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INFINITELY MANY HOMOCLINIC SOLUTIONS FOR DAMPED VIBRATION SYSTEMS WITH LOCALLY DEFINED POTENTIALS

  • Selmi, Wafa;Timoumi, Mohsen
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.693-703
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    • 2022
  • In this paper, we are concerned with the existence of infinitely many fast homoclinic solutions for the following damped vibration system $$(1){\hspace{32}}{\ddot{u}}(t)+q(t){\dot{u}}(t)-L(t)u(t)+{\nabla}W(t,u(t))=0,\;{\forall}t{\in}{\mathbb{R}},$$ where q ∈ C(ℝ, ℝ), L ∈ C(ℝ, ${\mathbb{R}}^{N^2}$) is a symmetric and positive definite matix-valued function and W ∈ C1(ℝ×ℝN, ℝ). The novelty of this paper is that, assuming that L is bounded from below unnecessarily coercive at infinity, and W is only locally defined near the origin with respect to the second variable, we show that (1) possesses infinitely many homoclinic solutions via a variant symmetric mountain pass theorem.

Age and Growth of the Yellow Goosefish, Lophius litulon (한국근해 황아귀, Lophius litulon의 연령과 성장)

  • CHA Byung-Yul;PARK Yeong-Chull;HUH Sung-Hoi
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.31 no.4
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    • pp.529-534
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    • 1998
  • Age and growth of the yellow goosefish, Lophius litulon, were studied using samples collected from the southwestern waters of Korea. Vertebrae of the fish had relatively clear annuli on their surface. The opaque zone of vertebrae was formed once a year between March and April. The oldest fish observed in this study was 8 years old for females and 5 years old for males. The relationship between the radius (R) of vertebral centrum and total length (L) was as follows: L=12.7+4.8R for females and L=9.8+5.6R for males. The relationship between total length and body weight (W) was as follows : $W=0.0089L^{3.0311}$ for females and $W=0.0329L^{2.7752}$ for males. Growth in length of the fish was expressed by the von Bertalanffy's equation as $L_t=127.60(1-e^{-0.1228(t+0.3851)})$ for females and $L_t=82.23(1-e^{-0.1832(t+0.6431)})$ for males.

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Diagnostic Criteria of T1-Weighted Imaging for Detecting Intraplaque Hemorrhage of Vertebrobasilar Artery Based on Simultaneous Non-Contrast Angiography and Intraplaque Hemorrhage Imaging

  • Lim, Sukjoon;Kim, Nam Hyeok;Kwak, Hyo Sung;Hwang, Seung Bae;Chung, Gyung Ho
    • Investigative Magnetic Resonance Imaging
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    • v.25 no.4
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    • pp.323-331
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    • 2021
  • Purpose: To investigate the diagnostic criteria of T1-weighted imaging (T1W) and time-of-flight (TOF) imaging for detecting intraplaque hemorrhage (IPH) of a vertebrobasilar artery (VBA) compared with simultaneous non-contrast angiography and intraplaque hemorrhage (SNAP) imaging. Materials and Methods: Eighty-seven patients with VBA atherosclerosis who underwent high resolution MR imaging for evaluation of VBA plaque were reviewed. The presence and location of VBA plaque and IPH on SNAP were determined. The signal intensity (SI) of the VBA plaque on T1W and TOF imaging was manually measured and the SI ratio against adjacent muscles was calculated. The receiver-operating characteristic (ROC) curve was used to compare the diagnostic accuracy for detecting VBA IPH. Results: Of 87 patients, 67 had IPH and 20 had no IPH on SNAP. The SI ratio between VBA IPH and temporalis muscle on T1W was significantly higher than that in the no-IPH group (235.9 ± 16.8 vs. 120.0 ± 5.1, P < 0.001). The SI ratio between IPH and temporalis muscle on TOF was also significantly higher than that in the no-IPH group (236.8 ± 13.3 vs. 112.8 ± 7.4, P < 0.001). Diagnostic efficacies of SI ratios on TOF and TIW were excellent (AUC: 0.976 on TOF and 0.964 on T1W; cutoff value: 136.7% for TOF imaging and 135.1% for T1W imaging). Conclusion: Compared with SNAP, cutoff levels of the SI ratio between VBA plaque and temporalis muscle on T1W and TOF imaging for detecting IPH were approximately 1.35 times.

Magnetic Properties of Both Ni-W and (Ni-3%W)-Cu Textured Substrates for ReBCO Coated Conductor (고온초전도 박막선재용 Ni-$W_{xat.%}$ 및 (Ni-$W_{3at.%}$)-$CU_{xat.%}$ 이축배향 금속 기판들의 자기적 특성)

  • Song, K.J.;Kim, T.H.;Kim, H.S.;Ko, R.K.;Ha, H.S.;Ha, D.W.;Oh, S.S.;Park, C.;Yoo, S.I.;Joo, J.H.;Kim, M.W.;Kim, C.J.
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2006.11a
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    • pp.28-29
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    • 2006
  • The magnetic properties of a series of both annealed and as-rolled Ni-$W_y$ alloy tapes with compositions y = 0, 1, 3, and 5 at.%, were studied. To compare with Ni-W alloys, the magnetic properties of a series of both annealed and as-rolled $[Ni_{97at.%}W_{3at.%}]_{100-x}Cu_x$ alloy tapes with compositions x = 0, 1, 3, 5 and 7 at.%, were studied, as well. Both the isothermal mass magnetization M(H) of a series of samples, such as both Ni-W and [Ni-W]-Cu alloy tapes, at different fixed temperatures and M(T) in fixed field, were measured using a PPMS-9 (Quantum Design). The degree of ferromagnetism of Ni-$W_y$ alloys have reduced as W-content y increases. Both the saturation magnetization $M_{sat}$ and Curie temperature $T_c$ decrease linearly with W-content y, and both $M_{sat}$ and $T_c$ go to zero at critical concentration of $y_c$ ~ 9.50 at.% W. The effect of Cu addition on both the saturation magnetization $M_sat$ and Curie temperature $T_c$ decrease linearly with Cu-content x in $[Ni_{97at.%}W_{3at.%}]_{100-x}Cu_x$ alloy tapes with compositions x = 0, 1, 3, 5, and 7 at.%. The results confirm that [Ni-W]-Cu alloy tapes can have much reduced ferromagnetism as Cu-content x increases.

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Age and Growth of Black Rockfish, Sebastes schlegeli in the Tongyeong Marine Ranching Area in Korea Waters (통영바다목장에 서식하는 조피볼락, Sebastes schlegeli의 연령과 성장)

  • Park, Kyeong Dong;Kang, Yong Joo
    • Korean Journal of Ichthyology
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    • v.19 no.1
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    • pp.35-43
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    • 2007
  • Age and growth of black rockfish, Sebastes schlegeli sampled from the Tongyeong marine ranching area in Korea waters were determined from 1,173 otoliths from July, 2001 to May, 2004. Examination of outer margins of the otolith showed that the opaque zone was formed once a year. Marginal increment of the otolith formed annual ring from July. The von Bertalanffy growth curve had the growth parameters estimated from non-linear regression were $L_t=48.45(1-e^{-0.2139(t+0.4313)})$, $W_t=1,837.93(1-e^{-0.2139(t+0.4313)})^{3.02}$ 3.02 for females and, $L_t=49.32(1-e^{-0.1775(t+0.7403)})$, $W_t=1,887.83(1-e^{-0.1775(t+0.7403)})^3$ for males, where t is age (year) and Lt is body length (mm) at age t. Growth at the age of male and female shows significant difference (p<0.01).

$^{13}C$ Solid State NMR Study on the Dynamics of the Poly(vinyl butylal) with Various Water Contents

  • Hyun Namgoong;Kim, Jong-Soo;Han, Oc-Hee
    • Journal of the Korean Magnetic Resonance Society
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    • v.6 no.1
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    • pp.1-11
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    • 2002
  • Physical properties of PVB [Poly(vinyl butyral)] polymer are strongly correlated with water contents in the polymer. Thus dynamics of PVB containing 10~50(w/w) % of water were studied by $^{13}$ C CP/MAS/DD over the temperature range 293K -348K. From the Peak area, line width, chemical shift, and relaxation times ( $T_{1}$ $T_{1p}$) measured at 9.4 T, it was deduced that water facilitates molecular dynamics of the PVB molecules overall including conformational exchange of the racemic and meso butyaldehyde rings in the PVB. However, the influence of water was not linear to the amount of water in the PVB samples. It is suggested that water up to 30 w/w % of the sample is closely bound to the PVB polymer and water relatively free from the PVB polymer starts to appear when water is added more than 30 w/w %.%.

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Vibration Characteristics of the Tower Structure of a 750kW Wind Turbine Generator (750kW 풍력발전기 타워 구조의 진동 특성)

  • Kim, Seokhyun;Nam, Y.S.;Eun, Sungyoung
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.2 s.95
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    • pp.219-224
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    • 2005
  • Vibration response of the tower structure of a 750kW wind turbine (W/T) generator is investigated by measurement and analysis. Acceleration response of the W/T tower under various operation condition is monitored in real time by the vibration monitoring system using LabVIEW. Resonance state of the tower structure is diagnosed in the operating speed range. Resonance frequency range of the test model is investigated with the wind speed data of the test site. To predict the tower resonance frequency, tower is modeled as an equivalent beam with a lumped mass and Rayleigh energy method is applied. Calculated tower bending frequency is in good agreement with the measured value and the result shows that the simplified model can be used in the design stage of the W/T tower.

Seven Species of Olethreutini(Lepidoptera : Tortricidae) New to Korea (산애기잎말이나방족(族)의 한국(韓國) 미기록(未記錄) 7종(種))

  • Park, K.T.;Kawabe, A.
    • Korean journal of applied entomology
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    • v.25 no.4 s.69
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    • pp.193-200
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    • 1986
  • Seven species of Olethreutini(Lepidoptera : Tortricidae): Olethreutes siderana(T.), O. pryerana(W.), O. nigricrista, F., Pseudohedya retracta F., Apotomis capreana(H.), Cryptaspasma marginifasciata(W.) and C. angulicostana(W.) are reported for the first time from Korea by authors.

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A NOTE ON W-CLOSED SETS AND W-CONVERGENCES

  • Cho, Seong-Hoon
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.225-229
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    • 2001
  • In this paper, we obtain a topology T/sub w/ on X. Using this topology, we obtain a chracterization of w-convergence.