Algebraic Numbers

This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to the polynomial ring of ℚ[x] turns to be a field.Suginami-ku Matsunoki 6, 3-21 Tokyo, JapanMichael Francis Atiyah and Ian Grant Macdonald. Introduction to Commutative Algebra, volume 2. Addison-Wesley Reading, 1969.Jonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. Formalized Mathematics, 9(3):565–582, 2001.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990.Hideyuki Matsumura. Commutative Ring Theory. Cambridge University Press, 2nd edition, 1989. Cambridge Studies in Advanced Mathematics.Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339–346, 2001.Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391–395, 2001.Masayoshi Nagata. Theory of Commutative Fields, volume 125. American Mathematical Society, 1985. Translations of Mathematical Monographs.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329–334, 1990.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990.Oscar Zariski and Pierre Samuel. Commutative Algebra I. Springer, 2nd edition, 1975

Supplementary material for the article: Beškoski, V. P.; Yamamoto, A.; Nakano, T.; Yamamoto, K.; Matsumura, C.; Motegi, M.; Beškoski, L. S.; Inui, H. Defluorination of Perfluoroalkyl Acids Is Followed by Production of Monofluorinated Fatty Acids. Science of the Total Environment 2018, 636, 355–359. https://doi.org/10.1016/j.scitotenv.2018.04.243

Supplementary material for: [https://doi.org/10.1016/j.scitotenv.2018.04.243]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2168

Supplementary material for the article: Beškoski, V. P.; Yamamoto, A.; Nakano, T.; Yamamoto, K.; Matsumura, C.; Motegi, M.; Beškoski, L. S.; Inui, H. Defluorination of Perfluoroalkyl Acids Is Followed by Production of Monofluorinated Fatty Acids. Science of the Total Environment 2018, 636, 355–359. https://doi.org/10.1016/j.scitotenv.2018.04.243

Supplementary material for: [https://doi.org/10.1016/j.scitotenv.2018.04.243]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2168

Wheat‐ghretropins: novel ghrelin‐releasing peptides derived from wheat protein

Ghrelin is an endogenous orexigenic hormone mainly produced by stomach cells and is reported to influence appetite, gastrointestinal motility and growth hormone secretion. We observed that enzymatic digest of wheat gluten stimulated ghrelin secretion from mouse ghrelinoma 3-1, a ghrelin-releasing cell line. Further on, we characterized the ghrelin-releasing peptides present in the digest by comprehensive peptide analysis using liquid chromatography-mass spectrometry and structure-activity relationship. Among the candidate peptides, we found that SQQQQPVLPQQPSF, LSVTSPQQVSY and YPTSL stimulated ghrelin release. We then named them wheat-ghretropin A, B and C, respectively. In addition, we observed that wheat-ghretropin A increased plasma ghrelin concentration and food intake in mice after oral administration. Thus, we demonstrated that wheat-ghretropin stimulates ghrelin release both in vitro and in vivo. To the best of our knowledge, this is the first report of a wheat-derived exogenous bioactive peptide that stimulates ghrelin secretion

Differential gene expression profiles in neurons generated from lymphoblastoid B-cell line-derived iPS cells from monozygotic twin cases with treatment-resistant schizophrenia and discordant responses to clozapine

Schizophrenia is a chronic psychiatric disorder with complex genetic and environmental origins. While many antipsychotics have been demonstrated as effective in the treatment of schizophrenia, a substantial number of schizophrenia patients are partially or fully unresponsive to the treatment. Clozapine is the most effective antipsychotic drug for treatment-resistant schizophrenia; however, clozapine has rare but serious side-effects. Furthermore, there is inter-individual variability in the drug response to clozapine treatment. Therefore, the identification of the molecular mechanisms underlying the action of clozapine and drug response predictors is imperative. In the present study, we focused on a pair of monozygotic twin cases with treatment-resistant schizophrenia, in which one twin responded well to clozapine treatment and the other twin did not. Using induced pluripotent stem (iPS) cell-based technology, we generated neurons from iPS cells derived from these patients and subsequently performed RNA-sequencing to compare the transcriptome profiles of the mock or clozapine-treated neurons. Although, these iPS cells similarly differentiated into neurons, several genes encoding homophilic cell adhesion molecules, such as protocadherin genes, showed differential expression patterns between these two patients. These results, which contribute to the current understanding of the molecular mechanisms of clozapine action, establish a new strategy for the use of monozygotic twin studies in schizophrenia research

抽象的代数幾何学におけるコホモロジー環の幾何学的構造

京都大学0048新制・課程博士理学博士理博第6号新制||理||3(附属図書館)22京都大学大学院理学研究科数学専攻(主査)教授 秋月 康夫, 教授 小堀 憲, 教授 小松 醇郎学位規則第5条第1項該当Kyoto UniversityDA