## 2017 °­¿ø°æ±â¼öÇÐÈ¸, ÃæÃ»¼öÇÐÈ¸ °øµ¿ ÇÐ¼ú ´ëÈ¸ ¹× Á¤±âÃÑÈ¸

### ÁÖÃÖ : °­¿ø°æ±â¼öÇÐÈ¸, ÃæÃ»¼öÇÐÈ¸ ÁÖ°ü : ´Ü±¹´ëÇÐ±³ ¼öÇÐ°ú, °íµî°úÇÐ¿ø

1. ÀÏ½Ã : 2017³â 6¿ù 8~10ÀÏ
2. Àå¼Ò : ´Ü±¹´ëÇÐ±³ Ãµ¾ÈÄ·ÆÛ½º »êÇÐÇù·Â°ü
- ±³ÅëÆí ¹× À§Ä¡ Áöµµ

¨ç ±³ÅëÆí : ¿À½Ã´Â ±æ
¨è Campus Map : Ä·ÆÛ½º Áöµµ

3. ÇÐ¼ú´ëÈ¸ÀÏÁ¤ : (ÀÏÁ¤Àº ÇâÈÄ º¯°æµÉ¼ö ÀÖ½À´Ï´Ù.)

(ÇÁ·Î±×·¥ ´Ù¿î·Îµå)

6¿ù 8ÀÏ (¸ñ)
¡Û 15 : 00 ~ 18 : 00 : ´ëÇÑ¼öÇÐÈ¸ ÁöºÎÇÐÈ¸ ¹ßÀü¹æ¾È °£´ãÈ¸

6¿ù 9ÀÏ (±Ý)
¡Û 09 : 00 ~ 16 : 40 : µî    ·Ï
¡Û 09 : 30 ~ 10 : 30 : ºÐ°ú¹ßÇ¥ 1
¡Û 10 : 30 ~ 10 : 40 : ÈÞ  ½Ä
¡Û 10 : 40 ~ 11 : 00 : °³ È¸ ½Ä
¡Û 11 : 00 ~ 11 : 25 : 2016³âµµ °­¿ø°æ±â¼öÇÐÈ¸ ÇÐ¼ú»ó ¼ö»ó°­¿¬ (±è±¤ÈÖ ±³¼ö, °­³²´ëÇÐ±³)
¡Û 11 : 25 ~ 11 : 50 : 2016³âµµ ÃæÃ»¼öÇÐÈ¸ ÇÐ¼ú»ó ¼ö»ó°­¿¬ (¼º¼öÇÐ ±³¼ö, ¹èÀç´ëÇÐ±³)
¡Û 11 : 50 ~ 12 : 00 : »çÁø ÃÔ¿µ
¡Û 12 : 00 ~ 13 : 00 : Á¡½É ½Ä»ç
¡Û 13 : 00 ~ 14 : 00 : ºÐ°ú¹ßÇ¥ 2
¡Û 14 : 00 ~ 14 : 20 : ÈÞ  ½Ä
¡Û 14 : 20 ~ 15 : 20 : ºÐ°ú¹ßÇ¥ 3
¡Û 15 : 20 ~ 15 : 30 : ÈÞ  ½Ä
¡Û 15 : 30 ~ 16 : 10 : ´ëÁß°­¿¬ 1
¡Û 16 : 10 ~ 16 : 50 : ´ëÁß°­¿¬ 2
¡Û 16 : 50 ~ 17 : 00 : ÇÑ±¹¿¬±¸Àç´Ü »ê¾÷¼öÇÐ ½Å±Ô»ç¾÷ ¼³¸í
¡Û 17 : 00 ~ 17 : 10 : ÈÞ  ½Ä
¡Û 17 : 10 ~ 17 : 40 : Á¤±âÃÑÈ¸
¡Û 18 : 00 ~ 21 : 00 : ¿¬  È¸

6¿ù 10ÀÏ (Åä)
¡Û 10 : 00 ~ 12 : 00 : »ê¾÷¼öÇÐ Æ¯º°°­¿¬

4. ±âÅ¸ »çÇ×
¡Û µî·Ïºñ : ±³¼ö (2¸¸¿ø), ´ëÇÐ¿ø»ý(1¸¸¿ø)
¡Û ¸¸ÂùÀå : (TBA)
¡Û ¼÷¼Ò ¿¹¾à ¶Ç´Â ÃÊ·ÏÁ¢¼ö µî ¹®ÀÇ »çÇ×ÀÌ ÀÖÀ¸½Å ºÐÀº ¾Æ·¡ ÇÐ¼ú´ëÈ¸ ÁØºñÀ§¿øÈ¸·Î ¿¬¶ô ÁÖ½Ã±â ¹Ù¶ø´Ï´Ù.

ÇÁ·Î±×·¥ À§¿øÈ¸
±èº´ÇÐ ÆíÁýºÎÈ¸Àå (bhkim@khu.ac.kr),

Á¶Á÷À§¿øÈ¸
¹Ú¿µÈ£ È¸Àå (Chair) (yhpark@kangwon.ac.kr),
ÀÌÁ¤·Ê ºÎÈ¸Àå (jrlee@daejin.ac.kr),
¹Ú»óµ· ÃÑ¹«ÀÌ»ç (sdpark@hknu.ac.kr),

Manager for this system:
Deok-Kyu Jang (Journal Manager) kkms@kangwon.ac.kr

## µî·ÏµÈ ÃÊ·Ï Tentative Abstracts

• A finite element dual singular function method to solve the Stokes equations including corner singularities
Jae-Hong Pyo*, Kangwon National University, jhpyo@kangwon.ac.kr

Abstract: The finite element dual singular function method [FE-DSFM] has been constructed and analyzed accuracy by Z. Cai and S. Kim to solve the Laplace equation on a polygonal domain with one reentrant corner. In this paper, we impose FE-DSFM to solve the Stokes equations via the mixed finite element method. To do this, we compute the singular and the dual singular functions analytically at a non-convex corner. We prove well-posedness by using the contraction mapping theorem and then estimate errors of the algorithm. We obtain optimal accuracy $O(h)$ for velocity in ${\bf{H}}^1(\Omega)$ and pressure in $L^2(\Omega)$, but we are able to prove only $O(h^{1+\lambda})$ error bounds for velocity in $L^2(\Omega)$ and stress intensity factor, where $\lambda$ is the eigenvalue. However, we get optimal accuracy results in numerical experiments.

Subject: Applied Math
Abstract Number : SS-A8-502173401 [Modifiy] [Delete] (with private passwords)

• Infinitely many solutions for a class of the elliptic systems
Tacksun Jung*, Kunsan National University, tsjung@kunsan.ac.kr
Q-Heung Choi, Inha University
Abstract: We get a result that shows the existence of infinitely many solutions for a class of the elliptic systems involving subcritical Sobolev exponents nonlinear terms with even functionals on the bounded domain with smooth boundary. We get this result by variational method and critical point theory induced from invariant subspaces and invariant functional.

Subject: Analysis
Abstract Number : SS-A8-503120617 [Modifiy] [Delete] (with private passwords)

• Codes over rings
Young Ho Park*, Kangwon National University, yhpark@kangwon.ac.kr

Abstract: Codes were originally defined over the field of two elements. Later some binary codes were shown to be Gray images of "linear" codes over the ring of integers modulo 4. Since then, codes over rings have been studied by many authors. We introduce the "right" codes over rings to use the powerful machinery of algebraic codes. We also explain the p-adic codes and their projections to integers modulo powers of p, and their generalization to q-adic codes, if time permits.

Subject: algebra
Abstract Number : SS-A8-508140216 [Modifiy] [Delete] (with private passwords)

• Bishop-Phelps-Bollobas property
Sun Kwang Kim*, Kyonggi University, lineksk@gmail.com
Han Ju Lee, Dongguk University, Miguel Martin, University of Granada
Abstract: In 1963, Lindenstrauss studied extensions of the Bishop-Phelps theorem to the vector-valued case which is the starting point of norm attaining operators theory. In 2008, Acosta, Aron, Garc\'{i}a and Maestre started the study of vector-valued versions of the Bishop-Phelps-Bollob\'{a}s theorem. This is called now a days Bishop-Phelps-Bollob\'{a}s property. In this talk, we introduce some results on this topic and possible extension to other mappings.

Subject: Analysis
Abstract Number : SS-A8-511165830 [Modifiy] [Delete] (with private passwords)

• Steady state positive solution to population model with competition
Joon Hyuk Kang*, Andrews University, kang@andrews.edu

Abstract: We investigate mathematical conditions to guarantee the existence and uniqueness of positive solutions to a general elliptic mathematical model.
This result generalizes the existence and uniqueness of positive steady state solutions to a Lotka-Volterra competition model with homogeneous boundary conditions for two species of animals competing in the same environment. Under what conditions do they coexist peacefully? It is natural to say that they can coexist peacefully if their reproduction rates and self-limitation rates are relatively larger than those of competition rates. In other words, they can survive if they interacts strongly among themselves and weakly with others.

Subject: Applied Math
Abstract Number : SS-A8-511222237 [Modifiy] [Delete] (with private passwords)

• Rectifying space-like submanifolds in Pseudo-Euclidean spaces
Yun Myung Oh*, Andrews University, ohy@andrews.edu
Bang-Yen Chen, Michigan State University
Abstract: Rectifying subspace and rectifying submanifold were defined by Bang-Yen Chen in 2016 [Int. Electron. J. Geom. 9] and he obtained several fundamental properties of rectifying submanifold in Euclidean space. In this talk, further results will be discussed for the rectifying space-like submanifolds in Pseudo-Euclidean spaces with codimension greater one.

Subject: Geometry
Abstract Number : SS-A8-511233004 [Modifiy] [Delete] (with private passwords)

• The structural and spectral properties of Riordan graphs
Seyed Ahmad Mojallal*, Applied Algebra and Optimization Research Center, Sungkyunkwan University, Suwon 16419, Rep. of Kore, mojallal@skku.edu
Gi-Sang Cheon, Sungkyunkwan University
Abstract: Riordan arrays are infinite lower triangular matrices defined by two generating functions [L. V. Shapiro, S. Getu, W. J. Woan, L. Woodson, The Riordan group, Discrete Appl. Math. 34 (1991) 229--239]. Considering an $n \times n$ Riordan matrix in modulo two, we define Riordan graph $RG_n$ of order $n$. In this talk, we study some structural and spectral invariants of Riordan graphs.

Subject: Linear Algebra
Abstract Number : SS-A8-515162030 [Modifiy] [Delete] (with private passwords)

• The classification of self-dual codes over Galois rings
Whan-Hyuk Choi*, Gangwon Natl' University., whanhyuk@gmail.com

Abstract: We classify the self-dual codes of length 4 over Galois rings $GR(p^2,1)$, $GR(p,2)$ and $GR(p^2,2)$ for all primes $p$ up to equivalence in terms of their automorphism groups and obtain the necessary and sufficient conditions for existence of each classes. We also obtain the number of inequivalent classes for all primes.

Subject: Coding theory
Abstract Number : SS-A8-516134603 [Modifiy] [Delete] (with private passwords)

• A Case Study of College Math Courses with Self-Directed Team Learning
Sook Min*, Yonsei University at Wonju, sookmin@yonsei.ac.kr

Abstract: This study aims to find the pedagogical utility and educational impact of self-directed learning method in the context of basic undergraduate calculus courses. A total of 133 engineering and science majoring students participated in the 16-week long class study administered in self-directed learning teaching styles in Spring 2015. Three major forms of self-directed teaching format were utilized: (1) a self-chosen syllabus, (2) self-engaged group problem solving, and (3) self-directed team projects. The qualitative analysis of students' final reports demonstrated that students experienced a high level of successful mastery experience in math, an ample opportunities of interactive vicarious learning, and a good amount of positive social influence from their classmates. Implications and future directions for the practice of self-directed learning on math education are discussed.

Subject: Math Education
Abstract Number : SS-A8-516171228 [Modifiy] [Delete] (with private passwords)

• Integral transform and generalized convolution product for functionals on Wiener space
Byoung Soo Kim*, School of Liberal Arts, Seoul National University of Technology, Seoul 01811, Korea, mathkbs@seoultech.ac.kr
Il Yoo, Department of Mathematics, Yonsei University, Wonju 26493, Korea, iyoo@yonsei.ac.kr
Abstract: In 1982, Lee defined an integral transform ${\mathcal F}_{\gamma,\eta}$ of analytic functionals on an abstract Wiener space. For certain values of the parameter $\gamma$ and $\eta$ and for certain classes of functionals, the Fourier-Wiener transform, the Fourier-Feynman transform, and the Gauss transform are special cases of his integral transform ${\mathcal F}_{\gamma,\eta}$. We introduce a generalized convolution product $(F*G)_{\vec\alpha,\vec\beta}$ for integral transform ${\mathcal F}_{\gamma,\eta}$ for functionals defined on $K[0,T]$. We study some interesting properties of the generalized convolution product. In particular we give a necessary and sufficient conditions for the generalized convolution product to be commutative. We also study an associativity result of the generalized convolution product.

Subject: Analysis
Abstract Number : SS-A8-517105004 [Modifiy] [Delete] (with private passwords)

• Weighted $L_{p,q}$-estimates for higher order parabolic systems
Jongkeun Choi*, Korea University, jkchoi2749@gmail.com
Doyoon Kim, Korea University
Abstract: We prove weighted $L_{p,q}$-estimates for divergence type higher order elliptic and parabolic systems with irregular coefficients on Reifenberg flat domains.
In particular, in the parabolic case the coefficients do not have any regularity assumptions in the time variable.
As functions of the spatial variables, the leading coefficients are permitted to have small mean oscillations.
The weights are in the class of Muckenhoupt weights $A_p$.

Subject: Analysis
Abstract Number : SS-A8-517133227 [Modifiy] [Delete] (with private passwords)

• Superconvergence of finite element methods and its application
Kwang-Yeon Kim*, Kangwon National University, eulerkim@kangwon.ac.kr

Abstract: In this talk we discuss some superconvergence results for the continuous finite element approximation $u_h$ of second order elliptic equations on uniform and mildly structured meshes. Based on the superconvergence analysis of Bank and Xu in 2003, we first present some key identities for the standard nodal interpolant $u_I$ of the exact solution $u$. Then, by combining these identities with the properties of uniform and mildly structured meshes, we establish the super-closeness between $u_h$ and $u_I$ with respect to the $H^1$ norm. As an application of this super-closeness, we show that a simple averaging of the discrete gradient $\nabla u_h$ can give a superconvergent approximation to $\nabla u$ and prove the asymptotic exactness of some a posteriori error estimators based on this gradient recovery.

Subject: Applied Math
Abstract Number : SS-A8-517141731 [Modifiy] [Delete] (with private passwords)

• Horizontal and Vertical Formulas for Exponential Riordan Matrix
Ji-Hwan Jung*, Sungkyunkwan University, jh56k@skku.edu
Gi-Sang Cheon, Sungkyunkwan University, Paul Barry, School of Science Waterford Institute of Technology
Abstract: In this talk, we show that an infinite lower triangular matrix $R=[r_{ij}]_{i,j\in\mathbb{N}_0}$ is an exponential Riordan matrix $R=\mathcal {E}(g,f)$ given by $\sum_{i\ge j}r_{ij}{z^i/i!}=gf^j/j!$ if and only if there exist both horizontal pair $\{h_n;\tilde{h}_{n}\}_{n\ge0}$ and vertical pair $\{v_n;\tilde{v}_{n}\}_{n\ge0}$ of the sequences such that
\begin{eqnarray*}
\end{eqnarray*}
and
\begin{eqnarray*}
\end{eqnarray*}
where $x^{\overline n}$ and $x^{\underline n}$ are the rising and falling factorials of $x\ge0$ defined by
\begin{eqnarray*}
x^{\overline n}=x(x+1)\cdots(x+n-1)\;\;{\rm and}\;\; x^{\underline n}=x(x-1)\cdots(x-n+1),\quad n\ge1
\end{eqnarray*}
with $x^{\overline 0}=x^{\underline 0}=1$. Applying this result, we obtain that if the horizontal and vertical pairs of an exponential Riordan matrix are identical then the matrix is involution. In addition, this concept can be applied to obtain the determinants of the Hessenberg matrices and some conditions for $d$-orthogonality of the Sheffer polynomial sequences.

Subject: Algebra
Abstract Number : SS-A8-517155512 [Modifiy] [Delete] (with private passwords)

• Multi-dimensional orthogonal polynomials and the support of the measure
Hyun Jae Yoo*, Hankyong National University, yoohj@hknu.ac.kr
Ameur Dhahri, Chungbuk National University, Nobuaki Obata, Tohoku University
Abstract: In this talk we discuss the multi-dimensional orthogonal polynomials for probability measures. Our point is to look at the theory by using quantum probability. By introducing the creation, annihilation, and preservation operators (CAP operators), we develop interacting Fock space and thereby the coordinate variables, which are understood as multiplication operators, are decomposed into the sum of CAP operators. We investigate the support of the measure by using the concept of deficiency rank for the Jacobi operators. This is a joint work with Ameur Dhahri and Nobuaki Obata.

Subject: Analysis
Abstract Number : SS-A8-517161524 [Modifiy] [Delete] (with private passwords)

• Vanishing theorems of the basic harmonic forms on a complete foliated manifold
Seoung Dal Jung*, Jeju National University, sdjung@jejunu.ac.kr

Abstract: On a compact foliated Riemannian manifold, it is well known that there are no nontrivial basic harmonic forms by M. Min-Oo et al. In this talk, we extend this results to a complete foliated Riemannian manifold. That is, on a foliated manifold whose all leaves are compact and the mean curvature is bounded, if the curvature endomorphism is positive-definite, then any basic harmonic forms with a finite global norm are trivial.

Subject: Geometry
Abstract Number : SS-A8-518162856 [Modifiy] [Delete] (with private passwords)

• A measurable function over continuous paths similar to the Paley-Wiener-Zygmund integral
Cho, Dong Hyun *, Kyonggi University, j94385@kyonggi.ac.kr
Ma, Yong-Ki, Kongju National University
Abstract: Let $C[0,T]$ denote the space of continuous real-valued functions on the interval $[0,T]$. On the space $C[0,T]$ we introduce a finite measure $w_{\alpha,\beta;\varphi}$ and investigate its properties, where $\varphi$ is arbitrary finite initial measure on $(\mathbb R, \mathcal B(\mathbb R))$. Using this finite measure $w_{\alpha,\beta;\varphi}$ we also introduce a measurable function on $C[0,T]$ which is similar to the Paley-Wiener-Zygmund integral on the generalized analogue of Wiener space. As applications we introduce a Banach algebra which corresponds the Cameron-Storvick's Banach algebra $\mathcal S$ on the classical Wiener space. We note that if $\varphi(\mathbb R)=1$, then $w_{\alpha,\beta;\varphi}$ is a probability measure with the mean function $\alpha$ and the variance function $\beta$, and that the measurable function is the Paley-Wiener-Zygmund integral on the analogue of Wiener space $C[0,T]$.

Subject: Analysis
Abstract Number : SS-A8-518175401 [Modifiy] [Delete] (with private passwords)

• The mass formula of self-orthogonal codes over GF(q)
Kwang Ho Kim*, Kangwon National University, prime229@gmail.com

Abstract: There exists already mass formula which is the number of self orthogonal codes in $GF(q)^n$, but not proof of it. We describe some theories about finite geometry and by using them proved the mass formula when $q = p^m$, $p$ is odd prime.

Abstract Number : SS-A8-518205007 [Modifiy] [Delete] (with private passwords)

• Numerical simulation of a shear-flow instability with surface tension
Suyeon Shin*, Korea University, angelic52@korea.ac.kr
Sung-Ik Sohn, Gangneung-Wonju National University, Woonjae Hwang, Korea University.
Abstract: One of the most well known instabilities in fluid mechanics is the instability at the interface between parallel shear flow of different velocities, which is called Kelvin-Helmholtz instability. When surface tension is present on the interface, numerical computation is not an easy talk, due to the aliasing instability. We develop a stable numerical method by using the vortex sheet model and present long-time evolutions of the Kelvin-Helmholtz instability with surface tension and density jump. A variety of interesting behaviors by the interaction of singularity and surface tension will be demonstrated.

Subject: Applied Math
Abstract Number : SS-A8-520140204 [Modifiy] [Delete] (with private passwords)

• Numerical Analysis of the Helmholtz Equation on an Annnular Domain
June Gi Kim*, Kangwon National University, junekim@kangwon.ac.kr

Abstract: We construct generalize usual basis functions for numerical approximation of the Helmholtz equations on an annular domain. The basis functions constructed in the way
catch the symmetries of the domain and the fundamental solutions of the Helmholtz equation and give effective approach in calculating complex eigenvalues of the equation.

Subject: Applied Math
Abstract Number : SS-A8-522101216 [Modifiy] [Delete] (with private passwords)

• On the 2nd order mock theta functions
Soon-Yi Kang*, Kangwon National University, sy2kang@kangwon.ac.kr

Abstract: We compute shadows of the second order mock theta functions and show that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. We further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

Subject: Algebra
Abstract Number : SS-A8-522150803 [Modifiy] [Delete] (with private passwords)

• Some characterizations of real hypersurfaces in complex Grassmannians with rank two
Hyunjin Lee*, Kyungpook National University, lhjibis@hanmail.net
Young Jin Suh, Kyungpook National University
Abstract: A main objective in submanifold geometry is the classification of homogeneous hypersurfaces arise as principal orbits of cohmogeneity one actions, and so their classification is equivalent to the classification of cohomogeneity one actions up to orbit equivalence. Actually, the classifications of cohomogeneity one actions in irreducible simply connceted Riemannian symmetric spaces of rank~$2$ of (non)compact type was obtained by J. Berndt and Y.J. Suh for complex two-plane Grassmannians~$SU_{2+m}/S(U_{2}U_{m})$ and complex hyperbolic two-plane Grassmannians~$SU_{2,m}/S(U_{2}U_{m})$. From these classifications, in (Suh, Adv. Appl. Math. 50, 645-659, 2013) Suh classified real hypersurfaces with isometric Reeb flow in $SU_{2,m}/S(U_{2}U_{m})$, $m \geq 3$. Each one can be described as a tube over a totally geodesic $SU_{2,m-1}/S(U_{2}U_{m-1})$ in $SU_{2,m}/S(U_{2}U_{m})$ or a horosphere whose center at infinity is singular. By using this result, we want to give another characterization for these model spaces with respect to the derivatives of (1,1) type tensor on real hypersurfaces in complex Grassmannians with rank two.

Subject: Geometry
Abstract Number : SS-A8-523092611 [Modifiy] [Delete] (with private passwords)

• Enumerations of vertices among all rooted ordered trees with levels and degrees
Seunghyun Seo*, Kangwon National University, shyunseo@kangwon.ac.kr
Sen-Peng Eu, National Taiwan Normal University, Heesung Shin, Inha University
Abstract: In this talk, we enumerate the cardinalities and give bijections for the following four sets of vertices among all rooted ordered trees of a fixed size: (i) all first children of degree $k$ at level $\ell$, (ii) all non-first children of degree $k$ at level $\ell-1$, (iii) all leaves having $k-1$ elder siblings at level $\ell$, and (iv) all non-leaves of outdegree $k$ at level $\ell-1$. Our results unite and generalize several previous works in the literature.

Subject: Algebra
Abstract Number : SS-A8-526113041 [Modifiy] [Delete] (with private passwords)

• A study on application of GeoGebra in high school mathematics course
Seon Min Baek*, Kyung Hee University, selenbaek@naver.com
Kyungsoo Kim, Kyung Hee University
Abstract: Recently, it is recommended to use engineering tools in mathematics education
in order to enhance student understanding by visualizing fundamental concepts and corresponding figures. In this study, the GeoGebra was utilized to develop a teaching-learning guidance for high school mathematics course. A class worksheet for definite integral with the GeoGebra was designed as a case study.

Subject: Math Education
Abstract Number : SS-A8-526194225 [Modifiy] [Delete] (with private passwords)

• Application of principal component analysis and support vector machine to data sets with weak correlation
Yunkyung Park*, Kyung Hee University, marion25@naver.com
Kyungsoo Kim, Kyung Hee University
Abstract: The principal component analysis (PCA) and the support vector machine (SVM) are widely used data analysis tools. In this study, these data analysis tools were applied to investigate the relationship between two data sets that have weak or no correlation. The data sets were the grade point averages and academic satisfaction scores of 222 university students in six groups.

Abstract Number : SS-A8-526194350 [Modifiy] [Delete] (with private passwords)

• Some additive $rho$-functional inequalities and applications
Choonkil Park*, Hanyang University, baak@hanyang.ac.kr
Jung Rye Lee, Daejin University
Abstract: In this talk, we solve the additive $\rho$-functional inequalities
\begin{eqnarray} \|f(x+y+z)- f(x)-f(y)- f(z)\| \le \left\|\rho\left(2 f\left(\frac{x+y}{2}+z \right)-f(x) - f(y)- 2f(z) \right)\right\|,
\end{eqnarray}
where $\rho$ is a fixed complex number with $|\rho|<1$, and
\begin{eqnarray}
\left\|2 f\left(\frac{x+y}{2}+z \right)-f(x) - f(y)- 2f(z)\right\| \le \|\rho(f(x+y+z)- f(x)-f(y)- f(z))\| ,
\end{eqnarray}
where $\rho$ is a fixed complex number with $|\rho|<1$.

Furthermore, we prove the Hyers-Ulam stability of the above additive $\rho$-functional inequalities in complex Banach spaces. This is applied to investigate homomorphisms in $C^*$-algebras, Lie $C^*$-algebras and $JC^*$-algebras, and derivations on $C^*$-algebras, Lie $C^*$-algebras and $JC^*$-algebras associated with the above additive $\rho$-functional inequalities.

Subject: Analysis
Abstract Number : SS-A8-527050720 [Modifiy] [Delete] (with private passwords)

• Cauchy-Jensen $rho$-functional inequalities
Eun Hwa Shim*, Hanyang University, stareun01@nate.com
Choonkil Park, Hanyang University
Abstract: In this talk, we solve the additive $\rho$-functional inequalitie
\begin{eqnarray}
\|f(x+y)-f(x) -f(y)\| \le \left\|\rho \left(2f\left(\frac{x+y}{2}\right)- f(x) - f(y)\right)\right\| ,
\end{eqnarray}
where $\rho$ is a fixed complex number with $|\rho|<1$, and
\begin{eqnarray}
\left\|2f\left(\frac{x+y}{2}\right)- f(x) - f(y) \right\| \le \left\|\rho\left(f(x+y)-f(x)-f(y)\right)\right\| ,
\end{eqnarray}
where $\rho$ is a fixed complex number with $|\rho|<1$.

Furthermore, we prove the Hyers-Ulam stability of the above additive $\rho$-functional inequalities in complex Banach spaces.

Abstract Number : SS-A8-527051231 [Modifiy] [Delete] (with private passwords)

• Analytic real algebras
Young Joo Seo *, Hanyang University, bejesus@hanyang.ac.kr
Hee Sik kim,Hanyang University
Abstract: In this paper we construct some real algebras by using<br />
elementary functions, and discuss some relations between<br />
several axioms and its related conditions for such functions.<br />
We obtain some conditions for real-valued functions to<br />
be a (edge) d-algebra.

Abstract Number : SS-A8-527085334 [Modifiy] [Delete] (with private passwords)

• Hyperstability and stability of a functional equation with four vaiables
Kim, Gwang Hui*, Kangnam University, ghkim@kangnam.ac.kr

Abstract: The superstability of the cosine functional equation (d'Alembert), Wilson equation, trigonometric equation
$f(x+y) \pm f(x-y) = 2f(x)g(y)$, and the sine functional equation $f(\frac{x+y}{2})^2 \pm f(\frac{x-y}{2})^2 = f(x)f(y)$ in two vaiables is investigated.
As extension to four variables, we considered stability of the equation $f(pr, qs) + f(ps, qr) = f(p,q) f(r, s)$,$f(pr, qs) + f(ps, qr) = \theta(pq, rs) f(p,q)\, f(r, s)$ : $\theta$ a cocycle,
$f(pr, qs) + f(ps, qr) = \theta(p,q,r,s) f(p,q)\, f(r, s)$ : $\theta$ a mapping,
which is related to distance measure.
We can consider the logarithm-type functional equation
$f(pr, qs)+f(ps, qr)=2f(p,q)+2f(r,s)$.

In this paper, we investigate the hyperstability and stability of the above functional equation as follows :
if f satisfies a stability inequality for the above equation then it is also a solution of this equation
or we can find an another solution of it which has the small error bound.

Subject: Analysis
Abstract Number : SS-A8-529183344 [Modifiy] [Delete] (with private passwords)