• The Mathematical Education
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• v.48 no.3
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.679-690
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• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.565-584
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• 2020

The nonlinear thermo-electro-elastic buckling behavior of viscoelastic nanoplates under magnetic field is investigated based on nonlocal elasticity theory. Employing nonlinear strain-displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen's nonlocal elasticity theory considers the effect of small size, which enables the present model to become effective in the analysis and design of nano-sensors and nano actuators. Based on Kelvin-Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the buckling analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small scale effects, elastomeric medium, magnetic field, temperature effects, the viscidity and aspect ratio of the nanoplate on its nonlinear buckling characteristics. It is explicitly shown that the thermo-electro-elastic nonlinear buckling behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates as fundamental elements in nanoelectromechanical systems.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.21 no.5
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• pp.27-33
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• 2011

At FDTC'05 and CISC-W'10, the authors showed that if they decrease the number of rounds of AES and Triple-DES by using the fault injections, it is possible to recover the secret key of the target algorithms, respectively. In this paper, we propose a key recovery attack on HMAC by using the main idea of these attacks. This attack is applicable to HMAC based on MD-family hash functions and can recover the secret key with the negligible computational complexity. Particularly, the attack result on HMAC-SHA-2 is the first known key recovery attack result on this algorithm.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.21 no.5
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• pp.15-25
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• 2011

A differential fault analysis(DFA) is one of the most important side channel attacks on block ciphers. Most block ciphers, such as DES, AES, ARIA, SEED and so on., have been analysed by this attack. In 2008, Wei et al. proposed the first DFA on ARIA-128. Their attack can recover the 128-bit secrey key by about 45 faulty ciphertexts. In this paper, we propose an improved DFA on ARIA-128. We can recover the 12S-bit secret key by only 4 faulty ciphertexts with the computational complexity of O($2^{32}$).

• Journal of information and communication convergence engineering
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• v.20 no.4
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• pp.303-308
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• 2022

Simulating the heat transfer in a composite material is an important topic in material science. Difficulties arise from the fact that adjacent materials cannot match perfectly, resulting in discontinuity in the temperature variables. Although there have been several numerical methods for solving the heat-transfer problem in imperfect contact conditions, the methods known so far are complicated to implement, and the computational times are non-negligible. In this study, we developed a ResNet-type deep neural network for simulating a heat transfer model in a composite material. To train the neural network, we generated datasets by numerically solving the heat-transfer equations with Kapitza thermal resistance conditions. Because datasets involve various configurations of composite materials, our neural networks are robust to the shapes of material-material interfaces. Our algorithm can predict the thermal behavior in real time once the networks are trained. The performance of the proposed neural networks is documented, where the root mean square error (RMSE) and mean absolute error (MAE) are below 2.47E-6, and 7.00E-4, respectively.

• Advances in concrete construction
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• v.13 no.5
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• pp.367-376
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• 2022

Theoretical study of vibration distinctiveness of rotating cylindrical are examined for three volume fraction laws viz.: polynomial, exponential and trigonometric. These laws control functionally graded material composition in the shell radius direction. Functionally graded materials are controlled from two or more materials. In practice functionally graded material comprised of two constituent materials is used to form a cylindrical shell. For the current shell problem stainless steel and nickel are used for the shell structure. A functionally graded cylindrical shell is sanctioned into two types by interchanging order of constituent materials from inner and outer side for Type I and Type II cylindrical shell arrangement. Fabric composition of a functionally graded material in a shell thickness direction is controlled by volume fraction law. Variation of power law exponent brings change in frequency values. Influence of this physical change is investigated to evade future complications. This procedure is capable to cater any boundary condition by changing the axial wave number. But for simplicity, numerical results have been evaluated for clamped- simply supported rotating cylindrical shells. It has been observed from these results that shell frequency is bifurcated into two parts: one is related to the backward wave and other with forward wave. It is concluded that the value of backward frequency is some bit higher than that forward frequency. Influence of volume fraction laws have been examined on shell frequencies. Backward and forward frequency curves for a volume fraction law are upper than those related to two other volume fraction laws. The results generated furnish the evidence regarding applicability of present shell model and also verified by earlier published literature.

• East Asian mathematical journal
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• v.39 no.2
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• pp.93-117
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• 2023

The aim of this study is to explore the pre-service math teachers' characteristics of education to develop their AI literacy and SW competency, and to derive some implications. We conducted a 14-hours AI and SW education program for pre-service teachers with theory and practice, and an analysis on class observation data, video frames of classes and interview, Python programming assignments and papers. The results of this case study for 3 pre-service teachers are as follows. First, two students understood artificial neural network and deep learning system accurately, furthermore, all students conducted a couple of explorations related with performance improvement of deep learning system with interest. Second, coding and exploration activities using Python improved students' computational thinking as well as SW competency, which help them give convergence education in the future. Third, they responded positively to the necessity of AI literacy and SW competency development, and to applying coding to math class. Lastly, it's necessary to endeavor to give a coding education to the student's eye level according to his or her prerequisite and to ease the burden of student's studying AI technology.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.285-301
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• 2022

In this paper, we mainly study the random sampling and reconstruction of signals living in the subspace V^p(𝚽, 𝚲) of L^p(ℝ^d), which is generated by a family of molecules 𝚽 located on a relatively separated subset 𝚲 ⊂ ℝ^d. The space V^p(𝚽, 𝚲) is used to model signals with finite rate of innovation, such as stream of pulses in GPS applications, cellular radio and ultra wide-band communication. The sampling set is independently and randomly drawn from a general probability distribution over ℝ^d. Under some proper conditions for the generators 𝚽 = {𝜙_λ : λ ∈ 𝚲} and the probability density function 𝜌, we first approximate V^p(𝚽, 𝚲) by a finite dimensional subspace V^p_N (𝚽, 𝚲) on any bounded domains. Then, we prove that the random sampling stability holds with high probability for all signals in V^p(𝚽, 𝚲) whose energy concentrate on a cube when the sampling size is large enough. Finally, a reconstruction algorithm based on random samples is given for signals in V^p_N (𝚽, 𝚲).

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.493-500
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• 2023

The multiparameter eigenvalue method can be used to solve the damped finite element model updating problems. This method transforms the original problems into multiparameter eigenvalue problems. Comparing with the numerical methods based on various optimization methods, a big advantage of this method is that it can provide all possible choices of physical parameters. However, when solving the transformed singular multiparameter eigenvalue problem, the proposed method based on the generalised inverse of a singular matrix has some computational challenges and may fail. In this paper, more details on the transformation from the dynamic model updating problem to the multiparameter eigenvalue problem are presented and the structure of the transformed problem is also exposed. Based on this structure, the rigorous mathematical deduction gives the upper bound of the number of possible choices of the physical parameters, which confirms the singularity of the transformed multiparameter eigenvalue problem. More importantly, we present a row and column compression method to overcome the defect of the proposed numerical method based on the generalised inverse of a singular matrix. Also, two numerical experiments are presented to validate the feasibility and effectiveness of our method.