• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.411-419
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• 1997

Using the theory of strongly continuous cosine families, we prove controllable of nonlinear second order control system and give an application.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.895-909
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• 1997

We state the necessary conditions on optimizing the parameters which the damping differential operators contain in abstract linear damped second order evolution equation on the Gelfand five fold.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.273-284
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• 2006

In this paper, we study nonoscillatory solutions of a class of second order nonlinear neutral delay differential equations with positive and negative coefficients. Some sufficient conditions for existence of nonoscillatory solutions are obtained.

• The korean journal of orthodontics
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• v.51 no.1
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• pp.32-42
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• 2021

Objective: To investigate the three-dimensional forces created by clear aligners on mandibular teeth during differential activation with en-masse retraction and/or intrusion in vitro. Methods: Six sets of clear aligners were designed for differential en-masse retraction and/or intrusion procedures in a first premolar extraction model. Group A0 was a control group with no activation. Groups A1-5 underwent different degrees of retractions and/or intrusions. Each group consisted of 10 aligners. Aligner forces were measured on a multi-axis force/torque transducer measurement system in real-time. Results: In the en-masse retraction groups (A1 and A2), lingual and extrusive forces were observed on the incisors; the canines mainly received distal forces; intrusive forces were seen on the second premolars; and the molars received mesial forces. In the en-masse retraction and intrusion groups (A3, A4, and A5), incisors also received lingual and extrusive forces; canines received distal and intrusive forces; mesial and extrusive forces were seen on the second premolars; and the second molars received distal and intrusive forces. The vertical forces on the incisors did not differ significantly among groups A1, A3, and A5. However, the vertical forces on the second premolars reversed from intrusion in group A1 to extrusion in groups A3 and A5. Conclusions: With clear aligners, the "bowing effect" is seen during en-masse anterior teeth retraction and can be partially relieved by performing en-masse retraction accompanied by anterior teeth intrusion. Vertical control of incisors remained unsolved during en-masse retraction, even when intrusive activation was added to the anterior teeth.

• Korean Journal of Radiology
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• v.23 no.8
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• pp.803-810
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• 2022

Objective: To investigate the clinical application of differential subsampling with Cartesian ordering (DISCO) contrast-enhanced (CE) magnetic resonance angiography for anterolateral thigh (ALT) flap transplantation, using operative findings as a reference. Materials and Methods: Thirty patients (21 males and nine females; mean age ± standard deviation, 45.5 ± 15.6 years) who were scheduled to undergo reconstruction with ALT flaps between June 2020 and June 2021 were included in the prospective study. Before ALT flap transplantation, patients were scanned using CE-DISCO imaging. All acquired DISCO images of the 60 lower limbs (both sides from each patient) were analyzed using maximum intensity projection and volume rendering methods. Two experienced radiologists were employed to examine the patterns of the lateral circumflex femoral artery (LCFA), its branches, and perforators and their skin termini, which were compared with the operative findings. Results: Using CE-DISCO, the patterns of the LCFA and its branches were clearly identified in all patients. Four different origins of the LCFA were found among the 60 blood vessels: type I (44/60, 73.3%), type II (6/60, 10.0%), type III (8/60, 13.3%), and type IV (2/60, 3.3%). Owing to a lack of perforators entering the skin, two patients did not undergo ALT flap transplantation. For the remaining 28 patients, the ALT flaps in 26 patients were successfully operated without flap reselection during the operation, while the remaining two patients underwent other surgical procedures due to the thin diameter of the perforator or injury of the perforator during the operation. The success rate of flap transplantation was 92.8% (26/28). All transplanted flaps exhibited good blood supply and achieved primary healing without infection or delayed healing. Conclusion: CE-DISCO imaging can be an effective method for preoperative perforator imaging before ALT flap transplantation.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.6 s.360
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• pp.60-68
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• 2007

A technique is presented to extract differential second harmonic output from common source nodes of a cross-coupled P-& N-FET oscillator. Provided the impedances at the common source nodes are optimized and the fundamental swing at the VCO core stays in a proper mode, it is found that the amplitude and phase errors can be kept within $0{\sim}1.6dB$ and $+2.2^{\circ}{\sim}-5.6^{\circ}$, respectively, over all process/temperature/voltage corners. Moreover, an impedance-tuning circuit is proposed to compensate any unexpectedly high errors on the differential signal output. A Prototype 5-GHz VCO with a 2.5-Hz LC resonator is implemented in $0.18-{\mu}m$ CMOS. The error signal between the differential outputs has been measured to be as low as -70 dBm with the aid of the tuning circuit. It implies the push-push outputs are satisfactorily differential with the amplitude and phase errors well less than 0.34 dB and $1^{\circ}$, respectively.

• Journal of computational fluids engineering
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• v.21 no.4
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• pp.102-111
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• 2016

In this paper a computation of turbulent natural convection in enclosures with the elliptic-blending based differential and algebraic flux models is presented. The primary emphasis of the study is placed on an investigation of accuracy of the treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for the turbulent natural convection flows. The turbulent heat fluxes in this study are treated by the elliptic-blending based algebraic and differential flux models. The previous turbulence model constants are adjusted to produce accurate solutions. The proposed models are applied to the prediction of turbulent natural convections in a 1:5 rectangular cavity and in a square cavity with conducting top and bottom walls, which are commonly used for validation of the turbulence models. The relative performance between the algebraic and differential flux model is examined through comparing with experimental data. It is shown that both the elliptic-blending based models predict well the mean velocity and temperature, thereby the wall shear stress and Nusselt number. It is also shown that the elliptic-blending based algebraic flux model produces solutions which are as accurate as those by the differential flux model.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1049-1070
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• 2004

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.