• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.39-57
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• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Animal Bioscience
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• v.34 no.11
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• pp.1739-1748
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• 2021

Objective: In recent years, long noncoding RNAs (lncRNAs) have been identified in many species, and some of them have been shown to play important roles in muscle development and myogenesis. However, the differences in lncRNAs between Kazakh cattle and Xinjiang brown cattle remain undefined; therefore, we aimed to confirm whether lncRNAs are differentially expressed in the longissimus dorsi between these two types of cattle and whether differentially expressed lncRNAs regulate muscle differentiation. Methods: We used RNA-seq technology to identify lncRNAs in longissimus muscles from these cattle. The expression of lncRNAs were analyzed using StringTie (1.3.1) in terms of the fragments per kilobase of transcript per million mapped reads values of the encoding genes. The differential expression of the transcripts in the two samples were analyzed using the DESeq R software package. The resulting false discovery rate was controlled by the Benjamini and Hochberg's approach. KOBAS software was utilized to measure the expression of different genes in Kyoto encyclopedia of genes and genomes pathways. We randomly selected eight lncRNA genes and validated them by quantitative reverse transcription polymerase chain reaction (RT-qPCR). Results: We found that 182 lncRNA transcripts, including 102 upregulated and 80 downregulated transcripts, were differentially expressed between Kazakh cattle and Xinjiang brown cattle. The results of RT-qPCR were consistent with the sequencing results. Enrichment analysis and functional annotation of the target genes revealed that the differentially expressed lncRNAs were associated with the mitogen-activated protein kinase, Ras, and phosphatidylinositol 3-kinase (PI3k)/Akt signaling pathways. We also constructed a lncRNA/mRNA coexpression network for the PI3k/Akt signaling pathway. Conclusion: Our study provides insights into cattle muscle-associated lncRNAs and will contribute to a more thorough understanding of the molecular mechanism underlying muscle growth and development in cattle.