No abstract

Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be C2 continuous for a non-uniform knot vector. For a special value, the generated curves can be C(2n-1)  (n=1,2,3,…) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be C2 continuous for a nonuniform knot vector. When given a special value, the related surfaces can be C(2n-1)  (n=1,2,3,…) continuous for a uniform knot vector. A new class of trigonometric Bernstein–Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein–Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for G1 continuous jointing two DT BB-like patches over the triangular domain is deduced.

This special issue, “Internet Finance, Green Finance, and Sustainability”, is focused on the prosperous financial industry and the relationship between finance and sustainability. It especially gathers papers pertaining to the hot topic of internet finance and green finance in this field, as well as the manuscripts exploring the operating mechanism between finance and sustainability, both of which are closely linked to the hot spots and pressing demands of society. Therefore, this special issue is of particular valuable for both academic research and the development of society.

In recent years, men who have sex with men (MSM) constitute a major group of HIV transmission in China. High primary drug-resistance (PDR) rate in MSM also represents a serious challenge for the Chinese antiretroviral therapy (ART) program. To assess the efficiency of ART in controlling HIV/AIDS infection among MSM, we developed a compartmental model for the annually reported HIV/AIDS MSM from 2007 to 2019 in the Zhejiang Province of China. R 0 was 2.3946 (95% CI (2.2961-2.4881)). We predict that 90% of diagnosed HIV/AIDS individuals will have received treatment till 2020, while the proportion of the diagnosed remains as low as 40%. Even when the proportion of the diagnosed reaches 90%, R 0 is still larger than the level of AIDS epidemic elimination. ART can effectively control the spread of HIV, even in the presence of drug resistance. The 90-90-90 strategy alone may not eliminate the HIV epidemic in Chinese MSM. Behavioural and biologic interventions are the most effective interventions to control the HIV/AIDS epidemic among MSM.