• Korean Journal of Mathematics
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• 제27권1호
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• pp.165-173
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• 2019

In this paper, the definition b-numerical radius and b-norm is introduced and we present several b-numerical radius inequalities. Some applications of these inequalities are considered as well.

• 대한수학회보
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• 제60권3호
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• pp.677-685
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• 2023

For n ≥ 2 and a real Banach space E, 𝓛(ⁿE : E) denotes the space of all continuous n-linear mappings from E to itself. Let Π (E) = {[x^*, (x₁, . . . , x_n)] : x^*(x_j) = ||x^*|| = ||x_j|| = 1 for j = 1, . . . , n }. An element [x^*, (x₁, . . . , x_n)] ∈ Π(E) is called a numerical radius point of T ∈ 𝓛(ⁿE : E) if |x^*(T(x₁, . . . , x_n))| = v(T), where the numerical radius v(T) = sup_{[y^*,y1,...,yn]∈Π(E)}|y^*(T(y₁, . . . , y_n))|. For T ∈ 𝓛(ⁿE : E), we define Nradius(T) = {[x^*, (x₁, . . . , x_n)] ∈ Π(E) : [x^*, (x₁, . . . , x_n)] is a numerical radius point of T}. T is called a numerical radius peak n-linear mapping if there is a unique [x^*, (x₁, . . . , x_n)] ∈ Π(E) such that Nradius(T) = {±[x^*, (x₁, . . . , x_n)]}. In this paper we present explicit formulae for the numerical radius of T for every T ∈ 𝓛(ⁿE : E) for E = c₀ or l_∞. Using these formulae we show that there are no numerical radius peak mappings of 𝓛(ⁿc₀ : c₀).

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 추계 학술대회논문집
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• pp.127-133
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• 2007

This paper represents the numerical study on Taylor flow according to the radius ratio and the angular velocity for flow between tow cylinder. The numerical model is consisted of two cylinder which inner cylinder is rotating and outer cylinder is fix, and the axial direction is used the cyclic condition because of the length for axial direction is assumed infinite. The diameter of inner cylinder is assumed 86.8 mm, the numerical parameters are angular velocity and radius ratio. The numerical method is compared with the experimental results by Wereley, and the results are very good agreement. The critical Taylor number is calculated by theoretical and numerical analysis, and the results is showed the difference about ${\pm}10\;%$. As $Re/Re_c$ is increased, Taylor vortex is changed to wavy vortex, and then the wave number for azimuthal direction is increased. Azimuthal wave according to the radius ratio is showed high amplitude and low frequence in case of small radius ratio, and is showed low amplitude and high frequence in case of large radius ratio.

• Geomechanics and Engineering
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• 제16권1호
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• pp.59-69
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• 2018

This study focused on the mechanical and hydraulic characteristics of underwater tunnels based on Mohr-Coulomb (M-C), Hoek-Brown (H-B) and generalized H-B failure criteria. An improved approach for calculating stress, displacement and plastic radius of the circular tunnel considering hydraulic-mechanical coupling was developed. The innovation of this study was that the radius-incremental-approach was reconstructed (i.e., the whole plastic zone is divided into a finite number of concentric annuli by radius), stress and displacement of each annulus were determined in terms of numerical method and Terzaghi's effective stress principle. The validation of the proposed approach was conducted by comparing with the results in Brown and Bray (1982) and Park and Kim (2006). In addition, the Rp-pin curve (plastic radius-internal supporting pressure curve) was obtained using the numerical iterative method, and the plastic radius of the deep-buried tunnel could be obtained by interpolation method in terms of the known value of internal supporting pressure pin. Combining with the theories in Carranza and Fairhurst (2000), the improved technique for assessing the reliability of the tunnel support was proposed.

• 대한기계학회논문집B
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• 제28권9호
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• pp.1093-1100
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• 2004

Numerical analysis of the heat transfer associated with droplet impact on a hot solid surface is performed by solving the equations governing conservation of mass, momentum and energy in the liquid and gas phases. The deformed droplet shape is tracked by a level set method which is modified to achieve volume conservation and to include the effect of contact angle at the wall. The numerical method is validated through the calculations for the cases reported in the literature. Based on the numerical results, the heat transfer rate is found to depend strongly on the droplet spread radius. Decreased advancing/receding contact angles enlarge the splat radius and in turn enhance the wall heat flux. The effect of impact velocity on the droplet spread is reduced as the droplet size decreases. Also, droplet atomization is observed to significantly enhance the heat transfer rate and the effect is pronounced for a smaller size of droplet. An existing model equation to predict the maximum spread radius is improved for application to a micro droplet.

• 물과 미래
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• 제20권3호
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• pp.219-228
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• 1987

만내 및 입구부에 대한 흐름해석으로 천수방정식이 이용되었으며, 개방경계의 위치를 변화시키며 해석하였다. 만입구로부터의 거리를 변화시키며 설정된 반도형태의 개방경계에 대한 수치해석결과 적절한 개방경계의 위치는 만입구의 폭을 2B라 했을 때 이에 대한 관계로 표현할 수 있고 3B 이상인 경우에서 해는 안정한 상태로 되어 최적의 개방경계위치는 3B가 적절할 것으로 판단되었다. 천수방정식에 대한 수치기법으로는 전형적인 Galerkin 방법에 의한 유한요소법이 적용되었다.

• 한국정밀공학회지
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• 제15권12호
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• pp.81-88
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• 1998

Measurement and inspection of freeform surfaces are required in reverse design processes. In the case of surface measurement using a touch probe, probe radius compensation affects measuring accuracy. But current industrial practice depends upon an operator's experience to compensate for probe radius. In this paper, an on-the-machine measuring and inspection system for freeform surfaces is studied. Probe radius compensation methodology is investigated by modeling of B-spline surfaces based on digitized data. The accuracy and reliability of the developed system is verified through various kinds of numerical simulations and on-the-machine experiments.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.219-230
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• 2011

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

• Korean Journal of Hydrosciences
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• 제3권
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• pp.45-59
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• 1992

The flow characteristics varying with rate of the radius of curvature to width (Rc/B) in open channel bends are investigated with a simplified numerical model. Secondary flow velocity and transverise bed slope are formulated from the equations of momentum and force balance analysis, respectively. The conservation equations of mass and streamwise momentum are simplified by depth integration and its solution could be obtained from the explicit finite difference method. Three sets of computer simulation are executed. The rates of Rc/B adopted in simulations are 2.7, 5.4 and 8.1. The terms analyzed in this paper secondary flow velocity, streamwise velocity, the path of maximum steamwise velocity, deviation angle, and mass-shift velocity.

• 대한기계학회논문집B
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• 제29권10호
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• pp.1083-1091
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• 2005

Turbulent flow around a rotating circular cylinder is investigated by Direct Numerical Simulation. The calculation is performed at three cases of low Reynolds number, Re=161, 348 and 623, based on the cylinder radius and friction velocity. Statistically strong similarities with fully developed channel flow are observed. Instantaneous flow visualization reveals that the turbulence length scale typically decreases as Reynolds number increases. Some insight into the spacial characteristics in conjunction with wave number is provided by wavelet analysis. The budget of dissipation rate as well as turbulent kinetic energy is computed and particular attention is given to the comparison with plane channel flow.