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.

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.

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.

Zero-Knowledge Proofs from spLWE-based Commitments

김진수,김두영 영남수학회 2022 East Asian mathematical journal Vol.38 No.1

Recently, an LWE-based commitment scheme is proposed. Their construction is statistically hiding as well as computationally binding. On the other hand, the construction of related zero-knowledge protocols is left as an open problem. In this paper, we present zero-knowledge protocols with hardness based on the LWE problem. we show how to instantiate efficient zero-knowledge protocols that can be used to prove linear and sum relations among these commitments. In addition, we show how the variant of LWE, spLWE problem, can be used to instantiate efficient zero-knowledge protocols.

Research on the Development of College Student Education Based on Machine Learning ---Take the Physical Education of Yanbian University as an Example

Yu Quan,Wei-Jie Guo,Lin He,Zhe-Zhi Jin 영남수학회 2022 East Asian mathematical journal Vol.38 No.1

This paper is based on Yanbian University's physical test data, and uses statistical analysis methods to study the relationship between college students' physical test scores to promote college physical education. Firstly, using gender as categorical variables, we conduct a general analysis of students in different majors and different grades, and obtain the advantages and disadvantages of male and female college students; then we use Decision Trees and Random Forest algorithms to conduct modeling analysis to provide valuable suggestions for relevant departments of the university. the aiming of this research analyzing about the undergraduates physical test is that giving universities the targeted suggestions to improve the college graduate rate and promote the overall development of higher education, lay the foundation for achieving universal health.

초등수학영재를 위한 교수학습 자료 개발 및 적용

김성준,Kim, Sung Joon 영남수학회 2021 East Asian mathematical journal Vol.37 No.4

This study analyzes the characteristics of elementary math gifted classes through the development and application of teaching and learning materials. We used the guided reinvention methods including quasi-experiential perspectives. To this end, the applicability of Lakatos' quasi-empirical mathematical philosophy in elementary mathematics was examined, and the criteria for the development of teaching and learning materials for gifted students were presented, and then this study was conducted in this theoretical background. The subjects of the study were 21 elementary students at P University's Institute of Science and Gifted Education, and non-face-to-face real-time classes were conducted. Classes were divided into introduction, deployment1, deployment2, organization stages, and in each stage, small group cooperative learning was conducted based on group activities, and in this process, the characteristics of elementary mathematics gifted were analyzed. As a result of the study, elementary mathematics gifted students did not clearly present the essence of justification in the addition algorithm of fractions, but presented various interpretations of 'wrong' mathematics. They also showed their ingenuity in the process of spontaneously developing 'wrong' mathematics. On the other hand, by taking interest in new mathematics starting from 'wrong' mathematics, negative perceptions about it could be improved positively. It is expected that the development of teaching and learning materials dealing with various and original topics for the gifted students in elementary school will proceed through follow-up research.

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR A SCHRO ̈DINGER-TYPE SINGULAR FALLING ZERO PROBLEM

고은경 영남수학회 2023 East Asian mathematical journal Vol.39 No.3

Extending \cite{K23}, we establish the existence of multiple positive solutions for a Schr\"odinger-type singular elliptic equation:$$\left\{\begin{array}{rlll}-\Delta u +V(x) u&=&\lambda \frac{ f(u)}{u^\beta}, & x \in\Omega,\\u &=&0, & x \in \partial\Omega,\end{array}\right. $$where $0 \in \Omega$ is a bounded domain in $ \mathbb{R}^N, N\geq 1,$ with a smooth boundary $\partial\Omega,$ $\beta \in [0,1),$$f \in C[0,\infty)$, $V:\Omega \rightarrow \mathbb{R} $ is a bounded function and$\lambda$ is a positive parameter. In particular, when $f (s) >0 $ on $[0, \sigma) $ and $f(s) <0$ for $s > \sigma,$ we establish the existence of at least three positive solutions for a certain range of $\lambda$ byusing the method of sub and supersolutions.

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 $u=0$.

REMARKS ON GROUP EQUATIONS AND ZERO DIVISORS OF TOPOLOGICAL STRUCTURES

김성근 영남수학회 2023 East Asian mathematical journal Vol.39 No.3

The motivation in this paper comes from the recent results about Bell inequalities andtopological insulators from group theory. Symmetries which are interested in group theorycould be mainly used to find material structures. In this point of views, we study group extendingby adding one relator which is easily called an equation. So a relative group extension by a adding relator isaspherical if the natural injection is one-to-one and the group ring has no zero divisor. One of concepts of asphericity means that a new group by a adding relator is well extended. Also, we consider that several equations and relative presentations over torsion-free groups are related to zero divisors.