An inverse problem of the flux for minimal surfaces

For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here, an n-end catenoid is a complete minimal surface of genus 0 with ends asymptotic to the catenoids. In this paper, the problem is reduced to solving algebraic equation. Using this reduction, it is shown that, when n=4, the inverse problem for 4-end catenoid has solutions for almost all balanced 4 vectors. Further obstructions for n-end catenoids with parallel flux vectors are also discussed.Comment: 28 pages, AMSLaTeX 1.1, with 8 figures, To appear in Indiana University Mathematics Journa

A protocol for genetic analysis at different stages of the nuclear division cycle in Neurospora crassa

The filamentous fungus Neurospora crassa is an organism that contains multiple nuclei in the asexual conidia and hyphae. Since the nuclei of dormant conidia are arrested at various points in the nuclear division cycle, it has been difficult to analyze drug sensitivity at the specific point of the cycle in N. crassa. In this study, we have established a useful method for analysis at different stages of the nuclear division cycle in N. crassa. This assay will be a reference for researchers to use the synchronized culture in other diverse analyses

Modeling photometric variations due to a global inhomogeneity on an obliquely rotating star: application to lightcurves of white dwarfs

We develop a general framework to compute photometric variations induced by the oblique rotation of a star with an axisymmetric inhomogeneous surface. We apply the framework to compute lightcurves of white dwarfs adopting two simple models of their surface inhomogeneity. Depending on the surface model and the location of the observer, the resulting lightcurve exhibits a departure from a purely sinusoidal curve that are observed for a fraction of white dwarfs. As a specific example, we fit our model to the observed phase-folded lightcurve of a fast-spinning white dwarf ZTF J190132.9+145808.7 (with the rotation period of 419s). We find that the size and obliquity angle of the spot responsible for the photometric variation are \dts \approx 60^\circ and \thetaS \approx 60^\circ or $90^\circ$, respectively, implying an interesting constraint on the surface distribution of the magnetic field on white dwarfs.Comment: 25 pages, 9 figures, accepted for publication in PAS