• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.259-264
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• 2007

In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was mode1ed as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the sealing center and the power function of the radial direction. By use of the mapping type infinite element, the consistent e1ements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.

• The Mathematical Education
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• v.51 no.3
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• pp.211-221
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• 2012

We discovered that definition of a Geometrical Progression(Sequence) have some differences in domestic textbooks & some foreign countries' books. This will be able to cause a chaos when students divide whether a sequence is a Geometrical Progression(Sequence) or not, and a question error when teachers compose questions about convergence conditions of Infinite Geometric progressions & series. We took a question investigation for students about definition of a Geometrical Progression(that is called G. P.), we discovered that high level students have an error about definition of a G. P.. So We modified expressions of terminology in domestic textbooks appropriately through a Geometrical Progression(Sequence), infinite series, & infinite geometrical series in some foreign countries' books.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.152-159
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• 1997

The asymptotic convergence of a coupled dynamic system, which is motivated from infinite dimensional adaptive systems, is investigated. The convergence analysis is formulated in abstract Banch spaces and is shown to applicable to a broad class of infinite dimensional systems including adaptive identification and adaptive control. Particularly it is shown that if a uniquely existing solution is p-th power integrable, then the solution converges to zero asymptotically. The persistence of excitation(PE) of a signal which arises in an infinite dimensional adaptive system is investigated. The PE property is not completely known yet for infinite dimensional adaptive systems, however it should be investigated in relation to spatial variable, boundary conditions as well as time variable.

• Kyungpook Mathematical Journal
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• v.31 no.2
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• pp.193-200
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• 1991

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.25-42
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• 2022

In this paper, we derive analogues of a couple of classes of infinite series identities with the confluent hypergeometric functions involving Dirichlet characters.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.71-80
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• 1989

In this paper, the concept of the infinite element is applied to the linear wave diffraction and radiation problems. The hydrodynamic pressure forces are assumed to be inertially dominated, and viscous effects are neglected. The near field region surrounding the solid body is modelled using the conventional finite elements, and the far field region is represented using the infinite elements .In order to represent the scattered wave potentials in the far field region more accurately, the infinite elements are developed using special shape functions derived from the asymptotic expressions for the analytical eigenseries solution of the scattered waves. The system matrices of the infinite elements are constructed by performing the integration in the infinite direction analytically to achieve computational efficiency. Numerical analyses are carried out for vertical axisymmetric bodies to validate the infinite elements developed here. Comparisons with the results by other available numerical solution methods show that the present method using the infinite elements gives fairly good results. Numerical experiments are per-formed to determine the suitable location of the infinite elements and the appropriate size of the finite elements which directly affect accuracy and efficiency of the solution.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.1-24
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• 2009

In this paper we have inferred the influence of Zeno on the construction of the potential infinite of Aristotle based on arguments of Zeno's paradoxes. When we examine the potential infinite of Aristotle as the basis of the ancient Greek mathematics, we can see that they did not permit the concept of the actual infinite necessary for calculus. The reason Why they recognized the potential infinite, denying the actual infinite as seen in Aristotle's physics could be found in their attempt to escape the illogicality shown in Zeno's arguments. Accordingly, this paper could provided one of reasons why the ancient Greeks had used uneasy exhaustion's method instead of developing the quadrature involving the limit concept.

• Journal of KSNVE
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• v.8 no.5
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• pp.974-980
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• 1998

The analysis of dynamic responses are carried out on several orthotropic systems due to transient line source. These include infinite and semi-infinite spaces. The media possess orthotropic or higher symmetry. The lode is in the form of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for responses of infinite media due to a harmonic line source. Subsequently the results for semi-infinite are derived by using superposition of the solution in the infinite medium together with a scattered solution from the boundaries. The sum of both solutions has to satisfy stress free boundary conditions thereby leading to the complete solutions. Explicit splutions for the displacements due to transient line loads are then obtaind by using Cargniard-DeHoop contour.

• Journal for History of Mathematics
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• v.30 no.6
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• pp.353-365
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• 2017

In general, there is summability among the mathematical tools that are the criterion for the convergence of infinite series. Many authors have studied on the summability of infinite series, the summability of Fourier series and the summability factors. Especially, $H{\ddot{u}}seyin$ Bor had published his important results on these topics from the beginning of 1980 to the end of 1990. In this paper, we investigate the minor academic genealogy of teachers and pupils from Fourier to $H{\ddot{u}}seyin$ Bor in section 2. We introduce the $H{\ddot{u}}seyin$ Bor's major results of the summability for infinite series from 1983 to 1997 in section 3. In conclusion, we summarize his research characteristics and significance on the summability of infinite series. Also, we present the diagrams of $H{\ddot{u}}seyin$ Bor's minor academic genealogy from Fourier to $H{\ddot{u}}seyin$ Bor and minor research lineage on the summability of infinite series.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.53-68
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• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.