转镜式傅里叶变换光谱仪光程差非线性的拟合法补偿

转镜式傅里叶变换光谱仪中光程差非线性带来了干涉图周期变化和相位误差,对非线性的拟合法补偿利用采样得到的干涉图进行重构,得到不含相位和周期误差的干涉图,再按照均匀采样函数对干涉图进行二次采样,消除非线性光程差对复原光谱的影响.经过二次采样的干涉图不含周期和相位误差,可以直接使用现有的软件进行光谱复原.计算机仿真实验证明这种方法行之有效,且利用4次多项式拟合干涉图效果更好.     

Very degenerate polynomial submersions and counterexamples to the real Jacobian conjecture

Until recently, the only known examples of non-injective polynomial local diffeomorphisms of the plane were the Pinchuk maps discovered in 1994. These maps have the form $(p,q)$, where p is a fixed polynomial of degree 10, and q satisfies certain relation. The lowest possible degree of q in a Pinchuk map is 25. In 2021, with the same p of a Pinchuk map, another example was given with q of degree 15. Aiming to find different examples, with the first components having lower degrees, we look for polynomials of degree less than or equal to 9 sharing some properties with the polynomial p of a Pinchuk map. We find precisely one polynomial of degree 7 and some ones of degree 9. By using one of the polynomials of degree 9 in the first component we construct a non-injective polynomial local diffeomorphism of the plane, with degree 15.