• The Journal of Korean Association of Computer Education
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• v.7 no.4
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• pp.7-14
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• 2004

Since the science of information is appearing no less important than mathematics and natural science as our society is rapidly becoming information-oriented, the necessity to distinguish prodigies of this field and to educate them as early as possible is also being emphasized. Unfortunately, however, the pertinent study is still in its beginning stage. In this study, I have reviewed the character, definition and method to distinguish prodigies and the procedure of developing a test, as well as researching and analyzing the proper process of distinguishing prodigies, through theoretical contemplation on the method of distinguishing the gifted children. Also, I have characterized and defined the information prodigies after clarifying the character of 'Discrete Mathematics' which becomes the basis of the science of information, paving the way to make a test method that can distinguish those information prodigies. As a result of our applying the system by using the distinction test, it turned out that the distinction test was pretty reliable. Accordingly, it can be utilized as a significant distinction test for information prodigies in the forthcoming future.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• Journal of the Korean Operations Research and Management Science Society
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• v.41 no.3
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• pp.23-36
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• 2016

We consider a model that minimizes the total cost incurred by assigning available weapons to existing targets in order to reduce enemy threats, which is called the weapon target assignment problem (WTAP). This study addresses the stochastic versions of WTAP, in which data, such as the probability of destroying a target, are given randomly (i.e., data are identified with certain probability distributions). For each type of random data or parameter, we provide a stochastic optimization model on the basis of the expected value or scenario enumeration. In particular, when the probabilities of destroying targets depending on weapons are stochastic, we present a stochastic programming formulation with a simple recourse. We show that the stochastic model can be transformed into a deterministic equivalent mixed integer programming model under a certain discrete probability distribution of randomness. We solve the stochastic model to obtain an optimal solution via the mixed integer programming model and compare this solution with that of the deterministic model.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.571-586
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• 2021

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.917-928
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• 2022

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension r^I(M, N) and artinianness dimension a^I(M, N) of M, N with respect to I by r^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not representable} and a^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not artinian} and we show that a^I(M, N) = r^I(M, N) = inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{a^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩_t>0I^tN is artinian we prove that inf{i : H^I_i(M, N) is not minimax}=inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)＼Max(R)}.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.8
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• pp.2473-2489
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• 2022

Urban development has brought about the increasing saturation of urban traffic demand, and traffic congestion has become the primary problem in transportation. Roads are in a state of waiting in line or even congestion, which seriously affects people's enthusiasm and efficiency of travel. This paper mainly studies the discrete domain path planning method based on the flow data. Taking the traffic flow data based on the highway network structure as the research object, this paper uses the deep learning theory technology to complete the path weight determination process, optimizes the path planning algorithm, realizes the vehicle path planning application for the expressway, and carries on the deployment operation in the highway company. The path topology is constructed to transform the actual road information into abstract space that the machine can understand. An appropriate data structure is used for storage, and a path topology based on the modeling background of expressway is constructed to realize the mutual mapping between the two. Experiments show that the proposed method can further reduce the interpolation error, and the interpolation error in the case of random missing is smaller than that in the other two missing modes. In order to improve the real-time performance of vehicle path planning, the association features are selected, the path weights are calculated comprehensively, and the traditional path planning algorithm structure is optimized. It is of great significance for the sustainable development of cities.

• Journal of information and communication convergence engineering
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• v.20 no.2
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• pp.79-89
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• 2022

To compute the mean and variance of component-based reliability software, we focused on path-based reliability analysis. System reliability depends on the transition probabilities of components within a system and reliability of the individual components as basic input parameters. The uncertainty in these parameters is estimated from the test data of the corresponding components and arises from the software architecture, failure behaviors, software growth models etc. Typically, researchers perform Monte Carlo simulations to study uncertainty. Thus, we considered a Markov chain Monte Carlo (MCMC) simulation to calculate uncertainty, as it generates random samples through sequential methods. The MCMC approach determines the input parameters from the probability distribution, and then calculates the average approximate expectations for a reliability estimation. The comparison of different techniques for uncertainty analysis helps in selecting the most suitable technique based on data requirements and reliability measures related to the number of components.

• The Mathematical Education
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• v.63 no.2
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• pp.123-138
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• 2024

This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.

• Journal of the Korean Data Analysis Society
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• v.20 no.6
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• pp.2829-2840
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• 2018

The random variable with an arbitrary value or more is called semi-continuous variable or zero-inflated one in case that its boundary value is more frequently observed than expected. This means the boundary value is likely to be practically observed more than it should be theoretically under certain probability distribution. When the distribution considered is continuous, the variable is defined as semi-continuous and when one of discrete distribution is assumed for the variable, we regard it as zero-inflated. In this study, we introduce the two-part model, which consists of one part for modelling the binary response and the other part for modelling the variable greater than the boundary value. Especially, the zero-inflated regression models are explained by using Poisson distribution and negative binomial distribution. In real data analysis, we employ the zero-inflated regression models to estimate the number of days under extreme heat-wave circumstances during the last 10 years in South Korea. Based on the estimation results, we create prediction maps for the estimated number of days under heat-wave advisory and heat-wave warning by using the universal kriging, which is one of the spatial prediction methods.

• School Mathematics
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• v.16 no.1
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• pp.19-37
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• 2014

This study investigated the degree of understanding pre-service teachers' random variable concept, based on the attention and the importance for developing pre-service teachers' ability on statistical reasoning in statistics education. To accomplish this, the subject of this study was 70 pre-service teachers belonged to three universities respectively. The teachers were given to 7 tasks on random variable and requested to solve them in 40 minutes. The tasks consisted of three contents in large; 1) one was on the definition of random variables, 2) the other was on the understanding of random variables in different/diverse conditions, and 3) another was on problem solving relevant to random variable concept. The findings are as follows. First, while 20% of pre-service teachers understood the definition of random variable correctly, most teachers could not distinguish between random variable and variable or probability. Second, there was a significant difference in understanding random variables in different/diverse conditions. Namely, the degree of understanding on the continuous random variable was superior to that of discrete random variable and also the degree of understanding on the equal distribution was superior to that of unequality distribution. Third, three types of problems relevant to random variable concept dealt with in this study were finding a sample space and an elementary event, and finding a probability value. In result, the teachers responded to the problem on finding a probability value most correctly and on the contrary to this, they had the mot difficulty in solving the problem on finding a sample space.