Assessment of tomographic window and sampling rate efects on GNSS water vapor tomography

The ground-based Global Navigation Satellite System(GNSS)water vapor tomography is increasingly important in GNSS meteorology.As the multi-GNSS and more ground-based GNSS sites can be incorporated into the regional water vapor tomographic model,determining the tomographic window and sampling rate is crucial for the modelling of the water vapor tomography.These two factors afect not only the number of available signal rays from the satellites,but also the number of tomographic voxels crossed by the signal rays.This study uses Hong Kong as the research area to explore the impact of 12 schemes with diferent tomographic window and sampling rate on the three water vapor tomography methods,including Least squares,Kalman fltering,and Multiplicative Algebraic Reconstruction Technique(MART).Numerical results show that the tomographic results with the three methods get better as the width of the tomographic window decreases and the sampling rate increases in these 12 schemes,and it is found that the Least squares method is most afected by the two factors,followed by Kalman fltering and MART methods.It is recommended to set a tomographic window width of 10 min and a sampling rate of 300 s in a GNSS water vapor tomographic experiment with dense GNSS site like Hong Kong.

The Least Eigenvalue of Unicyclic Graphs with Application to Spectral Spread

Let U^(g)_(n)be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),…,T_(g))∈U^(g)_(n)be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in an anticlockwise direction)by identifying v_(i)with the root of a rooted tree T_(i)of order n_(i)for each i=1,2,…,g,where n_(i)≥1 and∑^(g)_(i=1)n_(i)=n.In this note,the graph with the minimal least eigenvalue(and the graph with maximal spread)in C(T_(1),T_(2),…,T_(g))is determined.

Development and evaluation of the refined zenith tropospheric delay(ZTD)models

The tropospheric delay is a significant error source in Global Navigation Satellite System(GNSS)positioning and navigation.It is usually projected into zenith direction by using a mapping function.It is particularly important to establish a model that can provide stable and accurate Zenith Tropospheric Delay(ZTD).Because of the regional accuracy difference and poor stability of the traditional ZTD models,this paper proposed two methods to refine the Hopfield and Saastamoinen ZTD models.One is by adding annual and semi-annual periodic terms and the other is based on Back-Propagation Artificial Neutral Network(BP-ANN).Using 5-year data from 2011 to 2015 collected at 67 GNSS reference stations in China and its surrounding regions,the four refined models were constructed.The tropospheric products at these GNSS stations were derived from the site-wise Vienna Mapping Function 1(VMP1).The spatial analysis,temporal analysis,and residual distribution analysis for all the six models were conducted using the data from 2016 to 2017.The results show that the refined models can effectively improve the accuracy compared with the traditional models.For the Hopfield model,the improvement for the Root Mean Square Error(RMSE)and bias reached 24.5/49.7 and 34.0/52.8 mm,respectively.These values became 8.8/26.7 and 14.7/28.8 mm when the Saastamoinen model was refined using the two methods.This exploration is conducive to GNSS navigation and positioning and GNSS meteorology by providing more accurate tropospheric prior information.

Distance signless Laplacian eigenvalues of graphs

Suppose that the vertex set of a graph G is V(G) ={v1,v2,...,vn}.The transmission Tr(vi) (or Di) of vertex vi is defined to be the sum of distances from vi to all other vertices.Let Tr(G) be the n × n diagonal matrix with its (i,i)-entry equal to TrG(vi).The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G,defined as L(G) =Tr(G) + D(G),where D(G) is the distance matrix of G.In this paper,we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible.We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs.Moreover,we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees,and characterize extremal graphs.

Minimal least eigenvalue of connected graphs of order n and size m=n+k(5≤k≤8)

The least eigenvalue of a connected graph is the least eigenvalue of its adjacency matrix.We characterize the connected graphs of order n and size n+k(5≤k≤8 and n≥k+5)with the minimal least eigenvalue.