We prove that there exists a positive α such that for any integer d ≥ 3 and any topological types S1, . . . , Sn of plane curve singularities, satisfying μ(S1) + · · ·+ μ(Sn) ≤ αd, there exists a reduced irreducible plane curve of degree d with exactly n singular points of types S1, . . . , Sn, respectively. This estimate is optimal with respect to the exponent of d. In particular, we prove tha...

The objectives were to estimate (co)variance components and genetic parameters for lactation curve traits in Holstein dairy cows in Iran. The used data were records on Holstein cows collected during January 2003 to December 2012 by the Animal Breeding Center of Iran (Karaj, Iran). In order to describe the lactation curve, an incomplete gamma function was fitted to 691200 test-day records on 962...

Recently, the first Abel map for a stable curve of genus g ≥ 2 has been constructed. Fix an integer d ≥ 1 and let C be a stable curve of compact type of genus g ≥ 2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-n...

In the theory of elliptic functions, there are two kinds of determinantal formulae of Frobenius-Stickelberger [6] and of Kiepert [7], both of which connect the function σ(u) with ℘(u) and its (higher) derivatives through an determinantal expression. These formulae were naturally generalized to hyperelliptic functions by the papers [11], [12], and [13]. Avoiding generality, we restrict the story...

In the theory of elliptic functions, there are two kinds of formulae of FrobeniusStickelberger [FS] and of Kiepert [K], both of which connect the function σ(u) with ℘(u) and its (higher) derivatives through determinants. These formulae are naturally generalized to hyperelliptic functions by the papers [Ô1], [Ô2], and [Ô3]. Avoiding an unneceessary generality, we restrict the story only for the ...

3-D curve moments and curve moment invariants under similarity transformation are defined in this paper. 3-D curve moment invariants can be used as shape descriptors for the representation of parametric curves. We use them to describe some commonly used parametric curves and test the invariance of them in the experiment.

It is proved that the diffeomorphism type of the minimal symplectic fillings of the link of a simple singularity is unique. In the proof, the uniqueness of the diffeomorphism type of CP 2 \D, where D is a pseudo holomorphic rational curve with one (2, 3)cusp, is discussed.