• 한국학교수학회논문집
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• 제22권1호
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• pp.81-94
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• 2019

본 연구에서는 수학교수학습에서 CAS를 활용이 갖는 의미와 CAS의 도입으로 야기된 수학 교수 학습 상의 변화를 살펴보고, 이에 따라 변화하게 되는 평가의 방향을 논하였다. 특히, CAS를 도입했을 때 평가 문항의 몇 가지 분류에 대해 고찰하고 대안적 평가 방향을 제시한 후 그것이 갖는 의미를 논하였다.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.541-553
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• 2012

In this paper, we study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain on the generalized gambling system indexed by a tree by constructing a nonnegative martingale. As corollary, we obtain the property of the harmonic mean and the arithmetic mean of random transition probability for a second-order nonhomogeneous Markov chain indexed by a double root tree.

• 대한수학회논문집
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• 제16권3호
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• pp.519-541
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• 2001

Magnetic Resonance Electrical Impedance Tomography(MREIT) is a new medical imaging technique for the cross-sectional conductivity distribution of a human body using both EIT(Electrical Impedance Tomography) and MRI(Magnetic Resonance Imaging) system. MREIT system was designed to enhance EIT imaging system which has inherent low sensitivity of boundary measurements to any changes of internal tissue conductivity values. MREIT utilizes a recent CDI (Current Density Imaging) technique of measuring the internal current density by means of MRI technique. In this paper, a mathematical modeling for MREIT and image reconstruction method called the alternating J-substitution algorithm are presented. Computer simulations show that the alternating J-substitution algorithm provides accurate high-resolution conductivity images.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• International Journal of Computer Science & Network Security
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• 제23권2호
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• pp.55-64
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• 2023

The travelling salesman problem (TSP) is an important combinatorial optimization problem that is used in several engineering science branches and has drawn interest to several researchers and scientists. In this problem, a salesman from an arbitrary node, called the warehouse, starts moving and returns to the warehouse after visiting n clients, given that each client is visited only once. The objective in this problem is to find the route with the least cost to the salesman. In this study, a meta-based ant colony system algorithm (ACSA) is suggested to find solution to the TSP that does not use local pheromone update. This algorithm uses the global pheromone update and new heuristic information. Further, pheromone evaporation coefficients are used in search space of the problem as diversification. This modification allows the algorithm to escape local optimization points as much as possible. In addition, 3-opt local search is used as an intensification mechanism for more quality. The effectiveness of the suggested algorithm is assessed on a several standard problem instances. The results show the power of the suggested algorithm which could find quality solutions with a small gap, between obtained solution and optimal solution, of 1%. Additionally, the results in contrast with other algorithms show the appropriate quality of competitiveness of our proposed ACSA.

• 한국수학사학회지
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• 제24권3호
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• pp.37-58
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• 2011

수리 논리학의 발전은 상당 부분 힐버트 (D. Hilbert, 1862~1943)의 증명이론(Beweistheorie)에 뿌리를 두고 있다. 흔히 '힐버트 계획' (Hilbert's program)으로 불리는 이 계획의 목표는 형식적 공리론적 방법에 의해 수학의 모든 명제와 증명을 형식화하고 이 형식 체계의 완비성과 무모순성 증명을 통해 고전 수학을 '구원' 하고, 수학의 토대를 공고히 하자는 데에 있다. 1931년 괴델의 제 1정리에 의해 결정불가능 명제의 존재가 드러나면서 완전성이 위기를 맞고, 제 2정리에 의해 무모순성의 확립이 무산될 위기에 처한다. 그러나 '상대적' 내지 '부분적' 힐버트 계획은 효과적인 연구 프로그램으로서 살아 있다고 말하는 학자들이 적지 않다. 우리는 특히 힐버트 계획 이 오늘날 구성주의 수학의 발전에 동력을 제공하고 있다는 점을 커리-하워드 대응 (Curry-Howard Correspondence)을 통하여 부각시키고자 했다. 자연연역에서 증명 (proof) 이 바로 컴퓨터 프로그램 (computer program) 에 다름 아니라는 사실에 의해 수학의 형식화 (formalization)는 새로운 조명을 받게 된 것이다. 요컨대 힐버트 계획은 컴퓨터 과학에서 알고리듬 (algorithm) 이라는 핵심개념에 가장 잘 부합되는 것이다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권11호
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• pp.5324-5337
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• 2017

In this paper, we investigate the feasibility of interference alignment(IA) in signal space in the scenario of multiple cell and multiple user cellular networks, as the feasibility issue is closely related to the solvability of a multivariate polynomial system, we give the mathematical analysis to support the constraint condition obtained from the polynomial equations with the tools of algebraic geometry, and a new distribute IA algorithm is also provided to verify the accessibility of the constraint condition for symmetric system in this paper. Simulation results illustrate that the accessibility of the constraint condition is hold if and only if the degree of freedom(DoF) of each user can be divided by both the transmit and receive antenna numbers.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.245-252
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• 1996

We described a relationship of the $L_2$ norm of the $L_2$norm of a Bzier curve and l2 norm of its confrol points. The use of Bezier curves finds much application in the general description of curves and surfaces and provided the mathematical basis for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for the $L_2$ norm with respect to the $L_2$ norm for its control points for easy computation.

• Journal of Communications and Networks
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• 제16권4호
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• pp.415-420
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• 2014

Since the day the Internet became a common and reliable mechanism for communication and data transfer, security officers and enthusiasts rallied to enforce security standards on data transported over the globe. Whenever a user tries communicating with another recipient on the Internet, vital information is sent over different networks until the information is dropped, intercepted, or normally reaches the recipient. Critical information traversing networks is usually encrypted. In order to conceal the sender's identity, different implementations have proven successful - one of which is the invention of anonymous networks. This paper thoroughly investigates one of the most common and existing techniques used during data communication for avoiding traffic analysis as well as assuring data integrity - the onion router (TOR). The paper also scrupulously presents the benefits and drawbacks of TOR.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.157-162
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• 2019

Programming tools are essential for students learning numerical analysis. It is troublesome to go to a laboratory where a computer is located after taking a lecture. Nowadays most students have mobile phones which can be used for programming practice through the Internet. PHP is a server-side scripting language designed for web development but also used as a general-purpose programming language. However, PHP has many inconveniences, such as adding a dollar symbol ($) to every varable. This paper introduces a slightly modified language, NAPHP, and a system which is designed for students to use their own mobile phone to write down the language NAPHP and run it on the web page. The system NAPHP-SYS is an educational tool that turns NAPHP into PHP, run PHP code and show the results on the web.