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µî·ÏµÈ ÃÊ·Ï Tentative Abstracts
Beginner's guide to neural networks for the MNIST dataset using MATLAB Bitna Kim*, Kangwon National University, kbn0884@naver.com Young Ho Park, Kangwon National University Abstract: MNIST dataset is a database containing images of handwritten digits, with each image labeled by an integer from 0 to 9. It is used to benchmark the performance of machine learning algorithms. Neural networks for MNIST are regarded as the starting point of the studying machine learning algorithms. However it is not easy to start the actual programming. In this expository article, we will give a stepbystep instruction to build neural networks for MNIST dataset using MATLAB.<br /><br />
Subject: Applied Math Abstract Number : SSA8410145203 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180612
Additive (s,t)functional inequalities Choonkil Park*, Hanyang University, baak@hanyang.ac.kr
Abstract: In this talk, we introduce and solve the following additive $(\rho_1, \rho_2)$functional inequalities
\begin{eqnarray*}\left\f\left(x+y\right)  f(x ) f(y)\right\&\le &\\rho_1 (f(xy)f(x)+f(y))\ \\ &+ & \left\\rho_2 \left(f(yx)f(y)+f(x)\right)\right\,
\end{eqnarray*}
where $\rho_1$ and $\rho_2$ are fixed nonzero complex numbers with $\rho_1 + \rho_2 <1$, and
\begin{eqnarray*} \left\f\left(xy\right)  f(x )+ f(y)\right\ &\le &\\rho_1(f(x+y)f(x)f(y))\ \\ &+ &\left\\rho_2 \left( f(yx)f(y)+f(x)\right)\right\,
\end{eqnarray*}
where $\rho_1$ and $\rho_2$ are fixed nonzero complex numbers with $\rho_1 + \rho_2 <1$.
Using the fixed point method and the direct method, we prove the HyersUlam stability of the above additive $(\rho_1, \rho_2)$functional inequalities in complex Banach spaces.
Subject: Analysis Abstract Number : SSA8420202310 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180420
A general elliptic nonlinear system of two functions with application Joon Hyuk Kang*, Andrews University, kang@andrews.edu
Abstract:
We study mathematical conditions to guarantee the existence of positive solutions to a general nonlinear second order system of partial differential equations with homogeneous boundary conditions.
This result may apply to illustrate biological conditions under which species of animals residing in the same environment can peacefully coexist forever.
Subject: Applied Math Abstract Number : SSA8426095851 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180426
Involute and evolute of rectifying curves in 3D space Yun Myung Oh*, Andrews University, ohy@andrews.edu
Abstract: The idea of rectifying curves in $\mathbf{R}^{3}$ was introduced by B. Y. Chen in 2003 and many characterizations results have been found with applications in kinematics and mechanics. The idea has been generalized to the arbitrary dimension and it is now called the rectifying submanifold. In this project, we are going to investigate the involute and evolute of rectifying curves in $\mathbf{R}^{3}$ and find some characterizations of the curve.
Subject: Geometry Abstract Number : SSA8427053723 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180427
The application of topological method to the analysis of west capital Pyongyangbu map QHeung Choi*, Inha University, qheung@inha.ac.kr Tacksun Jung, Kunsan National University. Abstract: We analyse the map of the west capital Pyongyangbu of Old Korea(AD 920) by topological method and geometrical method and compare it with the map of North Korea Pyongyang. By the analyse of the map we find the real corresponding place of the old map. The analysing and finding the real place of the old map is a very good example of geometry education. Many Koreans had learned and recognized that Old Korea(AD 920) was a small country located in the south part of Ablok river. But, after reading this paper they change their old recognitions and they take prides in Great Old Korea.
Subject: Geometry Abstract Number : SSA8430154319 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180430
A modified Banach algebra over paths of bounded variation Dong Hyun Cho*, Kyonggi University, j94385@kyonggi.ac.kr Bong Jin Kim, Daejin University, Il Yoo, Yonsei University Abstract: Let $C[0,T]$ denote a generalized analogue of Wiener space, that is, the space of continuous, realvalued functions on $[0,T]$. In this talk we introduce two Banach algebras: one of them is defined on $C[0,T]$ and the other is a space of equivalence classes of measures over paths of bounded variation on $[0,T]$. We establish an isometric isomorphism between them, and evaluate analytic Feynman integrals of the functions in the Banach algebras which play important roles in the Feynman integration theories and quantum mechanics.
Subject: Analysis Abstract Number : SSA8503100211 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180503
Immersed Energy bending curve in hypersurface of Lorentzian Space Forms Woo Changhwa*, Woosuk University, legalgwch@naver.com Oscar J. Garay, Vascue University Abstract: We study geodesics in hypersurfaces of a Lorentzian space form ${M^{n+1}}_1(c)$, which are critical curves of the ${M^{n+1}}_1(c)$bending energy
functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully
immersed in a totally geodesic ${M^{3}}_1(c)$ and that they must be of three different types. Finally, we consider the classification of surfaces
in the Minkowski 3space foliated by critical geodesics.
Subject: Geometry Abstract Number : SSA8504101855 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180504
Real hypersurfaces with generalized TanakaWebster parallel shape operator in the complex quadric Hyunjin Lee*, Kyungpook National University, lhjibis@hanmail.net Young Jin Suh, Kyungpook National University Abstract: In the class of Hermitina symmetric spaces of rank 2, usually we can give examples of Riemannian symmetric spaces $SU_{m+2}/S(U_{2} U_{m})$ and $SU_{m,2}/S(U_{2} U_{m})$, which are said to be complex twoplane Grassmannians and complex hyperbolic twoplane Grassmannians, respectively.
In this talk, we will consider the complex quadric $SO_{m+2}/SO_{m} SO_{2}$ as another kind of Hermitian symmetric space with rank 2 of compact type different from the previous ones, which is a complex hypersurface in complex projective space ${\mathbb C}P^{m}$. And it can be regard as a kind of real Grassmann manifold of compact type with rank 2. Accordingly, the complex quadric admits both a complex conjugation structure $A$ and a Kaehler structure $J$, with anticommutes with each other, $JA=AJ$. By using these structures of the ambient space we classify real hypersurfaces with generalized TanakaWebster parallel shape operator in the complex quadric.
Subject: Geometry Abstract Number : SSA8508173251 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180508
Additive rhofunctional equations in nonArchimedean Banach spaces Eun Hwa Shim*, Daejin University, stareun01@nate.com Siriluk Paokanta, Hanyang University Abstract: In this paper, we solve the additive $\rho$functional equations
\begin{eqnarray*} f(x+y)+ f(xy)2f(x) = \rho\left(2 f\left(\frac{x+y}{2}\right)
+ f(xy ) 2f(x) \right),\end{eqnarray*}
where $\rho$ is a fixed nonArchimedean number with $\rho < 1$,
and
\begin{eqnarray*} f\left(\frac{x+y}{2}\right) + f(xy) 2 f(x) =\rho(f(x+y)+f(xy)2f(x)),
\end{eqnarray*}
where $\rho$ is a fixed nonArchimedean number with $\rho<2$.
Furthermore, we prove the HyersUlam stability of the above additive
$\rho$functional equations in nonArchimedean Banach spaces.
Subject: Analysis Abstract Number : SSA8513112346 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180516
Characterizations of PvMDs Gyu Whan Chang*, Incheon National University, whan@inu.ac.kr
Abstract: Let $D$ be an integral domain with quotient field $K$, $F(D)$ be the set of nonzero fractional ideals of $D$, and $f(D) = \{I \in F(D) \mid I$ is finitely generated$\}$. For $I \in F(D)$, let $I^{1} = \{x \in K \mid xI \subseteq D\}$; then $I^{1} \in F(D)$. Hence, $I_v = (I^{1})^{1}$ and $I_t = \bigcup \{J_v \mid J \subseteq I$ and $J \in f(D)\}$ are welldefined nonzero fractional ideals of $D$. We say that $I \in F(D)$ is $t$invertible if $(II^{1})_t = D$, and a Pr\"ufer $v$multiplication domain (P$v$MD) is an integral domain in which every nonzero finitely generated ideal is $t$invertible. In this talk, we give some new characterizations of P$v$MDs.
Subject: Algebra Abstract Number : SSA8515183418 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180515
An efficient method for the CahnHilliard equation in complex domains Darae Jeong*, Kangwon National University, tinayoyo@kangwon.ac.kr Junxiang Yang, Korea University, Junseok Kim, Korea University Abstract: In this study, we present a practical and efficient numerical method for the CahnHilliard (CH) equation in the two and threedimensional complex domains. We propose a simple mathematical model for the binary mixture in the complex domains. The model is based on the ternary CH system. An arbitrary domain is represented by the third phase, which is fixed during the temporal evolution of the other phases. Using the local conservation of the sum of the phases, we only need to solve a binary CH equation with a source term. For the numerical solution, we use a practically unconditionally gradient stable scheme for the multicomponent CH system. Computational experiments are presented to demonstrate the performance and effectiveness of the proposed method. The numerical results confirm that the proposed algorithm can deal with the complex domains efficiently.
Subject: Applied Math Abstract Number : SSA8521105935 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180521
The GaugeUzawa method to solve the nonconstant variable desity flows Pyo, JaeHong*, Kangwon National University, jhpyo@kangwon.ac.kr
Abstract: The GaugeUzawa method [GUM], which is a projection type algorithm
to solve the time depend NavierStokes equations, has been constructed and
extended to more complicated problems.
Because the studies on GUM have been performed with the first order
backward Euler scheme, we have been concentrated to impose BDF2 algorithm.
But the classical second order GUM displays weak stability behavior.
Recently, the second order stabilized GaugeUzawa method has been
newly constructed.
In this talk, we will extend to solve time evolution NavierStokes equations
with variable density. We will present theoretical results for stabilities
and numerical simulations for air bubble rising in water and RayleighTaylor.
Subject: Applied math Abstract Number : SSA8521172825 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180521
Corrected Heston's Stochastic Volatility Model for Vunlerable Option MinKu Lee*, Kunsan National University, mgcorea@kunsan.ac.kr JeongHoon Kim, Yonsei University Abstract: Fouque et al. [1] introduced the corrected Heston's stochastic volatility model. This research studied the price of the vulnerable options [2] and analyzed the features of the vulnerable options under the corrected Heston's stochastic volatility model.
[1] Fouque. J.P., Papanicolaou, G., Sircar, R., Solna. K. (2011) Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, Cambridge University Press.
[2] Klein, P., Inglis, M. (2011) Pricing Vulnerable European Options When the Option's Payoff can Increase the risk of Financial Distress, Journal of Banking and Finance, 25, 9931012.
Subject: Applied Math Abstract Number : SSA8525195140 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180525
On selfdual codes with fixedpoint free involution automorphism WhenHyuk Choi*, Kangwon National University, whanhyuk@gmail.com
Abstract: Selfdual codes which have a fixedpoint free involution as an automorphism is to be investigated.<br />
That class of codes is permutationequivalent to a code C that has the reverse permutation in its automorphism group.
We classify this class of selfdual code over Galois rings of moderate length.
Subject: algebra Abstract Number : SSA8528062641 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180528
A survey on high school education using history of mathematics Jae Min Chung*, Kyung Hee University, kyungsoo@khu.ac.kr Jae Min Chung, Kyung Hee University, Kyungsoo Kim, Kyung Hee University Abstract: It has been reported that using history of mathematics is helpful for students to understand mathematics in the classroom. However, it may be difficult to introduce the history of mathematics in high school classess. In this talk, we present the analysis results of a survey on high school education using history of mathematics.
Subject: Math Education Abstract Number : SSA8528184612 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180602
Fundamental mathematics in Bayesian deep learning Kyungsoo Kim*, Kyung Hee University, kyungsoo@khu.ac.kr Daehoon Gwak, Kyung Hee University, Dasol Hwang, Kyung Hee University, Hyunho Lee, Kyung Hee University, Kyungsoo Kim, Kyung Hee University Abstract: Since conventional deep learning model is a point estimation model that deterministically predicts values, it is difficult to quantify the reliability of the model. The Bayesian deep learning is recently introduced from a stochastic approach to overcome this drawback. In this talk, we present fundamental mathematics in bayesian deep learning. (* Daehoon Gwak, Dasol Hwang, and Hyunho Lee contributed equally to this study as first authors.)
Subject: Applied Math Abstract Number : SSA8528185232 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180605
Incompressible flows *, , joroh@hallym.ac.kr
Abstract: In this talk, we will consider the incompressible flows on an unbounded domain.
Then we will see very special properties of the solutions of the incompressible flows on an unbounded domain.
As a result we will look at the Euler equations on an unbounded domain.
Subject: Abstract Number : SSA8530145947 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180530
Continued fractions of Lucas numbers Seunghyun Seo*, Kangwon National University, shyunseo@kangwon.ac.kr
Abstract: Given nonnegative integer $n$, let $F_n$ and $L_n$ denote the $n$th Fibonacci and Lucas number.
In 1989, Vajda gave the identity
\begin{align}
\frac{F_{m(r+1)}}{F_{mr}}
=
L_m + \cfrac{(1)^m}{
L_m + \cfrac{(1)^m}{
L_m + \cfrac{(1)^m}{
\ddots + \cfrac{(1)^m}{
L_m}}}},
\end{align}
for positive integer $m$ and $r$, where $L_m$ appears $r$ times.
In this talk, we prove the identity combinatorially, which was asked by Benjamin and Quinn in 2003.
This is joint work Heesung Shin(Inha University).
Subject: Algebra Abstract Number : SSA8601115704 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180601
Analytic real algebras Young Joo Seo*, Daejin University, heekim@hanyang.ac.kr
Abstract: In this talk, we construct some real algebras by using elementary functions and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for realvalued functions to be a dalgebra.
Subject: Algebra Abstract Number : SSA8601140929 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180601
Almost psifuzzy semiideals in groupoids Hee Sik Kim*, Hanyang University, heekim@hanyang.ac.kr
Abstract: In this talk, we introduce the notions of an almost psifuzzy subalgebra and an almost psifuzzy semiideal in groupoids, which are generalizations of a fuzzy subalgebra and a fuzzy ideal, respectively. We generalize several properties related to fuzzy algebraic structures.
Subject: Algebra Abstract Number : SSA8601141614 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180601
An additive double rhofunctional inequality in betahomogeneous Fspaces Sungsik Yun*, Hanshin University, ssyun@hs.ac.kr
Abstract: In this talk, we solve the following additive double $\rho$function inequalities
\begin{eqnarray*}
\begin{split}
& \f(x+y+z)+f(xy)f(z)2f(x)\\\
&\leq\\rho_{1}(f(x+y+z)f(x)f(y)f(z))\+\\rho_{2}(f(x+y+z)f(x+y)f(z))\
\end{split}\end{eqnarray*}
where $\rho_{1},\rho_{2}$ are fixed complex numbers with $2\rho_{1}^{\beta_2}+\rho_{2}^{\beta_2}< 1$, and
\begin{eqnarray*}
\begin{split}
& \f(x+y+z)f(x)f(y)f(z)\\\
&\leq\\rho_{1}(f(x+y+z)+f(xy)f(z)2f(x))\+\\rho_{2}(f(x+y+z)f(x+y)f(z))\,
\end{split}\end{eqnarray*}
where $\rho_{1},\rho_{2}$ are fixed complex numbers with $\rho_{1}^{\beta_2}+\rho_{2}^{\beta_2}< 1$, and prove the HyersUlam stability of the additive double $\rho$functional inequalities in $\beta$homogeneous Fspaces
Subject: Analysis Abstract Number : SSA8601142110 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180601
Setvalued additive functional equations Dong Yun Shin*, University of Seoul, dyshin@uos.ac.kr
Abstract: In this talk, we introduce setvalued additive functional equations and prove the HyersUlam stability of the setvalued additive functional equations by using the fixed point method.
Subject: Analysis Abstract Number : SSA8601142615 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180601
C*ternary Jordan bimultipliers in C*ternary algebras and its applications Jung Rye Lee*, Daejin University, jrlee@daejin.ac.kr
Abstract: In this talk, we use the fixed point method to investigate the
HyersUlam stability of $C^*$ternary bimultipliers and $C^*$ternary Jordan bimultipliers on $C^*$ternary algebras for the following 2dimensional functional equation
$$ f(x+y,z+w)+f(x+y,zw)+f(xy,z+w)+f(xy,zw)=4f(x,z).$$
Subject: Analysis Abstract Number : SSA8601142910 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180601
The superstability of a generalized trigonometric functioal equations Gwang Hui kim*, Kangnam university, ghkim@kangnam.ac.kr
Abstract: In this Talk, we study the superstability of the Wilson (generalized cosine) equation and the sine functional equation from the following generalized difference type cosine functional equation
\begin{align*}
f(x+y) g(xy)=\lambda \cdot h(x)k(y) \;\;\;\; \lambda : constant,
\end{align*}
which $f,g,h,k: V \to A$ can be considered the mixed functional equation of the cosine type functions, and the Wilson type functional equations, $V$ is a vector space and $A$ is a unital normed space.
Subject: Analysis Abstract Number : SSA8602131446 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180602
Introduction to regularity theory for elliptic equations of $p$Laplacian type Jihoon Ok*, Kyung Hee University, jihoonok@khu.ac.kr
Abstract: In this talk, we discuss with basic regularity results for elliptice equations of $p$Laplacian type and related topics.
Subject: Analysis Abstract Number : SSA8604100238 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180604
Lifts of the duadic codes over $Z_{p^e}$ Kwang Ho Kim*, Kangwon National University, prime229@gmail.com
Abstract: Quadratic residue codes are duadic codes when the length is prime. We restrict the length $n$ of the duadic codes to prime. If $p$ and the length $n$ are given, we can find the lifts of them over arbitrary $e$ containing the lifts of quadratic residue codes.
Subject: algebra Abstract Number : SSA8604143813 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180604
Numerical approaches for option pricing under mixed fractional Brownian motion Younhee Lee*, Chungnam National University, lyounhee@cnu.ac.kr Heungsu Choi, Chungnam National University Abstract: In this talk, a mixed fractional Brownian motion (mfBm) is considered to describe longrange dependence in the financial market. We develop numerical methods for pricing European and American options under the mfBm and analyze the stability of these proposed methods. Numerical simulations are carried out to show our analysis results.
Subject: Applied Mathematics Abstract Number : SSA8605110651 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180605
On the wavebreaking phenomena and global existence for the periodic rotationtwocomponent CamassaHolm system Byungsoo Moon*, Incheon National University, bsmoon@inu.ac.kr
Abstract: In this talk, we discuss the periodic rotationtwocomponent CamassaHolm system, which can be derived from the fplane governing equations for the geophysical water waves with a constant underlying current. The nonlocal nonlinearities on blowup criteria and wavebreaking phenomena are established. Finally, a sufficient condition for global solutions is obtained by using a method of the Lyapunov function.
Subject: Analysis Abstract Number : SSA8607164601 [Modifiy] [Delete] (with private passwords) Last Modified Date : 20180607
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