On generalized Frame-Stewart numbers

For the multi-peg Tower of Hanoi problem with $k \geqslant 4$ pegs, so far the best solution is obtained by the Stewart's algorithm based on the the following recurrence relation: $\mathrm{S}\_k(n)=\min\_{1 \leqslant t \leqslant n} \left\{2 \cdot \mathrm{S}\_k(n-t) + \mathrm{S}\_{k-1}(t)\right\}$, $\mathrm{S}\_3(n) = 2^n -- 1$. In this paper, we generalize this recurrence relation to $\mathrm{G}\_k(n) = \min\_{1\leqslant t\leqslant n}\left\{ p\_k\cdot \mathrm{G}\_k(n-t) + q\_k\cdot \mathrm{G}\_{k-1}(t) \right\}$, $\mathrm{G}\_3(n) = p\_3\cdot \mathrm{G}\_3(n-1) + q\_3$, for two sequences of arbitrary positive integers $\left(p\_i\right)\_{i \geqslant 3}$ and $\left(q\_i\right)\_{i \geqslant 3}$ and we show that the sequence of differences $\left(\mathrm{G}\_k(n)- \mathrm{G}\_k(n-1)\right)\_{n \geqslant 1}$ consists of numbers of the form $\left(\prod\_{i=3}^{k}q\_i\right) \cdot \left(\prod\_{i=3}^{k}{p\_i}^{\alpha\_i}\right)$, with $\alpha\_i\geqslant 0$ for all $i$, arranged in nondecreasing order. We also apply this result to analyze recurrence relations for the Tower of Hanoi problems on several graphs.Comment: 13 pages ; 3 figure

Geometric Visual Instruments Having Pinnate Forms

Abstract A visual instrument is an instrument that generates geometrically and aesthetically appealing temporal-spatial patterns if it is skillfully manipulated by a player. We present new types of geometric visual instruments having pinnate forms that are used by rolling one instrument along the other. We designed and fabricated the proposed visual instruments and confirmed that they can be manipulated skillfully and they provide a way to explore new types of manipulative play and performances

Effect of evaporation time on the pervaporation characteristics through homogeneous aromatic polyamide membranes. II. Pervaporation performances for ethanol/water mixture

Pervaporation of ethanol/water mixtures through symmetric dense aromatic polyamide membranes was investigated. The membrane structure was controlled by varying the solvent evaporation time before gelation. The membranes were water-selective and the selectivity increased with an increase in the solvent evaporation time. On the other hand, the water flux as well as the ethanol flux decreased with an increase in the evaporation time. These results were consistent with the morphology change of the membrane which takes place with solvent evaporation: the decrease in the channel size. The effects of the downstream pressure on the pervaporation performances were also studied for membranes with different solvent evaporation times. the ethanol concentration in the permeate side increased with an increase in the downstream pressure to certain point, showed a maximum there, then decreased thereafter. The water flux decreased with an increase in the downstream pressure for all membranes studied; the dependence was expressed by a parabolic curve in the lower pressure range. The ethanol flux also decreased with an increase in the downstream pressure for the membrane with shorter evaporation time, while this flux was slightly affected by the downstream pressure for the membrane with longer evaporation time.Peer reviewed: YesNRC publication: Ye

Study of teacher off-the-job-training at an attached junior high school: the development of mathematics teachers

広島県内の中学校数学教師の実践力向上を目指し，授業を中心に据えた現職教員研修システムの構築を目的として，広島県中学校数学教育実践研修会を開催している。今年度は，６月と12月に実施した実践研修会に向け， チーム会を６回実施した。本研究では， 中学校数学教師が実践力を向上させていく場面を特定するために，実践研修会やチーム会のエピソード分析を行った。その結果，「珍しい公開授業は参会者に刺激を与えられること」，「公開授業で参会者は授業者の“術”も見ていること」，「良い教材について議論する協議会は有益であること」の３点を明らかにすることができた。このような若手教員の実践力向上を目指した研修会はあまり行われておらず，貴重である。今後は，さらに効果的な研修システムを創造し，実現することにより本会の内容を充実させ， 広島県の学校教育に還元していきたい。The focus of this study was on the development of mathematics teachers via teacher off-the-job-training at an attached junior high school. In this paper, we analyzed the comments of mathematics teachers participating in teacher off-the-job-training．The followings outcomes were identified: a) Demonstration classes were conducted in a unique way, where participants observed two classes in which the the same unit was taught but in different ways. This was beneficial to participants. b) Participants in the demonstration class were able to carefully observe the behavior of the instructor. c) This method enabled participants to fully discuss the strengths of the teaching materials

Functional Analyses of MMPs for Aragonite Crystal Formation in the Ligament of Pinctada fucata

The mollusk class, Bivalvia, plays an important role in the formation of calcium carbonate in the ocean. The bivalve hinge ligament is a hard but pliant tissue that resists the stress placed on the hinge during opening and closing. The ligament comprises a fine microstructure of fibrous aragonite crystals surrounded by a dense organic matrix. The matrix consists of organic fibers that are aligned with the fibrous aragonite crystals. Previous studies identified a tissue inhibitor of metalloproteinase (Pf-TIMP: Pinctada fucata-Tissue Inhibitor of Metalloproteinase) in the organic fibers of P. fucata ligaments. This enzyme exhibited strong inhibition of matrix metalloproteinase (MMP) activity in vitro, suggesting that MMPs also play a role in formation of the organic fibers of the ligament. Using transcriptome data, we identified MMP genes from the mantle isthmus, which is a soft tissue attached to the ligament. To investigate the function of MMP genes in vivo, we performed RNA interference experiments. The expression of MMP14973 and MMP07860 genes was inhibited after injection of each dsRNA. Cumulative injection of MMP07860 dsRNA induced aggregated aragonite fiber orientation, whereas the injection of MMP14973 showed minor effects. When the decalcified ligament was incubated in a solution saturated with calcium carbonate, aragonite fibers aligned along the surface. When the decalcified ligament was treated with recombinant human (hr) MMP-13, the precipitation of calcium carbonate was inhibited. To investigate general MMP functions in calcium carbonate crystallization in detail, we precipitated aragonite crystals in collagen gels treated with or without recombinant human (hr) MMP-1. Treatment with hrMMP-1 increased the interaction between collagen gels and calcium carbonate. These results imply that Pinctada fucata (Pf)-MMPs degrade extracellular matrices in the ligament to produce the fine organic fibers that regulate the orientation of fibrous aragonite crystals

Clonal Diversity of the Expression of MHC Class I Antigens. and Endogenous Retroviral Antigens on the Oncogene-Induced Cell Transformation of BALB3T3 Cells-Different Regulatory Mechanisms for the Expression of Antigens

The effect of the activated oncogene transfection on the expression of MHC class I H-2Kd, Dd and Ld and endogenous retroviral antigens was analyzed on 21 clones independently derived from the same parental BALB3T3. These clones were obtained by transfecting BALB3T3 with EJ-ras, PyMT, c-myc, and v-src oncogenes. The expression of MHC class I H-2Ld and H-2Kd antigens was reduced in clones with high anchorage independent growth potential. However, clones with low or no anchorage independent growth potential displayed almost the same degree of expression as parental BALB3T3. The H-2Dd antigen was for the most part conserved. The reduced expression of H-2Kd antigen was com-pletely restored by IFN treatment, whereas that of H-2Ld antigen was only par-tially restored. Meanwhile, MuLV and MMTV antigens were expressed on parental BALB3T3. These antigens was down-modulated in all of the EJ-ras and in one of the v-src-transfected clones. However, all the PyMT-transfected clones expressed the antigens as much as parental BALB3T3 even in the clones with high anchorage independent growth potential. These data suggest that the MHC class I antigen expression is modulated with the transforming process of cells, whereas the endogenous retroviral antigen expression might be dependent upon the transfected oncogenes rather than the transforming phenotype of the cells

MEFV gene mutations in neuro-Behçet's disease and neuro-Sweet disease

ArticleAnnals of clinical and translational neurology. 6(12): 2595-2600 (2019)journal articl