• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.10a
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• pp.157-162
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• 1998

Dynamic loads may arise from rotating parte of pump if they are insufficiently balanced. The magnitude of pump induced vibrations varies according to the weight, eccentricity, and unbalanced mass of pump. This is a study to estimate the pump induced vibration in time and frequency domain by transfer function. The transfer function has real and imaginary information of signals, and response function has also real and imaginary information. So the vibration force can be obtained from the response and transfer function by complex calculation. The amplitudes and components of 50Hp pump vibration force are suggested.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• East Asian mathematical journal
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• v.40 no.1
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• pp.95-107
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• 2024

Let K be an imaginary quadratic field with ring of integers 𝓞_K and N be a positive integer. By K_(N) we mean the ray class field of K modulo N𝓞_K. In this paper, for each prime p of K relatively prime to N𝓞_K we explicitly describe the action of the Artin symbol (${\frac{K_{(N)}/K}{p}}$) on special values of modular functions of level N. Furthermore, we extend the Kronecker congruence relation for the elliptic modular function j to some modular functions of higher level.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.323-326
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• 2015

We prove that if a subfield of the Hilbert class field of an imaginary quadratic field k meets the anticyclotomic $\mathbb{Z}_p$-extension $k^a_{\infty}$ of k, then it is contained in $k^a_{\infty}$. And we give an example of an imaginay quadratic field k with ${\lambda}_3(k^a_{\infty}){\geq}8$.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.317-326
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• 2021

Let K be an imaginary quadratic field other than ℚ(${\sqrt{-1}}$) and ℚ(${\sqrt{-3}}$), and let 𝒪_K be its ring of integers. Let N be a positive integer such that N = 5 or N ≥ 7. In this paper, we generate the ray class field modulo N𝒪_K over K by using a single x-coordinate of an elliptic curve with complex multiplication by 𝒪_K.

• East Asian mathematical journal
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• v.28 no.3
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• pp.333-337
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• 2012

Finiteness of regular normal binary Hermitian lattices are known in several articles. In this article, we point out that there are infinitely many imaginary quadratic fields that admit a regular subnormal binary Hermitian lattice.

• Journal of Periodontal and Implant Science
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• v.45 no.6
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• pp.216-222
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• 2015

Purpose: After extraction, the alveolar bone tends to undergo atrophy in three-dimensions. The amount of alveolar bone loss in the horizontal dimension has been reported to be greater than the amount of bone loss in the vertical dimension, and is most pronounced in the buccal aspect. The aim of this study was to monitor the predictive alveolar bone level following the extraction of anterior teeth seriously involved with advanced chronic periodontitis. Methods: This study included 25 patients with advanced chronic periodontitis, whose maxillary anterior teeth had been extracted due to extensive attachment loss more than one year before the study. Periapical radiographs were analyzed to assess the vertical level of alveolar bone surrounding the edentulous area. An imaginary line connecting the mesial and the distal ends of the alveolar crest facing the adjacent tooth was arbitrarily created. Several representative coordinates were established in the horizontal direction, and the vertical distance from the imaginary line to the alveolar crest was measured at each coordinate for each patient using image analysis software. Regression functions predicting the vertical level of the alveolar bone in the maxillary anterior edentulous area were identified for each patient. Results: The regression functions demonstrated a tendency to converge to parabolic shapes. The predicted maximum distance between the imaginary line and the alveolar bone calculated using the regression function was $1.43{\pm}0.65mm$. No significant differences were found between the expected and actual maximum distances. Likewise, the predicted and actual maximum horizontal distances did not show any significant differences. The distance from the alveolar bone crest to the imaginary lines was not influenced by the mesio-distal spans of the edentulous area. Conclusions: After extraction, the vertical level of the alveolar ridge increased to become closer to the reference line connecting the mesial and distal alveolar crests.

• Journal of Biomedical Engineering Research
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• v.28 no.4
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• pp.520-529
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• 2007

An efficient method for implementing image reconstruction algorithms for Compton cameras is presented. Since Compton scattering formula establishes a cone surface from which the incident photon must have originated, it is crucial to implement a computationally efficient cone-surface integration method for image reconstruction. In this paper we assume that a cone is made up of a series of ellipses (or circles) stacked up one on top of the other. In order to reduce computational burden for tracing ellipses formed by the intersection of a cone and an image plane, we propose a new method using a series of imaginary planes perpendicular to the cone axis so that each plane contains a circle, not an ellipse. In this case the cone surface integral can be performed by simply accumulating the circles along the cone axis. To reduce the computational cost of tracing circles, only one of the circles in the cone is traced and the rest are determined by using simple trigonometric ratios. For our experiments, we used the three different schemes for tracing ellipses; (i) using the samples generated by the ellipse equation, (ii) using the fixed number of samples along a circle on the imaginary plane, and (iii) using the fixed sampling interval along a circle on the imaginary plane. We then compared performance of the above three methods by applying them to the two reconstruction algorithms - the simple back-projection method and the expectation-maximization algorithm. The experimental results demonstrate that our proposed methods (ii) and (iii) using imaginary planes significantly improve reconstruction accuracy as well as computational efficiency.

• Journal of the Korea institute for structural maintenance and inspection
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• v.12 no.1
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• pp.183-192
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• 2008

Generally, application of steel pipe pile as deep foundation member needs special requirement for the connection method between steel pipe pile and concrete footing. Even though two types of connection method are suggested in the korea highway bridge code, type-B method is prevalent. In this study, vertical, lateral, and tension loading test are done for two types of type B connection to review stress concentration, formation and behavior of imaginary RC column in the footing. Welding type and hook type as the connection method are considered in this study. Test results show that welding type have the more reserve capacity than hook type and the specimens connected by the welding type behave as the imaginary RC column in the footing. However, the specimens connected by the hook type did not behave as the imaginary RC column in the footing but behave as the hinge.