• Kyungpook Mathematical Journal
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• 제52권1호
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• pp.13-20
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• 2012

In a previous paper, the author proved that all odd cycles, except five cycles, are highly Ramsey-infinite. In this paper, we fill in the missing case, and show that five cycles are highly Ramsey-infinite.

• Journal of the Chungcheong Mathematical Society
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• 제24권3호
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• pp.481-502
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• 2011

B. C. Berndt [4, 5] evaluated several classes of infinite series and established many relations between various infinite series. In this paper, continuing his work, we derive new relations between infinite series.

• Bulletin of the Korean Mathematical Society
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• 제60권6호
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• pp.1427-1437
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• 2023

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

• Journal of the Korean School Mathematics Society
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• 제10권2호
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• pp.237-246
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• 2007

According to 7-th curriculum, irrational number should be introduced using non-repeating infinite decimals. A rational number is defined by a number determined by the ratio of some integer p to some non-zero integer q in 7-th grade. In 8-th grade, A number is rational number if and only if it can be expressed as finite decimal or repeating decimal. A irrational number is defined by non-repeating infinite decimal in 9-th grade. There are misconceptions about a non-repeating infinite decimal. Although 1.4532954$\cdots$ is neither a rational number nor a irrational number, many high school students determine 1.4532954$\cdots$ is a irrational number and 0.101001001$\cdots$ is a rational number. The cause of misconceptions is the definition of a irrational number defined by non-repeating infinite decimals. It is a cause of misconception about a irrational number that a irrational number is defined by a non-repeating infinite decimals and the method of using symbol dots in infinite decimal is not defined in text books.

• Journal of Educational Research in Mathematics
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• 제24권4호
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• pp.595-605
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• 2014

Infinite decimals have an infinite number of digits, chosen arbitrary and independently, to the right side of the decimal point. Since infinite decimals are ambiguous numbers impossible to write them down completely, the infinite decimal representation accompanies unavoidable opaqueness. This article focused the transparent aspect of infinite decimal representation with respect to the completeness axiom of real numbers. Long before the formalization of real number concept in $19^{th}$ century, many mathematicians were able to deal with real numbers relying on this transparency of infinite decimal representations. This analysis will contribute to overcome the double discontinuity caused by the different conceptualizations of real numbers in school and academic mathematics.

• KSCE Journal of Civil and Environmental Engineering Research
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• 제26권3A호
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• pp.439-445
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• 2006

Analysis problems of tunnels whose geometrical dimensions are very small compared with surrounding media can be treated as infinite region problems. In such cases, even if finite element models can be applied, excessive number of elements is required to obtain satisfactory accuracy. However, inaccurate results may be produced due to assumed artificial boundary conditions. To solve these problems, a hybrid model, which models the region of interest with finite elements and the surrounding infinite media with infinite elements, is introduced for the analysis of infinite region. Three-dimensional isoparametric infinite elements with various decay characteristics are formulated in this paper and the corresponding parameters are presented by means of parametric studies. Three-dimensional tunnel analysis performed on a representative example verifies the applicability of hybrid model using infinite elements.

• KSCE Journal of Civil and Environmental Engineering Research
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• 제12권4호
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• pp.81-93
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• 1992

Numerical modeling of problems having infinite and semi-infinite boundaries is studied using a coupled method of distinct elements and boundary elements. The regions which are restricted on stress concentration area of loading points, excavation surface, and geometric discontinuity in the underground structures, are modeled using distinct elements, while the infinite and semi-infinite regions are modeled using linear boundary elements. Linear boundary elements for infinite and semi-infinite region are respectively composed using the Kelvin's and the Melan's solution, respectively. For the completeness, the boundary element method, the distinct element, and the coupled method of distinct elements and boundary elements are studied independently. The coupled method is verified and is applied to underground structures of infinite and semi-infinite regions. Through the comparison of the results, it is concluded that the coupled analysis may be used for discontinuous underground structures in the effective manner.

• Communications of Mathematical Education
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• 제34권3호
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• pp.355-372
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• 2020

The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

• Transactions of the Korean Society of Mechanical Engineers
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• 제17권5호
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• pp.1066-1073
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• 1993

Using regular finite elements and infinite elements simultaneously, elastic boundary value problems with infinite domain can be analyzed more effectively and accurately. In this paper, two dimensional infinite elements have been formulated by means of applying the derived mapping function to the coordinates and multiplying the regular displacement shape functions by a decay function. Orders(m, n) of the mapping and decay functions are found for the purpose of obtaining the convergent solutions without respect to the various decay lengthes. As a result of numerical tests for an infinite plate with a hole under internal pressure, two sets of function orders are obtained as follows. (a) n=0, m=1.5 (b) n=m=0.65

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.365-374
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• 2009

Under certain conditions, we use augmented Lagrangians to transform a class of generalized semi-infinite min-max problems into common semi-infinite min-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.