Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such curves over k have the same zeta function (i.e., the same number of points over all extensions of k) if and only if their corresponding Jacobi...

The number of pedestrians walking the streets or gathered in public spaces is a valuable piece of information for shop owners, city governments, event organizers and many others. However, automatic counting that takes place day and night is challenging due to changing lighting conditions and the complexity of scenes with many people occluding one another. To address these challenges, this paper...

for the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. when the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. in this paper we will consider the polynomial planar vector fields ...

In a point-of-care (POC) setting, it is critically important to reliably count the number of specific cells in a blood sample. Software-based cell counting, which is far faster than manual counting, while much cheaper than hardware-based counting, has emerged as an attractive solution potentially applicable to mobile POC testing. However, the existing software-based algorithm based on the norma...