• 대한수학회지
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• 제36권2호
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• pp.299-316
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• 1999

We consider two finite difference approxiamations to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is shown that the rates of convergence are O(h) and O($h^2$), respectively. An iterative scheme is introduced which converges to the solution of the finite difference equations. Finally the numerical experiments are given

• 대한수학회지
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• 제41권4호
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• pp.681-715
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• 2004

Mathematical formulation and numerical solutions of an optimal Dirichlet boundary control problem for the Boussinesq equations are considered. The solution of the optimal control problem is obtained by adjusting of the temperature on the boundary. We analyze finite element approximations. A gradient method for the solution of the discrete optimal control problem is presented and analyzed. Finally, the results of some computational experiments are presented.

• 대한수학회지
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• 제57권4호
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• pp.987-1004
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• 2020

Motivated by the traffic flow model with Arrhenius looka-head relaxation dynamics introduced in [25], this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, comparing to other well-known macroscopic traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects.

• 한국해양공학회지
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• 제18권6호
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• pp.22-28
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• 2004

A mathematical model has been developed to evaluate the capability of sea water exchanges under tidal and diffusive environments and has been verified through comparison with numerical experiments. From the mathematical analysis, this study presents the rates of sea water exchanges due to the tidal inflow and diffusion process. The port characteristic length $L_p$ is the most significant evaluation index.

• 대한수학회지
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• 제49권4호
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• 대한수학회지
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• 제59권1호
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• pp.35-51
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• 2022

We give secure parameter suggestions to use sparse secret vectors in LWE based encryption schemes. This should replace existing security parameters, because homomorphic encryption (HE) schemes use quite different variables from the existing parameters. In particular, HE schemes using sparse secrets should be supported by experimental analysis, here we summarize existing attacks to be considered and security levels for each attacks. Based on the analysis and experiments, we compute optimal scaling factors for CKKS.

• 한국수학교육학회지시리즈A:수학교육
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• 제62권4호
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• pp.473-490
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• 2023

국내외 선행연구들에서는 교수실험을 통하여 학생들의 연속적인 변화에 대한 추론 방식에 대한 정보를 축적해가고 있다. 이들 연구에서는 연속적인 변화를 매끄러운 추론과 덩어리 추론을 하는 학생들이 교수실험에서 함께 수학적 결과물을 구성해가는 장면들을 다루고 있는데, 이들의 결과를 보다 세밀하게 분석하기 위해서는 특정 방식으로 연속적인 변화를 추론하는 학생이 이전 선행 연구들에서의 과제들에 대하여 어떠한 결과물을 구성해가는지 확인할 필요가 있다. 이러한 연구의 필요에 따라, 연구자는 덩어리 추론을 하는 것으로 확인된 고등학교 1학년 학생 한 명을 대상으로 총 14차시의 교수실험을 진행하였다. 본 연구에서는 덩어리 추론을 하는 학생이 '이전 선행연구에서 연속적인 변화에 대한 추론 방식이 다양한 학생들이 구성하였던 수학적 결과물'과 유사한 산출물을 구성해가는 장면을 관찰할 수 있었다. 특히 본 연구에 참여한 학생에게서 '시간-거리함수에서 시간-속력함수를 구성하는 일관된 구성 방식'이 관찰되었으며, 이러한 학생의 독특한 구성 방식에 대한 정보가 후속 연구에 도움이 될 것이라 기대하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제20권1호
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• pp.11-19
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• 2016

Investigating students' lived mathematical experiences presents dual challenges for the researcher. On the one hand, we must respect that students' experiences are not directly accessible to us and are likely very different from our own experiences. On the other hand, we might not want to rely upon the students' own characterizations of what constitutes mathematics because these characterizations could be limited to the formal products students learn in school. I suggest a characterization of mathematics as objectified action, which would lead the researcher to focus on students' operations-mental actions organized as objects within structures so that they can be acted upon. Teachers' and researchers' models of these operations and structures can be used as a launching point for understanding students' experiences of mathematics. Teaching experiments and clinical interviews provide a means for the teacher-researcher to infer students' available operations and structures on the basis of their physical activity (including verbalizations) and to begin harmonizing with their mathematical experience.

• Journal of Plant Biotechnology
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• 제2권3호
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• pp.157-163
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• 2000

Optimization of chemicals in the large scale sea water medium and inoculum for biomass and natural colourants production in the marine cyanobacteria, Phomidium tenue BDU 46241 (phycoerythrin producer) and P.valderianum BDU 30501 (phycocyanin producer) was carried out by experiments in L8 orthogonal array. Mathematical analysis revealed the significance of these factors. The factor(s) that critically control the yield varied with the organism and the end-product further, the desirable level of these factors between the normal and a higher level tested was identified and improved media were evolved. In both cyanobacteria, higher level of $K_2$$HPO_4$, $NaNO_3$ and inoculum with normal level of ferric ammonium citrate was found to be desirable for biomass production and additionally, higher level of $MgSO_4$ for pigment production. The level of other factors varied with the organism and the end-product. Confirmation experiments showed that the clues obtained based on mathematical experimentation are valid. In P.tenue, the medium optimized for biomass production increased the yield of biomass by 495% and the medium optimized for phycoerythrin production increased the yield of biomass by 408% with 30% increase in phycoerythrin content of the biomass. Similarly in P.valderianum, the medium optimized for biomass production increased the yield of biomass by 224% and the medium optimized for phycocyanin production increased the yield of biomass by 143% with 44% increase in phycocyanin content of the biomass.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권2호
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• pp.101-126
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• 2007

We analyze the possibilities of using Information and Communication Technologies as a resource in the teaching/learning of Mathematics and we show the results of concrete experiments carried out with the games: "Adibu", "La ciudad perdida" and "Drood en el planeta siete", with fourteen students and two primary school teachers in a school in Santa Cruz de Tenerife (Spain). Our analysis of the games is made within a global framework in which individual, cooperative and collaborative learning are considered, taking as reference the theoretical frameworks set out by Piaget, Vygotsky, and the principles of collaborative learning (Computer Supported Collaborative Learning).