Establishment of European Regional Ionosphere Model Based on Spherical Harmonic Functions

In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.

Accurate estimation of Li/Ni mixing degree of lithium nickel oxide cathode materials

Li/Ni mixing negatively influences the discharge capacity of lithium nickel oxide and high-nickel ternary cathode materials.However,accurately measuring the Li/Ni mixing degree is difficult due to the preferred orientation of labbased XRD measurements using Bragg–Brentano geometry.Here,we find that employing spherical harmonics in Rietveld refinement to eliminate the preferred orientation can significantly decrease the measurement error of the Li/Ni mixing ratio.The Li/Ni mixing ratio obtained from Rietveld refinement with spherical harmonics shows a strong correlation with discharge capacity,which means the electrochemical capacity of lithium nickel oxide and high-nickel ternary cathode can be estimated by the Li/Ni mixing degree.Our findings provide a simple and accurate method to estimate the Li/Ni mixing degree,which is valuable to the structural analysis and screening of the synthesis conditions of lithium nickel oxide and high-nickel ternary cathode materials.

CLEBSCH-GORDAN COEFFICIENTS,SPHERICAL HARMONICS,AND d FUNCTIONS

Note： A square-root sign is to be understood over every coefficient, e.g., for -8/15 read - √8√15.

A Virtual Puncture Surgery System Based on Multi-Layer Soft Tissue and Force Mesh

Puncture is a common operation in surgery,which involves all kinds of tissue materials with different geometry and mechanical properties.As a new cross-disciplinary research area,Virtual Surgery(VS)makes simulation of soft tissue in puncture operation possible in virtual environment.In this paper,we introduce a VS-based puncture system composed by three-layer soft tissue,simulated with spherical harmonic function(SHF),which is covered with a force mesh,constructed by mass spring model(MSM).The two models are combined together with a parameter of SHF named surface radius,which provides MSM with real-time deformation data needed in force calculation.Meanwhile,force calculation,divided into the surface spring force and the puncture damping force,makes the force presentation better accord to the corresponding tissue characteristics.Moreover,a deformation resumption algorithm is leveraged to simulate the resumption phenomenon of the broken tissue surface.In evaluation experiment,several residents are invited to grades our model along with other four mainstream soft tissue models in terms of 7 different indicators.After the evaluation,the scores are analyzed by a comprehensive weighted grading method.Experiment results show that the proposed model has better performance during puncture operation than other models,and can well simulate surface resumption phenomenon when tissue surface is broken.

L^2 （R^n） boundedness for Calderon commutator with rough variable kernel

For b Е Lip（Rn）, the CalderSn commutator with variable kernel is defined by[b,T1]f（x）=p.v∫RnΩ（x,x-y）/｜x-y｜^n＋1（b（x））-b（y））f（y）dy In this paper, we establish the L2（Rn） boundedness for [b, T1] with Ω（x, z＇） ∈L∞（Rn）×Lq（Sn-1）（q〉2（n-1）/n）satisfying certain cancellation conditions.Moreover, the exponent q 〉2（n - 1）/n is optimal. Our main result improves a previous result of Calderon.

Boundedness of the Commutator of Marcinkiewicz Integral with Rough Variable Kernel

In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which is a substantial improvement and extension of some known results.