• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.571-574
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• 2000

A complex coefficient filter obtained by directly exchanging several reactance elements included in a real coefficient, filter for imaginary valued resistors is described. By using the proposed method, four varieties of complex coefficient filter are obtained. The stability problem is described. Finally, the frequency responses of the proposed kiters are shown.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.91-95
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• 2012

In this paper, we show how to construct the first layer $k^{\alpha}_{1}$ of anti-cyclotomic ${\mathbb{{Z}}}_{3}$-extension of imaginary quadratic fields $k(=\;{\mathbb{{Q}}}(\sqrt{-d}))$ when the Sylow subgroup of class group of k is 3-elementary, and give an example. This example is different from the one we obtained before in the sense that when we write $k^{\alpha}_{1}\;=\;k({\eta}),{\eta}$ is obtained from non-units of ${\mathbb{{Q}}}({\sqrt{3d}})$.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.107-113
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• 2010

In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the sufficient conditions for existence of imaginary roots of square length -2k ($k\;{\in}\;\mathbb{Z}$>0). We also give several relations between the roots on g(A).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.921-925
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• 2011

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, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• East Asian mathematical journal
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• v.38 no.5
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• pp.583-591
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• 2022

Let K be an imaginary quadratic field and 𝒪 be an order in K. Let H_𝒪 be the ring class field of 𝒪. Furthermore, for a positive integer N, let K_𝒪,N be the ray class field modulo N𝒪 of 𝒪. When the discriminant of 𝒪 is different from -3 and -4, we construct an extended form class group which is isomorphic to the Galois group Gal(K_𝒪,N/H_𝒪) and describe its Galois action on K_𝒪,N in a concrete way.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.395-406
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• 2023

As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(𝜏). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.853-860
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• 2010

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, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• Journal of Korean Physical Therapy Science
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• v.3 no.4
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• pp.207-214
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• 1996

Main cause of low back pain is a poor posture. Most low back pains are due to a poor posture. The poor posture induces muscle tension and finaliy low back pain. The poor posture arehabitually trained from the childhood by the environmetal factors. In general, maintaining good posture during working and sleeping hours are the first line of defence against back pam. (1) Supine posture is the easiest posture that relaxes and fixes muscles. Supine posture is thus a starting position for on exercise. Lying down releases the weight pressures of head and shoulder and thus body can be relaxed and extended which are helpful for treating back pain. However, supine posture can increase the pressure in ribcage posture aspect and disphragram due to visceral oragans. (2) Sitting in one position for a long time results in fatigue and relaxation of spinal muscies. Finally, body strength is weakened and sitting posture will become poor. If this poor posture continues for a longer time, pain will be accompanied due to overelongation of muscle ligaments. The habitual poor posture could induce intervertebral disc distortion. If the intervertebral disc is damaged, sitting in one position or movement causes pain. (3) Abnormal lumbar curve induces the tention of abdominal muscle and paravertebral muscle groups as well as tention of lower limb muscle group connected to pelvis. For a person with weak body strength, muscle relaxation increases curvature in lumbar, chest and cervical regions. This will induce a pelvic anterior tilting of the imaginary line between A. S. I. S. and P. S. I. S. Hip joint extensor muscle acts on releasing the pelvic anterior tilting. Contrections of hamstring muscle and femoral muscle recover the imaginary line between A.S.LS. and P.S.I.S. from pelvic anterior tilting. thus, contraction of rectus abdominis muscle are required to maintain the normal lumbar curve.

• 한국연소학회:학술대회논문집
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• 2004.11a
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• pp.79-84
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• 2004

For the non-premixed interacting jet flames, it has been reported that if eight small nozzles are arranged along the circle of 40 $^{\sim}$ 72 times the diameter of single jet, the flames are not extinguished over 2oom/s. In this research, experiments were extended to the partially premixed cases to reduce both flame temperature and NOx emission. Nine nozzles were used- eight was evenly located along the perimeter of the imaginary circle and one at the geometric centre. The space between nozzles, S, the equivalence ratio, ${\Phi}$, the exit velocity and the role of the jet from the centre nozzle were considered. Normally, flame was lifted and flame base was located inside the imaginary circle made by the nozzle. As nozzles went away from each other, blowout velocity increased and then decreased. The maximum blowout velocity diminished with the addition of air to the fuel stream. When the fuel and/or oxidizer were not fed through the centre nozzle, the maximum blowout velocity obtained by varying Sand ${\Phi}$ was around 160m/s. Optimum nozzle separation distance at which peak blowout velocity obtained also decreased with ${\Phi}$ decrease. Flame base became leaner as approaching to the blowout. It seemed that lots of air was supplied to the flame stabilizing region by the entrainment and partially premixing. To approve this idea and to enhance the blowout velocity, fuel was supplied to the centre region. With the small amount of fuel through the centre nozzle, partially premixed flame could be sustained till sonic velocities. It seemed that the stabilizing mechanism in partially premixed interacting flame was different from that of non-premixed case because one was stabilized by the fuel supply through the centre nozzle but the other destabilized.

• Journal of Ocean Engineering and Technology
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• v.29 no.1
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• pp.45-55
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• 2015

Because of the high stress concentration near the toe of a welded joint, the calculation of local stress using the finite element method which is relevant to the fatigue strength of the weld toe crack, is a challenging task. This is mainly caused by the sensitivity of finite element analysis, which usually occurs near the area of a dramatically changing stress field. This paper presents a novel numerical method through which a less mesh-sensitive local stress calculation can be achieved based on the 3D solid finite element, strictly sticking to the original definition of hot spot stress. In order to achieve the goal, a traction stress, defined at 0.5t and 1.5t away from the weld toe, was calculated using either a force-equivalent or work-equivalent approach, both of which are based on the internal nodal forces on the imaginary cut planes. In the force-equivalent approach, the traction stress on the imaginary cut plane was calculated using the simple force and moment equilibrium, whereas the equivalence of the work done by both the nodal forces and linearized traction stress was employed in the work-equivalent approach. In order to confirm the validity of the proposed method, five typical welded joints widely used in ships and offshore structures were analyzed using five different solid element types and four different mesh sizes. Finally, the performance of the proposed method was compared with that of the traditionally used surface stress extrapolation method. It turned out that the sensitivity of the hot spot stress for the analyzed typical welded joints obtained from the proposed method outperformed the traditional extrapolation method by far.