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DETERMINATION OF ALL SUBFIELDS OF CYCLOTOMIC FUNCTION FIELDS WITH GENUS ONE
JUNG, HWAN-YUP,AHN, JAE-HYUN Korean Mathematical Society 2005 대한수학회논문집 Vol.20 No.2
In this paper we determine all subfields with genus one of cyclotomic function fields over rational function fields explicitly.
IMAGINARY BICYCLIC FUNCTION FIELDS WITH THE REAL CYCLIC SUBFIELD OF CLASS NUMBER ONE
Jung, Hwan-Yup Korean Mathematical Society 2008 대한수학회보 Vol.45 No.2
Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.
Jung, Jae Hwan,Park, Tae Jung,Lee, Sang Yup,Seo, Tae Seok WILEY‐VCH Verlag 2012 Angewandte Chemie Vol.124 No.23
<P><B>Ein Mikrofluidik‐Tropfen‐Generator</B> schließt einheitlich eine gleiche Zahl an modifizierten <I>E.‐coli</I>‐Zellen sowie Eisen‐ und Manganionen in gleicher Konzentration in Tropfen identischer Größe ein. In der Zuschrift auf S. 5732 ff. stellen T. S. Seo, S. Y. Lee et al. die Synthese homogener biogener paramagnetischer Nanopartikel in rekombinanten <I>E.‐coli</I>‐Zellen durch ihren Einschluss in Nanoliter‐große Tropfen vor.</P>
8-RANKS OF CLASS GROUPS OF IMAGINARY QUADRATIC NUMBER FIELDS AND THEIR DENSITIES
Jung, Hwan-Yup,Yue, Qin Korean Mathematical Society 2011 대한수학회지 Vol.48 No.6
For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.
GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS
Jung, Hwan-Yup,Ahn, Jae-Hyun Korean Mathematical Society 2007 대한수학회지 Vol.44 No.3
Let m, n be positive integers or monic polynomials in $\mathbb{F}_q[T]$ with n|m. Let $K_m\;and\;K^+_m$ be the m-th cyclotomic field and its maximal real subfield, respectively. In this paper we define two matrices $D^+_{m,n}\;and\;D^-_{m,n}$ whose determinants give us the ratios $\frac{h(\mathcal{O}_{K^+_m})}{h(\mathcal{O}_{K^+_n})}$ and $\frac{h-(\mathcal{O}_K_m)}{h-(\mathcal{O}_K_n)}$ with some factors, respectively.
A NOTE ON CYCLOTOMIC UNITS IN FUNCTION FIELDS
Hwan yup Jung 충청수학회 2007 충청수학회지 Vol.20 No.4
Let A = Fq[T] and k = Fq(T). Assume q is odd, and ¯xa prime divisor ` of q ¡1. Let P be a monic irreducible polynomial in A whose degree d is divisible by `. In this paper we de¯ne a subgroup e CF of O¤F which is generated by F¤q and f´¿i: 0 · i ·` ¡ 1g in F = k( `pP) and calculate the unit-index [O¤F : e CF ] =``¡2h(OF ). This is a generalization of [3, Theorem 16.15].
THAINE’S THEOREM IN FUNCTION FIELD
Hwan yup Jung 충청수학회 2009 충청수학회지 Vol.22 No.1
Let F be a finite real abelian extension of a global function field k with G = Gal(F/k). Assume that F is an extension field of the Hilbert class field Ke of k and is contained in a cyclotomic function field Kn. Let ` be any prime number not dividing phk|G|. In this paper, we show that if 2 Z[G] annihilates the Sylow `-subgroup of O×F /CF, then (q−1) annihilates the Sylow `-subgroup of ClF.
ON HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS
Hwan yup Jung 충청수학회 2010 충청수학회지 Vol.23 No.3
In this paper we prove that real quadratic function ¯eld F over Fq(T) has in¯nite 2-class ¯eld tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when q ´ 3 mod 4.
( Kyoungwon Jung ),( Hye-kyung Jung ),( Joong Goo Kwon ),( Chung Hyun Tae ),( Ki Bae Bang ),( Jong Kyu Park ),( Ju Yup Lee ),( Cheol Min Shin ),( Jung Hwan Oh ),( Kyung Ho Song ),( Oh Young Lee ),( My 대한소화기기능성질환·운동학회 2022 Journal of Neurogastroenterology and Motility (JNM Vol.28 No.1
Background/Aims Patient-reported outcomes (PROs) are essential for clinical decision making, conduction of clinical research, and drug application acquisition in functional gastrointestinal disorders. The aim of this study is to develop a PRO instrument and to determine the respondents’ perception of the efficacy of therapeutic agents for functional dyspepsia (FD). Methods A self-evaluation questionnaire for dyspepsia (SEQ-DYSPEPSIA) was developed and validated through a structured process. The 2-week reproducibility was evaluated, and the construct validity was assessed by correlating the scores of SEQ-DYSPEPSIA (including typical and major FD symptom subscales). Finally, the response to medication was assessed by comparing the changes after 4 weeks of treatment. Results A total of 193 Korean patients (age 48.5 ± 13.6 years, 69.4% women) completed the questionnaire. SEQ-DYSPEPSIA with 11 items had a good internal consistency (alpha = 0.770-0.905) and an acceptable test-retest reliability (intraclass correlation coefficient = 0.733-0.859). The self-evaluation questionnaire (SEQ)-major FD score highly correlated with the postprandial fullness/early satiety domain of the Patient Assessment of Gastrointestinal Symptom Severity Index (correlation coefficient r = 0.741, P < 0.001), Nepean Dyspepsia Index-Korean version (NDI-K) (r = 0.839, P < 0.001), and NDI-K quality of life (r = -0.275 to -0.344, P < 0.001). After medical treatment, decrease in the SEQ-typical FD and SEQ-major FD was significantly greater in the responder group than in nonresponder group (P = 0.019 and P = 0.009, respectively). Conclusion This study suggests that the Korean version of SEQ-DYSPEPSIA has good reliability and validity, and can be a useful PRO measurement tool in patients with FD. (J Neurogastroenterol Motil 2022;28:111-120)