Extended supersymmetry and its reduction on a circle with point singularities

We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of singularities compatible with supersymmetry is clarified. In our formulation, the supersymmetry can be reduced to $M$-extended supersymmetry for any integer $M<N$. The degeneracy of the spectrum and spontaneous supersymmetry breaking are also studied.Comment: 36 pages, 5 figures, 2 table

Hierarchy of QM SUSYs on a Bounded Domain

We systematically formulate a hierarchy of isospectral Hamiltonians in one-dimensional supersymmetric quantum mechanics on an interval and on a circle, in which two successive Hamiltonians form N=2 supersymmetry. We find that boundary conditions compatible with supersymmetry are severely restricted. In the case of an interval, a hierarchy of, at most, three isospectral Hamiltonians is possible with unique boundary conditions, while in the case of a circle an infinite tower of isospectral Hamiltonians can be constructed with two-parameter family of boundary conditions.Comment: 15 pages, 3 figure

Coating and Density Distribution Analysis of Commercial Ciprofloxacin Hydrochloride Monohydrate Tablets by Terahertz Pulsed Spectroscopy and Imaging

Terahertz pulsed spectroscopy was used to qualitatively detect ciprofloxacin hydrochloride monohydrate (CPFX·HCl·H2O) in tablets, and terahertz pulsed imaging (TPI) was used to scrutinize not only the coating state but also the density distribution of tablets produced by several manufacturers. TPI was also used to evaluate distinguishability among these tablets. The same waveform, which is a unique terahertz absorption spectrum derived from pure CPFX·HCl·H2O, was observed in all of the crushed tablets and in pure CPFX·HCl·H2O. TPI can provide information about the physical states of coated tablets. Information about the uniformity of parameters such as a coating thickness and density can be obtained. In this study, the authors investigated the coating thickness distributions of film-coated CPFX·HCl·H2O from four different manufacturers. Unique terahertz images of the density distributions in these commercial tablets were obtained. Moreover, B-scan (depth) images show the status of the coating layer in each tablet and the density map inside the tablets. These features would reflect differences resulting from different tablet-manufacturing processes

Identification of the sex-determining factor in the liverwort Marchantia polymorpha reveals unique evolution of sex chromosomes in a haploid system

半数体生物の性染色体上の性決定遺伝子を解明 --コケがもつ現生生物最古の起源の性染色体--. 京都大学プレスリリース. 2021-11-08.Sex determination is a central process for sexual reproduction and is often regulated by a sex determinant encoded on a sex chromosome. Rules that govern the evolution of sex chromosomes via specialization and degeneration following the evolution of a sex determinant have been well studied in diploid organisms. However, distinct predictions apply to sex chromosomes in organisms where sex is determined in the haploid phase of the life cycle: both sex chromosomes, female U and male V, are expected to maintain their gene functions, even though both are non-recombining. This is in contrast to the X-Y (or Z-W) asymmetry and Y (W) chromosome degeneration in XY (ZW) systems of diploids. Here, we provide evidence that sex chromosomes diverged early during the evolution of haploid liverworts and identify the sex determinant on the Marchantia polymorpha U chromosome. This gene, Feminizer, encodes a member of the plant-specific BASIC PENTACYSTEINE transcription factor family. It triggers female differentiation via regulation of the autosomal sex-determining locus of FEMALE GAMETOPHYTE MYB and SUPPRESSOR OF FEMINIZATION. Phylogenetic analyses of Feminizer and other sex chromosome genes indicate dimorphic sex chromosomes had already been established 430 mya in the ancestral liverwort. Feminizer also plays a role in reproductive induction that is shared with its gametolog on the V chromosome, suggesting an ancestral function, distinct from sex determination, was retained by the gametologs. This implies ancestral functions can be preserved after the acquisition of a sex determination mechanism during the evolution of a dominant haploid sex chromosome system