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µî·ÏµÈ ÃÊ·Ï Tentative Abstracts
Nonlinear biderivations in complex Banach algebras Choonkil Park*, Hanyang University, baak@hanyang.ac.kr
Abstract: Using the fixed point method and the direct method, we prove the HyersUlam stability of biderivations and bihomomorphisms in Banach algebras,
associated with the biadditive functional inequality \begin{eqnarray*}
&& \ f(x+y, z+w) + f(x+y, zw) + f(xy, z+w) + f(xy, zw) 4f(x,z)\ \\ && \le \left \s \left(2f\left(x+y, zw\right) + 2f\left(xy, z+w\right)  4f(x,z )+ 4 f(y, w)\right)\right\ ,
\end{eqnarray*}
where $s$ is a fixed nonzero complex number with $s < 1$.
Subject: Analysis Abstract Number : SSA8429140054 [Modifiy] [Delete] (with private passwords)
Refined enumeration of vertices among all rooted ordered dtrees Seunghyun Seo*, Kangwon National University, shyunseo@kangwon.ac.kr Sangwook Kim, Chonnam National University, Heesung Shin, Inha University Abstract: In this talk, we enumerate the cardinalities for the set of all vertices of outdegree $\ge k$ at level $\ge \ell$ among all rooted ordered $d$trees with $n$ edges. Our results unite and generalize several previous works in the literature.
Subject: Discrete Math/Combinatorics Abstract Number : SSA8515164424 [Modifiy] [Delete] (with private passwords)
Mathematics Teachers' concerns and Needs to enhance mathematical competency Yun Hee Hwang*, Hongcheon Girls' Middle school, 0411hyh@naver.com Sun Hee Kim, Kangwon National University Abstract: The 2015 revised mathematics curriculum is aimed at enhancing the capacity of students, and instruction and assessment should be changed to match the growth of the capacity. 40 math teachers who completed the processfocused assessment training for enhancing students' math competence were asked to responce the open questions. We examined math competency to nurture students through mathematics education, the appearance and improvement of their math classes and evaluations, and the concerns and requirements for improving math instructions and assessments. We analyzed the responses using network analysis methods, and repetitive comparison analysis. Implications for instructions and assessments in accordance with teachers' requirements were derived.
Subject: math education Abstract Number : SSA8520183615 [Modifiy] [Delete] (with private passwords)
Simple evaluation formulas for generalized conditional Wiener integrals over paths Dong Hyun Cho*, Kyonggi University, j94385@kyonggi.ac.kr
Abstract: Let $C[0,T]$ denote a generalized Wiener space, the space of realvalued continuous functions on the interval $[0,T]$. In this survey talk we will introduce various simple formulas for the generalized conditional Wiener integrals of functions on $C[0,T]$ with several vectorvalued conditioning functions having a drift and then investigate their relationships. As applications of the formulas we evaluate more generalized conditional Wiener integrals of functions on $C[0,T]$ including a time integral which are of interest in the Feynman integration theories and quantum mechanics.
Subject: Plenary talk Abstract Number : SSA8523112922 [Modifiy] [Delete] (with private passwords)
A simple formula for a RandonNikodym derivative with its applications Dong Hyun Cho*, Kyonggi University, j94385@kyonggi.ac.kr Bong Jin Kim, Daejin University, Il Yoo, Yonsei University Abstract: Let $C[0,T]$ denote an analogue of Wiener space, the space of realvalued continuous functions on the interval $[0,T]$. For a partition $0=t_0<t_1<\cdots<t_n<t_{n+1}=T$ of $[0,T]$, define $X_n:C[0,T]\to\mathbb R^{n+1}$ by $X_n(x)=(x(t_0),x(t_1),\ldots,x(t_n))$. In this talk we derive a simple evaluation formula for RadonNikodym derivatives similar to the conditional expectations of functions on $C[0,T]$ with the conditioning function $X_n$ which has a drift and does not contain the present position of paths. As applications of the formula with $X_n$, we evaluate the RadonNikodym derivatives of the functions $\int_0^T[x(t)]^md\lambda(t)(m\in\mathbb N)$ and $[\int_0^Tx(t)d\lambda(t)]^2$ on $C[0,T]$, where $\lambda$ is a complexvalued Borel measure on $[0,T]$. Finally we derive two translation theorems for the RadonNikodym derivatives of the functions on $C[0,T]$.
Subject: Analysis Abstract Number : SSA8523123134 [Modifiy] [Delete] (with private passwords)
The Problem Posing Types and the Recognition of Teaching and Leaning of PreService Mathematics Teachers Lee, Myoung Hwa*, Graduate School, Kangwon National University, hahahoho98@nate.com Kim, Sun Hee(Kangwon National University) Abstract: This study investigated the types of problems made by preservice mathematics teachers and their recognition of teaching and learning of problemposing. When closing the unit 'relation and function' of the set theory in the course of foundations of mathematics for the firstyear preservice teachers of university, they performed the problemposing activity, and then solved and scored the problems with peer students. About 70% of preservice teachers suggested textbook problem, acceptance problem, and acceptanceextension problem while the rest 30% suggested challenge problem and creative problem. preservice teachers recognized that the problemposing activity was helpful for their own learning by strengthening and enriching the basic concept of mathematics. However, some of them were not sure if they would use the problemposing activity for class if they become mathematics teachers because of errors in the problemposing process or fear of insufficient problems. This could be overcome through the activity of modifying the errors of problems together with peers in the scoring process.
Subject: Math Education Abstract Number : SSA8524152122 [Modifiy] [Delete] (with private passwords)
Maximum principle in some unbounded domains for a bounded subsolution to second order elliptic operator in nondivergence form Sungwon Cho *, Gwangju national university of education, scho@gnue.ac.kr
Abstract: The maximal principle has an important role in elliptic and parabolic partial differential equations. It is immediate to have a uniqueness of a solution to the corresponding boundary value problem. But, the principle does not hold in unbounded domains, in general.
We study the maximum principle for (wG)domain, which can be unbounded.
Using a Safonov's growth lemma, we treat the operator when the first order coefficients belong to nintegrable Lebesgue space for a bounded subsolution to second order elliptic operator in nondivergence form.
We also present diverse examples for a subsolution in unbounded domains.
Subject: Analysis Abstract Number : SSA8525144613 [Modifiy] [Delete] (with private passwords)
Group Completion and its Generalization Yong Ho Lee*, Inha University, yooooongh@gmail.com
Abstract: The multiplication property of a loop space is the start point of Algebraic Topology. For a topological $M$ with a multiplication which is a topological monoid, the difference between $M$ and $\Omega BM$ has been studies. The group completion theorem is about an isomorphism $H_\ast(M) \rightarrow H_\ast(\Omega BM)$. In this paper we study generalize the classical group completion theorem to the case of simplicial topological monoid. We state a concrete version of the generalized group completion theorem and find its application.
Subject: Topology Abstract Number : SSA8527132651 [Modifiy] [Delete] (with private passwords)
Number of equivalent classes and weighted counts in the integer partitions Byungchan Kim*, SeoulTech, bkim4@seoultech.ac.kr
Abstract: The Durfee square decomposition of integer partitions consists of $(d, \lambda_1, \lambda_2)$, where $d$ is the size of Durfee square and $\lambda_1$ and $\lambda_2$ is a partition into parts $\leq d$. One may ask what happens if we append two more additional partitions in the decomposition or what if we use a triangle instead of the square. In this talk, I will present several partition identities motivated from these simple questions.
Subject: Discrete Math/Combinatorics Abstract Number : SSA8527165752 [Modifiy] [Delete] (with private passwords)
Analysis of the Graph Unit for the first grade of Middle School according to the 2015 Revised Mathematics Curriculum Yunmim, Kim. *, Keimyung University, yunmin@gw.kmu.ac.kr BuMi, Kim. Wonkwang University Abstract: This study compared the newly introduced 'Graph' unit in the mathematics textbook for first grade school students according to the 2015 revised national curriculum. the results of the study are as follows. First, the frequency analysis of the construction and interpretation of graphs of each textbook on context, translation, approach, type, method and evaluation questions revealed a statistically significant difference. In addition, the results of crossanalysis by graph type, textbook areas and publishers were all statistically significant differences. Seconds, we examined how various graphs were encountered in composition and interpretation activities of graph and qualitatively analyzed the contexts of increase and decrease of graph, and the contexts of periodic change.
Subject: Math Education Abstract Number : SSA8527111434 [Modifiy] [Delete] (with private passwords)
Rectified regular polytope numbers Hyun Kwang Kim*, Deaprtment of Mathematics, POSTECH, hkkim@postech.ac.kr
Abstract: The polytope numbers were introduced as a higher dimensional analogue of polygonal numbers which are 2dimensional polytope numbers. In this talk, we first briefly introduced history of polytope numbers. In the next we discuss basic properties of polytope numbers.Finally we represnt our recent results on rectified regular polytope numbers.
Subject: Algebra Abstract Number : SSA8528083528 [Modifiy] [Delete] (with private passwords)
On a path induced saturated graph EunKyung Cho*, Hankuk University of Foreign Studies, ourearth3@gmail.com Ilkyoo Choi, Hankuk University of Foreign Studies, Boram Park, Ajou University Abstract: Let $G$ and $H$ be graphs. We say that $G$ is an $H$saturated graph if $H$ is not a subgraph of $G$, but $H$ is a subgraph of $G+e$ for all $e \in E(\bar{G})$. We can always construct an $H$saturated graph for all $H$.
We say that $G$ is an $H$inducedsaturated if $H$ is not an induced subgraph of $G$, but $H$ is an induced subgraph of $G+e$ and $Gf$ for all $e \in E(\bar{G})$ and $f \in E(G)$. Unlike the $H$saturated graph, an $H$inducedsaturated graph does not always exist. In fact, Martin and Smith showed that $P_4$inducedsaturated graphs do not exist, where we use $P_n$ to denote a path on $n$ vertices. Axenovich and Csikos asked the existence of $P_n$inducedsaturated graphs for $n \ge 5$; it is easy to construct such graphs when $n\in\{2, 3\}$. Recently, Raty constructed a graph that is $P_6$inducedsaturated.
In this talk, we show some examples of $P_k$inducedsaturated graphs. In particular, we show a family of $P_{3m}$inducedsaturated graphs, where $m$ is a positive integer at least $2$.
Subject: Discrete Math Abstract Number : SSA8529145456 [Modifiy] [Delete] (with private passwords)
Additive functional inequalities and their applications Dong Yun Shin*, University of Seoul, dyshin@uos.ac.kr
Abstract: In this talk, we prove the following theorem: Let $A$ be a Banach algebra. Let $r > 2$ and $\theta$ be nonnegative real numbers and $f : A \rightarrow A$ be a mapping such that
\begin{eqnarray*}
\f(\mu (x+y+z)) \mu (f(x+y)+ f(z))\ \le \ s (f(x+yz) + f(xy+z ) 2f(x)) \ + \theta ( \x\^r + \y\^r +\z\^r) \end{eqnarray*} for all $\mu \in {\mathbb{T}}^1 : = \{ \lambda \in {\mathbb{C}} ~ \mid ~ \lambda=$ $1\}$ and all $x,y,z \in A$. Then there exists a unique $\mathbb{C}$linear mapping $P : A \rightarrow A$ such that
$\f(x) P(x) \ \le \frac{2 \theta }{2^r2} \x \^r $ for all $x \in A$. If, in addition, the mapping $f: A\to A$ satisfies $f(2x) = 2f(x)$ and \begin{eqnarray*}
\f\circ f(x y)  f(x) f(y) \ \le \theta ( \x\^r + \y\^r ), \quad \f(x^*)  f(x)^* \ \le \theta \x\^r \end{eqnarray*} for all $x, y \in A$, then the mapping $f$ is a partial multiplier.
Subject: Analysis Abstract Number : SSA8531113213 [Modifiy] [Delete] (with private passwords)
Functional inequalities and quasimultipliers on Banach algebras Sungsik Yun*, Hanshin University, ssyun@hs.ac.kr
Abstract: Let $A$ be a Banach algebra. Let $r > 2$ and $\theta$ be nonnegative real numbers and $f :
A^2 \rightarrow A$ be a mapping satisfying $f(x,0)=f(0,z) =0$ and
\begin{eqnarray*}
&& \nonumber \ f(\lambda(x+y), z+w) + f(\lambda(x+y), zw) +f(\lambda(xy), z+w)
+f(\lambda(xy), zw) 4\lambda f(x,z) \ \\ && \le \s (4f\left(\frac{x+y}{2}, zw\right)
+4 f\left(\frac{xy}{2}, z+w\right) 4 f(x,z )
+ 4 f(y, w))\ + \theta ( \x\^r + \y\^r) (\z\^r +\w\^r )
\end{eqnarray*} for all $\lambda \in {\mathbb{T}}^1 : = \{\nu \in {\mathbb{C}} ~:~ \nu=1\}$ and all $x,y,z, w \in A$. Then there exists a unique biadditive mapping $P : A^2 \rightarrow A$, which is $\mathbb{C}$linear in the first variable, such that $\f(x, z) P(x, z) \ \le \frac{ \theta }{2^r2} \x \^r \z \^r$ for all $x, z \in A$. If, in addition, the mapping $f: A^2 \to A$ satisfies $f(2x, z) = 2f(x, z)$ and \begin{eqnarray*}
\ f(x y, z)  x f(y, z) \ \le \theta ( \x\^r + \y\^r ) \z\^r ,
\quad
\f(x,z)  f(z,x)^*\ \le \theta \x\^r \z\^r \end{eqnarray*} for all $x, y, z \in A$, then the mapping $f: A^2 \to A$ is a quasi$*$multiplier.
Subject: Analysis Abstract Number : SSA8531114119 [Modifiy] [Delete] (with private passwords)
CYCLOTOMIC FIELDS ARE GENERATED BY CYCLOTOMIC HECKE LVALUES OF TOTALLY REAL FIELDS Lee Jungyun. *, Kangwon National University, lee9311@kangwon.ac.kr JUN BYUNGHEUP, UNIST, SUN HAESANG, UNIST. Abstract: We prove that a single HeckeLvalue of a totally real field with cyclotomic twist of sufficiently large prime power conductor generates the values of a tame character and the prime power roots of unity.
Subject: Algebra Abstract Number : SSA8531153359 [Modifiy] [Delete] (with private passwords)
Exploring Mathematical Belief Changes in Elementary School Preservice Teachers Ryu, Hyunah*, Chinju National University of Education, ryuha@cue.ac.kr Kim, Yunmin Keimyung university Abstract: The purpose of this study is to investigate the change of mathematical beliefs of elementary school pre  service teachers. This is a longitudinal study of the first year students of the year 2015 using the mathematical belief test tool every December. The results of the research for three years were analyzed as follows. First, we investigated the changes of mathematical beliefs for three years. Second, we investigated the changes of mathematical beliefs for three years according to gender. Third, we investigated the changes of mathematical beliefs for three years depending on major. The results of this study will provide suggestions for the improvement of education programs of elementary school pre  service teachers.
Subject: Math Education Abstract Number : SSA8601105644 [Modifiy] [Delete] (with private passwords)
Proof of Chapoton's conjecture on Newton polygons of qEhrhart polynomials Song Ukeun*, Sungkyunkwan University, sukeun319@gmail.com Jang Soo Kim, Sungkyunkwan University Abstract: Chapoton found a $q$analog of Ehrhart polynomials, which are polynomials in variable $x$ whose coefficients are rational functions in $q$. Chapoton conjectured the shape of the Newton polytope of the numerator of the $q$Ehrhart polynomial associated to an order polytope. In this presentation, we prove Chapoton's conjecture.
Subject: Discrete Math/Combinatorics Abstract Number : SSA8601113234 [Modifiy] [Delete] (with private passwords)
A POSTERIORI ERROR ESTIMATORS OF BANKWEISER TYPE FOR FINITE ELEMENT APPROXIMATIONS Juseong Park*, Kangwon National University, jspark@kangwon.ac.kr
Abstract: This study analyzes an a posteriori error estimator for linear and quadratic finite element approximations on triangular meshes. This error estimators are based on solving local Neumann problems  a methodology that was introduced in [Bank and Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44 (1985), 283301]. We prove that it is asymptotically exact for the diffusion problems when the underlying triangulations are mildly structured and the solution is smooth enough.
Subject: Applied Math Abstract Number : SSA8603023638 [Modifiy] [Delete] (with private passwords)
The Trends of International and National Math Assessment focused on mathematical competencies Haemee Rim *, Kongju National University, rimhaemee@kongju.ac.kr
Abstract: Recently, there has been a growing movement to teach and evaluate not only knowledge but also competencies through school education. The OECD has designed PISA to evaluate competencies based on the DeSeCo project, and Korea is also making various attempts to teach and evaluate competencies at national and classroom levels from the 2015 revised curriculum. In this presentation, we will look at the ongoing OECD Education 2030 project, the changes in PISA 2021 mathematics framework, the items of NAEA, and discuss the directions of the evaluation of mathematics in Korea.
Subject: Math Education Abstract Number : SSA8603122818 [Modifiy] [Delete] (with private passwords)
Simplicial wedge and classification of toric manifolds Hanchul Park*, Jeju National University, hanchulp@jejunu.ac.kr Suyoung Choi, Ajou University Abstract: A toric manifold is an even dimensional smooth manifold equipped with a "particularly good" halfdimensional torus action. They can be described using combinatorial data including simplicial spheres. In this talk, I briefly review toric manifolds and explain how to classify them using their combinatorial data, especially using simplicial wedge operation.
Subject: Topology Abstract Number : SSA8603151025 [Modifiy] [Delete] (with private passwords)
On $p$positivity of skew Schur $Q$functions JiSun Huh*, Sungkyunkwan University, hyunyjia@g.skku.edu Soojin Cho, Ajou University, SunYoung Nam, Sogang University Abstract: The symmetric functions $Q_{\lambda}:=Q_{\lambda}(x;1)$ were introduced in Schur's 1991 paper on the projective representations of the symmetric and alternating groups, where they play a role analogous to that of the Schur functions in connection with the linear representations of the symmetric groups. Let $\Gamma$ be the subring of the ring of symmetric functions which generated by $Q_{\lambda}$ with strict partitions $\lambda$. It is wellknown that the power sum symmetric functions $p_{\lambda}$ with odd partitions also generates $\Gamma$. In this talk, we consider the $p$positivity of skew Schur $Q$functions, $Q_{\lambda/\mu}$ for some skew partitions $\lambda/\mu$.
Subject: Discrete Math/Combinatorics Abstract Number : SSA8603145339 [Modifiy] [Delete] (with private passwords)
Computing volumes of flow polytopes using labeled Dyck paths Jihyeug Jang*, Sungkyunkwan University, ab4242@skku.edu Jangsoo Kim, Sungkyunkwan University Abstract: The Lidskii volume formula allows us to express the (normalized) volume of the flow polytope as a sum of the Kostant partition functions multiplied by certain numbers. In this talk, I explain how to compute Ehrhartlike polynomial for some graphs using labeled parenthesizations and labeled Dyck paths. Moreover, I introduce some properties of labeled Dyck paths.
Subject: Discrete Math/ Combinatorics Abstract Number : SSA8603160945 [Modifiy] [Delete] (with private passwords)
Toric Richardson varieties and Bott manifolds Seonjeong Park*, Ajou University, seonjeong1124@gmail.com Eunjeong Lee, IBSCGP, Mikiya Masuda, Osaka City University Abstract: The flag variety $\mathcal{F}\ell_n$ is a smooth projective variety consisting of chains $(\{0\}\subset V_1\subset\cdots\subset V_n=\mathbb{C}^n)$ of subspaces of $\mathbb{C}^n$ with $\dim_{\mathbb{C}} V_i=i$. Then the standard action of $\mathbb{T}=(\mathbb{C}^\ast)^n$ on $\mathbb{C}^n$ induces a natural action of $\mathbb{T}$ on $\mathcal{F}\ell_n$. For $v$ and $w$ in the symmetric group $\mathfrak{S}_n$ with $v\leq w$ in Bruhat order, the Richardson variety $X^v_w$ is defined to be the intersection of the Schubert variety $X_w$ and the opposite Schubert variety $w_0X_{w_0v}$, and it is an irreducible $\mathbb{T}$invariant subvariety of $\mathcal{F}\ell_n$. In this talk, we give some combinatorial interpretation of geometric properties of toric Richardson varieties, and show that every smooth toric Richardson variety is a Bott manifold. This talk is based on joint work with Eunjeong Lee and Mikiya Masuda.
Subject: Topology Abstract Number : SSA8603193656 [Modifiy] [Delete] (with private passwords)
Small covers and cohomological rigidity problem Suyoung Choi*, Ajou University, schoi@ajou.ac.kr
Abstract: In the lecture, I introduce recent achievements on topology of small covers, and its applications to the toric cohomological rigidity problem.
Subject: Topology Abstract Number : SSA8604083543 [Modifiy] [Delete] (with private passwords)
A practical adaptive grid method for the AllenCahn equation Darae Jeong*, Kangwon National University, tinayoyo@kangwon.ac.kr Junseok Kim, Korea University Abstract: We present a simple and practical adaptive finite difference method for the AllenCahn (AC) equation in the twodimensional space. We use a timedependent adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interfacial transition of the phasefield. We employ a recently developed explicit hybrid numerical scheme for the AC equation. Therefore, the computational algorithm on the narrow band discrete domain is simple and fast.<br />
We demonstrate the high performance of the proposed adaptive method for the AC equation through various computational experiments.
Subject: Applied Math Abstract Number : SSA8610150204 [Modifiy] [Delete] (with private passwords)
On the Asymmetric Beam Equation QHEUNG CHOI*, Inha University, qheung@inha.ac.kr Tacksun Jung, Kunsan National University Abstract: We investigate the nonlinear beam equation in an interval,
u_{tt} + u_{xxxx} + bu^+ = f(x,t),
where the nonlinearity (bu^+) crosses an eigenvalue. This equation represents a bending beam supported by cables under a load f. The constant b represents the restoring force if the cables stretch. The nonlinearity u+ models the fact that cables resist expansion but do not resist compression.
Subject: Analysis Abstract Number : SSA8615052704 [Modifiy] [Delete] (with private passwords)
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Department of Mathematics, Kangwon National University, Chuncheon 21341, Korea, Email: kkms@kangwon.ac.kr
