs were calculated. Furthermore, the relationship between thermodynamic parameters and the position and number （NPBS） of Brsubstitution were also discussed. To our interest, a good dependence can be observed among entro- py （Sθ）, ΔfHθ, ΔfGθ and NPBS. Ultimately, the theoretical stability order of isomers can be decided judging from the ΔfGθ value.

An improved method of angle measurement with a position sensitive detector

An improved method of angle measurement is proposed based on a parallel plate interferometer. A position detection system is incorporated into a parallel plate interferometer in order to realize large deflection angle measurement. A reflecting mirror is introduced for increasing the measurement resolution. In experiments, a deflection angle of a measured target was measured within ～3° with high accuracy. And as a phase modulating interferometer, it was used to measure a small angular displacement with a repeatability of 5.5 × 10^-8 rad.

Position optimization of particular solution sources for distributed source boundary point method by volume velocity-matching

Choosing particular solution source and its position have great influence on accu- racy of sound field prediction in distributed source boundary point method. An optimization method for determining the position of particular solution sources is proposed to get high accu- racy prediction result. In this method, tripole is chosen as the particular solution. The upper limit frequency of calculation is predicted by setting 1% volume velocity relative error limit using vibration velocity of structure surface. Then, the optimal position of particular solution sources, in which the relative error of volume velocity is minimum, is determined within the range of upper limit frequency by searching algorithm using volume velocity matching. The transfer matrix between pressure and surface volume velocity is constructed in the optimal position. After that, the sound radiation of structure is calculated by the matrix. The results of numerical simulation show that the calculation error is significantly reduced by the proposed method. When there are vibration velocity measurement errors, the calculation errors can be controlled within 5% by the method.

Review of rigid fruit and vegetable picking robots

The important indicators to measure the goodness of rigid fruit and vegetable picking robot have two aspects,the first is the reasonable structural design of the end-effector,and the second is having a high precision positioning recognition method.Many researchers have done a lot of work in these two aspects,and a variety of end-effector structures and advanced position recognition methods are constantly appearing in people’s view.The working principle,structural characteristics,advantages and disadvantages of each end-effector are summarized to help us design better fruit and vegetable picking robot.The authors start from the rigid fruit and vegetable picking robot grasping methods,separation methods,and position recognition methods,firstly introduce three different grasping methods and the characteristics of the two separation methods,then introduce the under-driven picking robot developed on the basis of the traditional rigid picking robot,then explain the single special,multi-feature,and deep learning location position recognition methods currently used,and finally make a summary and outlook on the rigid fruit and vegetable picking robot from the structural development and position recognition methods.

Vlasov-Fokker-Planck Simulations for High-Power Laser-Plasma Interactions

A review is presented on our recent Vlasov-Fokker-Planck(VFP)simulation code development and applications for high-power laser-plasma interactions.Numerical schemes are described for solving the kinetic VFP equation with both electronelectron and electron-ion collisions in one-spatial and two-velocity(1D2V)coordinates.They are based on the positive and flux conservation method and the finite volume method,and these twomethods can insure the particle number conservation.Our simulation code can deal with problems in high-power laser/beam-plasma interactions,where highly non-Maxwellian electron distribution functions usually develop and the widely-used perturbation theories with the weak anisotropy assumption of the electron distribution function are no longer in point.We present some new results on three typical problems:firstly the plasma current generation in strong direct current electric fields beyond Spitzer-H¨arm’s transport theory,secondly the inverse bremsstrahlung absorption at high laser intensity beyond Langdon’s theory,and thirdly the heat transport with steep temperature and/or density gradients in laser-produced plasma.Finally,numerical parameters,performance,the particle number conservation,and the energy conservation in these simulations are provided.