{"title":"EXPRESSIONS OF MEROMORPHIC SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR COMPLEX DIFFERENTIAL EQUATIONS","authors":"Junfan Chen, Gui-Sen Lian","doi":"10.4134/BKMS.B190744","DOIUrl":"https://doi.org/10.4134/BKMS.B190744","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1061-1073"},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45650323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.
{"title":"LINEAR AND NON-LINEAR LOOP-TRANSVERSAL CODES IN ERROR-CORRECTION AND GRAPH DOMINATION","authors":"M. Daǧlı, Bokhee Im, Jonathan D. H. Smith","doi":"10.4134/BKMS.B190204","DOIUrl":"https://doi.org/10.4134/BKMS.B190204","url":null,"abstract":"Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"295-309"},"PeriodicalIF":0.5,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47542526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The traditional educational model was designed in the industrial age of the 20th century. That model is outdated for various reasons. This paper is introducing a case study of a project, "The S-Cool Days Program," which applies new routines to reframe those aspects. The introduction of the Program does not require significant changes in the curriculum, can be realized in Art and Music classes, or as a homeroom activity in advisory class. The Program was implemented in Europe, in two countries, in 3 different school types, one American School, a School Start-up and a traditional public school. The activities are introduced by creative art and craft sessions, are engaging enough to invite students to present their passion projects in the classroom, to take the first steps towards purpose-driven learning, learn how to focus on monitoring and expressing of emotions, among other things. The goal is to have some school habits reframed, that results in mindset change. New values are introduced and through them, the class is transformed into a comfort zone for students to envision and follow their dreams. The expected changes can be realized by easy-to-do new routines, which maintain the newly introduced behaviors. The Program supports the 4C's; the 21st-century skills education is supposed to focus on: the creativity, communication, collaboration, and critical thinking. Education Science EPiC Series in Education Science Volume 3, 2020, Pages 122–131 Proceedings of the MIT LINC 2019 Conference C. Urrea (ed.), LINC 2019 (EPiC Series in Education Science, vol. 3), pp. 122–131 As visualized on social maps, the research realized before and after the Project shows changes in the social relations of the participating classes after the new routines were introduced. New mutual common choices were emerging in all participating grades, classes. The paper shares insights from participating teachers, how they felt in and after the Program, what changes did they identify in the classroom. 1. Personal Motivation I am a psychologist neither a scientist, nor a researcher, but a single mother, who dedicated her free time and resources in the last seven years for finding and sharing simple answers to complicated issues present in the education system. The first week, my son entered the elementary education, we started to face many challenges, difficulties other parents, teacher, and kids meet as well. I was brave enough to find my way, allowed my son to develop in his rhythm, find his way to follow his passion. On the other hand, understanding and deeply believing in the concept of social responsibility, dedicated my time and resources to find solutions to the challenges in a structured way so that more children, teachers, parents, schools, could benefit from it. 2. Theoretical Background, "The Mind Age" Today, in the Mind Age, the traditional frameworks of economy and society are collapsing a global society is emerging surrounded by a global business environment and a te
{"title":"Simple Answers to Difficult Issues about Learning and Learners Internationally at pK-12 Levels","authors":"Ildiko Gyori","doi":"10.29007/bkms","DOIUrl":"https://doi.org/10.29007/bkms","url":null,"abstract":"The traditional educational model was designed in the industrial age of the 20th century. That model is outdated for various reasons. This paper is introducing a case study of a project, \"The S-Cool Days Program,\" which applies new routines to reframe those aspects. The introduction of the Program does not require significant changes in the curriculum, can be realized in Art and Music classes, or as a homeroom activity in advisory class. The Program was implemented in Europe, in two countries, in 3 different school types, one American School, a School Start-up and a traditional public school. The activities are introduced by creative art and craft sessions, are engaging enough to invite students to present their passion projects in the classroom, to take the first steps towards purpose-driven learning, learn how to focus on monitoring and expressing of emotions, among other things. The goal is to have some school habits reframed, that results in mindset change. New values are introduced and through them, the class is transformed into a comfort zone for students to envision and follow their dreams. The expected changes can be realized by easy-to-do new routines, which maintain the newly introduced behaviors. The Program supports the 4C's; the 21st-century skills education is supposed to focus on: the creativity, communication, collaboration, and critical thinking. Education Science EPiC Series in Education Science Volume 3, 2020, Pages 122–131 Proceedings of the MIT LINC 2019 Conference C. Urrea (ed.), LINC 2019 (EPiC Series in Education Science, vol. 3), pp. 122–131 As visualized on social maps, the research realized before and after the Project shows changes in the social relations of the participating classes after the new routines were introduced. New mutual common choices were emerging in all participating grades, classes. The paper shares insights from participating teachers, how they felt in and after the Program, what changes did they identify in the classroom. 1. Personal Motivation I am a psychologist neither a scientist, nor a researcher, but a single mother, who dedicated her free time and resources in the last seven years for finding and sharing simple answers to complicated issues present in the education system. The first week, my son entered the elementary education, we started to face many challenges, difficulties other parents, teacher, and kids meet as well. I was brave enough to find my way, allowed my son to develop in his rhythm, find his way to follow his passion. On the other hand, understanding and deeply believing in the concept of social responsibility, dedicated my time and resources to find solutions to the challenges in a structured way so that more children, teachers, parents, schools, could benefit from it. 2. Theoretical Background, \"The Mind Age\" Today, in the Mind Age, the traditional frameworks of economy and society are collapsing a global society is emerging surrounded by a global business environment and a te","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"3 1","pages":"122-131"},"PeriodicalIF":0.5,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42691251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group Z ∗ Z, then there are only finitely many real structures on X, up to R-isomorphisms.
{"title":"ON THE FINITENESS OF REAL STRUCTURES OF PROJECTIVE MANIFOLDS","authors":"Jin Hong Kim","doi":"10.4134/BKMS.B190084","DOIUrl":"https://doi.org/10.4134/BKMS.B190084","url":null,"abstract":"Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group Z ∗ Z, then there are only finitely many real structures on X, up to R-isomorphisms.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"109-115"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce the new general concept of usual expansiveness which is called “positively weak measure expansiveness” and study the basic properties of positively weak measure expansive C1differentiable maps on a compact smooth manifold M . And we prove that the following theorems. (1) Let PWE be the set of all positively weak measure expansive differentiable maps of M . Denote by int(PWE) is a C1-interior of PWE. f ∈ int(PWE) if and only if f is expanding. (2) For C1-generic f ∈ C1(M), f is positively weak measure-expansive if and only if f is expanding.
{"title":"POSITIVELY WEAK MEASURE EXPANSIVE DIFFERENTIABLE MAPS","authors":"Jiweon Ahn, Manseob Lee","doi":"10.4134/BKMS.B181190","DOIUrl":"https://doi.org/10.4134/BKMS.B181190","url":null,"abstract":"In this paper, we introduce the new general concept of usual expansiveness which is called “positively weak measure expansiveness” and study the basic properties of positively weak measure expansive C1differentiable maps on a compact smooth manifold M . And we prove that the following theorems. (1) Let PWE be the set of all positively weak measure expansive differentiable maps of M . Denote by int(PWE) is a C1-interior of PWE. f ∈ int(PWE) if and only if f is expanding. (2) For C1-generic f ∈ C1(M), f is positively weak measure-expansive if and only if f is expanding.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"569-581"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations fnf (k) + Qd∗ (z, f) = R(z)eα(z) and fnf (k) + Qd(z, f) = p1(z)e α1(z) + p2(z)e2, where Qd∗ (z, f) and Qd(z, f) are differential polynomials in f with small functions as coefficients, of degree d∗ (≤ n − 1) and d (≤ n − 2) respectively, R, p1, p2 are non-vanishing small functions of f , and α, α1, α2 are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.
{"title":"SOME RESULTS ON MEROMORPHIC SOLUTIONS OF CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS","authors":"Nan Li, Lian-Zhong Yang","doi":"10.4134/BKMS.B190535","DOIUrl":"https://doi.org/10.4134/BKMS.B190535","url":null,"abstract":"In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations fnf (k) + Qd∗ (z, f) = R(z)eα(z) and fnf (k) + Qd(z, f) = p1(z)e α1(z) + p2(z)e2, where Qd∗ (z, f) and Qd(z, f) are differential polynomials in f with small functions as coefficients, of degree d∗ (≤ n − 1) and d (≤ n − 2) respectively, R, p1, p2 are non-vanishing small functions of f , and α, α1, α2 are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1095-1113"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M ⊗ RM ∗ → HomR(HomR(M,M), R) is a surjective homomorphism. Particularly, if G-gldim(R) 6 ∞ and ExtR(M,M) = 0 (i > 1), then M is projective.
{"title":"FINITELY GENERATED G-PROJECTIVE MODULES OVER PVMDS","authors":"Kui Hu, J. Lim, Shiqi Xing","doi":"10.4134/BKMS.B190531","DOIUrl":"https://doi.org/10.4134/BKMS.B190531","url":null,"abstract":"Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M ⊗ RM ∗ → HomR(HomR(M,M), R) is a surjective homomorphism. Particularly, if G-gldim(R) 6 ∞ and ExtR(M,M) = 0 (i > 1), then M is projective.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"12 1","pages":"803-813"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let M be a module over a commutative ring R. In this paper, we study Int(R,M), the module of integer-valued polynomials on M over R, and IntM (R), the ring of integer-valued polynomials on R over M . We establish some properties of Krull dimensions of Int(R,M) and IntM (R). We also determine when Int(R,M) and IntM (R) are nontrivial. Among the other results, it is shown that Int(Z,M) is not Noetherian module over IntM (Z) ∩ Int(Z), where M is a finitely generated Z-module.
{"title":"SOME RESULTS ON INTEGER-VALUED POLYNOMIALS OVER MODULES","authors":"A. Naghipour, J. S. Hafshejani","doi":"10.4134/BKMS.B190846","DOIUrl":"https://doi.org/10.4134/BKMS.B190846","url":null,"abstract":"Let M be a module over a commutative ring R. In this paper, we study Int(R,M), the module of integer-valued polynomials on M over R, and IntM (R), the ring of integer-valued polynomials on R over M . We establish some properties of Krull dimensions of Int(R,M) and IntM (R). We also determine when Int(R,M) and IntM (R) are nontrivial. Among the other results, it is shown that Int(Z,M) is not Noetherian module over IntM (Z) ∩ Int(Z), where M is a finitely generated Z-module.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1165-1176"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"SOBOLEV TRACE INEQUALITY ON W s,q (ℝ n )","authors":"H. Pak","doi":"10.4134/BKMS.B190826","DOIUrl":"https://doi.org/10.4134/BKMS.B190826","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1143-1149"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of 2ψ2 series ∞ ∑ n=−∞ (a, c; q)n (b, d; q)n z and Ramanujan’s sum ∞ ∑ n=−∞ (a; q)n (b; q)n z.
本文首先给出了Andrews[1]和Bringmann, Hikami和Lovejoy[5]定义的四种新的模拟函数的除数和表示。然后，在2ψ2级数∞∑n=−∞(a, c;Q)n (b, d;q)n z和∑n=−∞(a;问)n (b;q) n z。
{"title":"ON FOUR NEW MOCK THETA FUNCTIONS","authors":"Qiuxia Hu","doi":"10.4134/BKMS.B190236","DOIUrl":"https://doi.org/10.4134/BKMS.B190236","url":null,"abstract":"In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of 2ψ2 series ∞ ∑ n=−∞ (a, c; q)n (b, d; q)n z and Ramanujan’s sum ∞ ∑ n=−∞ (a; q)n (b; q)n z.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"345-354"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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