NEW TRIGONOMETRIC BASIS POSSESSING EXPONENTIAL SHAPE PARAMETERS

Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．

Modified Bases of PHT-Splines

Recently,it was found that during the process of certain refinement of hier-archical T-meshes,some basis functions of PHT-splines decay severely,which is not expected in solving numerical PDEs and in least square data fitting since the matrices assembled by these basis functions are likely to be ill-conditioned.In this paper,we present a method to modify the basis functions of PHT-splines in the case that the sup-ports of the original truncated basis functions are rectangular domains to overcome the decay problem.The modified basis functions preserve the same nice properties of the original PHT-spline basis functions such as partition of unity,local support,linear independency.Numerical examples show that the modified basis functions can greatly decrease the condition numbers of the stiffness matrices assembled in solving Poisson’s equation with Dirichlet boundary conditions.

Combining conservation tillage with nitrogen fertilization promotes maize straw decomposition by regulating soil microbial community and enzyme activities

Straw return can effectively improve farmland soil microenvironment and fertility.However,excessive straw in the topsoil adversely affects seed germination and crop growth.At present,the characteristics and key driving factors of straw decomposition in dry farmlands are unclear.Based on the interactions between tillage practices including zero tillage(ZT),chisel tillage(CT),and plow tillage(PT)and nitrogen(N)fertilization,i.e.,low N(N1,180 kg ha^(-1)),normal N(N2,240 kg ha^(-1)),and high N(N3,300 kg ha^(-1)),quantitative polymerase chain reaction technology and an enzymatic detection kit were used to investigate the effects of key straw C-degrading enzyme activities and microbial abundance in soil on maize straw decomposition during the growth period of winter wheat in the winter wheat/summer maize double cropping system in a dry farmland of the Loess Plateau,China.Between 2018 and 2020,ZT and CT significantly increased winter wheat yield(by 10.94%and 12.79%,respectively)and straw decomposition velocity(by 20%and 26.67%,respectively),compared with PT.Compared to N1 and N3,N2 significantly increased wheat yield(by 4.65%and 5.31%,respectively)and straw decomposition velocity(by 26.33%and 13.21%,respectively).The partial least squares pathway modelling showed significant positive direct effects of soil moisture,NO3-,NH4+,total N,bacteria,and cellulase,laccase,and xylanase activities on straw decomposition,while soil pH,fungi,and Actinomycetes had significant negative direct effects.Overall,conservation tillage(ZT and CT)combined with N2 was beneficial for straw decomposition in the drylands of the Loess Plateau and improved straw resource utilization and basic soil fertility.The results of the study clarified the key drivers of straw decomposition in dry farmlands and provided new ideas for developing updated soil management practices and adaptive N application strategies to promote the resource utilization of straw and achieve the goals of carbon peaking and carbon neutrality.