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DOUBLY NONLINEAR PARABOLIC EQUATIONS RELATED TO THE LERAY-LIONS OPERATORS: TIME-DISCRETIZATION
신기연,강수진 영남수학회 2010 East Asian mathematical journal Vol.26 No.3
In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.
정영우,김부윤,김동영,박주형,장민제 영남수학회 2015 East Asian mathematical journal Vol.31 No.4
In this study, we investigated whether the theorem is established even if we replace a ‘square’ element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.
허난 영남수학회 2017 East Asian mathematical journal Vol.33 No.4
This study is a basic study for developing a mathematical learning application program that can be used in smart devices for adaptive learning. We selected 20 mathematical learning applications including middle school contents and analyzed learning types. And we analyzed the contents and the learning process. As a result, most learning types of mathematics learning applications were problem-centered. Contents analysis results showed that the most applications have achievement goals. The factors that induce interest in learning were lacking and feedback was not provided sufficiently. Analysis of the learning process showed that most of the math learning applications were classified according to their purpose and characteristics.
대학 신입생들의 수학 기초학력 평가자료들 간의 상관관계 및 오류 유형 분석
장민우,표용수,Jang, Min Woo,Pyo, Yong-Soo 영남수학회 2016 East Asian mathematical journal Vol.32 No.4
In this paper, we analyzed the correlation among scores of the mathematics B-type grade of College Scholastic Ability Test(CSAT), scores of Mathematics Level Assessment(MLA) and written test scores of Basic Mathematics Subject(BMS) made by students. Especially, we examined the relationship between CSAT grade with results of MLA and results of BMS through survey of students who changed their grades and learned about reasons. In addition, we analyzed error types for the descriptive problem solving in BMS written tests..
Optimality Conditions and Duality in Nondifferentiable Robust Optimization Problems
김문희 영남수학회 2015 East Asian mathematical journal Vol.31 No.3
We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functionsand support functions as its objective function,continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.
Existence of Positive Solutions for Generalized Laplacian Problems with a Parameter
김찬균 영남수학회 2022 East Asian mathematical journal Vol.38 No.1
In this paper, we study singular Dirichlet boundary value problems involving $\varphi$-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity $f=f(u)$ has a positive falling zero and is either superlinear or sublinear at $u=0$.
Optimal Control for Self-organizing Target Detection Model in the 1D Case
유상욱 영남수학회 2022 East Asian mathematical journal Vol.38 No.1
This paper is concerned with the optimal control problem associated to the self-organizing target detection model in 1D domains. That is, we show the global existence of weak solution and the existence of optimal control.
Multiplicity of Positive Solutions to Schr\"odinger-type Positone Problems
고은경 영남수학회 2022 East Asian mathematical journal Vol.38 No.1
We establish multiplicity results for positive solutions to the Schr\"odinger-type singular positone problem:$-\Delta u+V(x)u=\lambda f(u)$ in $ \Omega, ~u=0 $ on $\partial \Omega,$where $\Omega$ is a bounded domain in $ \mathbb{R}^N, N >2, \lambda$ is a positive parameter,$V \in L^\infty(\Omega)$ and $f:[0, \infty) \rightarrow (0, \infty)$ is a continuous function. In particular, when $f$ is sublinear at infinitywe discuss the existence of at least three positive solutions for a certain range of $\lambda$. The proofs are mainly based on the sub- and supersolution method.
홍동화,서보억,박은익,유성훈,최은서 영남수학회 2015 East Asian mathematical journal Vol.31 No.4
While some studies have examined the concave and convex regular polygons respectively, very little work has been done to integrate and restructure polygon shapes. Therefore, this study aims to systematically reclassify the regular polygons on the through a comprehensive analysis of previous studies on the convex and concave regular polygons. For this study, the polygon’s consistency with respect to the number of sides and angles was examined. Second, the consistency on the number of diagonals was also examined. Third, the size of the interior and exterior angels of regular polygons was investigated in order to discover the consistent properties. Fourth, the consistency concerning the area in regular polygons was inspected. Last, the consistency of the central figure number in the “k-th” regular polygons was examined. Given these examinations, this study suggests a way to create a concave regular polygon from a convex regular polygon.
Ore Extensions over $\sigma$-rigid Rings
한준철,이양,심효섭 영남수학회 2022 East Asian mathematical journal Vol.38 No.1
Let $R$ be a ring with an endomorphism $\sigma$ and a $\sigma$-derivation$\delta$. $R$ is called ($\sigma$, $\delta$)-$Baer$(resp. ($\sigma$, $\delta$)-$quasi$-$Baer$, ($\sigma$,$\delta$)-$p.q.$-$Baer$, ($\sigma$, $\delta$)-$p.p.$) if the rightannihilator of every right ($\sigma$, $\delta$)-set (resp.,($\sigma$, $\delta$)-ideal, principal ($\sigma$, $\delta$)-ideal,($\sigma$, $\delta$)-element) of $R$ is generated by an idempotentof $R$. In this paper, for a given Ore extension $A$ = $R[x; \sigma, \delta]$of $R$, the following properties are investigated:If $R$ is a $\sigma$-rigid ringin which $\sigma$ and $\delta$ commute, then(1) $R$ is ($\sigma, \delta)$-Baer if and only if$R$ is ($\sigma, \delta)$-quasi-Baer if and only if $A$ is ($\bar{\sigma},\bar{\delta})$-Baer if and only if $A$ is ($\bar{\sigma},\bar{\delta})$-quasi-Baer;(2) $R$ is ($\sigma, \delta)$-p.p. if and only if$R$ is ($\sigma, \delta)$-$p.q.$-Baer if and only if $A$ is ($\bar{\sigma},\bar{\delta})$-$p.p.$ if and only if $A$ is ($\bar{\sigma},\bar{\delta})$-$p.q.$-Baer.