• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1419-1443
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• 2021

The asymmetric Laplace distribution arises as a limiting distribution of geometric summations of independent and identically distributed random variables with finite second moments. The main purpose of this paper is to study the weak limit theorems for geometric summations of independent (not necessarily identically distributed) random variables together with convergence rates to asymmetric Laplace distributions. Using Trotter-operator method, the orders of approximations of the distributions of geometric summations by the asymmetric Laplace distributions are established in term of the "large-𝒪" and "small-o" approximation estimates. The obtained results are extensions of some known ones.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.605-618
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• 2018

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

• Journal of Korean Society on Water Environment
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• v.21 no.4
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• pp.393-397
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• 2005

In this study, flow in a porous medium is analyzed using a computer-extended perturbation series solution. The flow is modelled as a creeping flow in a periodically constricted channel. The channel walls have a sinusoidally varying width and the flow is analyzed in terms of its vorticity and stream functions in the Stokes flow regime. The perturbation series in terms of a small parameter, average width to length ratio, is extended with a computer resulting in purely asymptotic series and Pade summation is used to obtain final results. Resulting flow shows flow separations in the widening section and immobile zones in the widest section of the flow regime with reattachment in the narrowing section. Analysis of the flow separation phenomena resulted in a correlation between the two geometric parameters of the channel walls to predict the onset of flow separation in the Stokes flow regime.

• Advances in biomechanics and applications
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• v.1 no.2
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• pp.85-93
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• 2014

In this paper, two procedures of enumerating the axial rotation are proposed using the unit sphere of the spherical rotation coordinate system specifying 3D rotation. If the trajectory of the movement is known, the integration of the axial component of the angular velocity plus the geometric effect equal to the enclosed area subtended by the geodesic path on the surface of the unit sphere. If the postures of the initial and final positions are known, the axial rotation is determined by the angular difference from the parallel transport along the geodesic path. The path dependency of the axial rotation of the three dimensional rigid body motion is due to the geometric effect corresponding to the closed loop discontinuity. Firstly, the closed loop discontinuity is examined for the infinitesimal region. The general closed loop discontinuity can be evaluated by the summation of those discontinuities of the infinitesimal regions forming the whole loop. This general loop discontinuity is equal to the surface area enclosed by the closed loop on the surface of the unit sphere. Using this quantification of the closed loop discontinuity of the axial rotation, the geometric effect is determined in enumerating the axial rotation. As an example, the axial rotation of the arm by the Codman's movement is evaluated, which other methods of enumerating the axial rotations failed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.281-284
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• 2000

For estimation manufacturing cost during the early design stage, desingers have to know compositon of manufacturmg cost. Manufacturing cost is summalion of material cost and processmg cost. To be able to control the manufacturmg cost, it is necessary to estimate the costs adequately and to store the cost data in a generic way. a generic system, which is the basis for the control of the production costs, takes into account geometric information, material information, process information and production planning information Manufacturing cost is summation of material cost and processing cost.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.12
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• pp.8654-8664
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• 2015

Beam-type structures with non-uniform cross sections are widely used in mechanical, architectural, and civil engineering fields. This paper deals with dynamic characteristics and vibration problems. Governing equations are first derived by using local coordinates. Their solutions are then assumed by using Galerkin's mode summation method. Bisection method is also applied in solving the determinant of the matrix which can provide natural frequencies. Whereas finite element methods adopt admissible functions satisfying only geometric boundary condition, in this study we apply Galerkin's mode summation method which uses eigen-functions satisfying both governing equations and boundary conditions. Modal analysis and experimental tests are finally performed using simply-supported beams with four different non-uniform cross-sections. Our analytical results then show good agreement with experimental ones.

• Computers and Concrete
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• v.19 no.1
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• pp.1-6
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• 2017

Prestressed concrete I-girders are subject to different load types at their construction stages. At the time of strand release, i.e., detensioning, prestressed concrete girders are under the effect of dead and prestressing loads. At this stage, the camber, total net upward deflection, of prestressed girder is summation of the upward deflection due to the prestressing force and the downward deflection due to dead loads. For the calculation of the upward deflection, it is generally considered that prestressed concrete I-girder behaves linear-elastic. However, the field measurements on total net upward deflection of prestressed I-girder after detensioning show contradictory results. In this paper, camber calculations with the linear-elastic beam and elastic-stability theories are presented. One of a typical precast I-girder with 120 cm height and 31.5 m effective span length is selected as a case study. 3D finite element model (FEM) of the girder is developed by SAP2000 software, and the deflections of girder are obtained from linear and nonlinear-static analyses. Only geometric nonlinearity is taken into account. The material test and field measurement of this study are performed at prestressing girder plant. The results of the linear-elastic beam and elastic-stability theories are compared with FEM results and field measurements. It is seen that the camber predicted by elastic-stability theory gives acceptable results than the linear-elastic beam theory while strand releasing.

• Advances in nano research
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• v.15 no.5
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• pp.485-493
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• 2023

Critical multi-field loads and free vibration responses of the sandwich piezoelectric/piezomagnetic microplate subjected to combination of magnetoelectromechanical loads based on a thickness-stretched higher order shear deformable model using Hamilton's principle. The lateral displacement is assumed summation of bending, shearing and stretching functions. The elasti core is sandwiched by a couple of piezoelectric/piezomagnetic face-sheets subjected to electromagnetocmechanical loads. The work of external force is calculated with considering the in-plane mechanical, electrical and magnetic loads based on piezomagnetoelasticity relations. The critical multi field loading and natural frequency analysis are performed to investigate influence of geometric and loading parameters on the responses. A verification is performed for justification of the numerical results.

• The Journal of the Acoustical Society of Korea
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• v.20 no.5
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• pp.83-91
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• 2001

This paper proposes the Focused beamforming to estimate the location of target residing near to the observation platform in the underwater environment. The Focused beamforming technique provides the location of target by the coherent summation of a series of incident spherical waveforms considering distinct propagation delay times at the sensor array. But due to the movement of the observation platform and the variation of the underwater environment, the shape of the sensor array is no longer to be linear but it becomes distorted as the platform moves. Thus the Focused beamforming should be peformed regarding to the geometric shape variation at each time. To estimate the target location, the artificial image plane comprised of cells is constructed, and the delays are calculated from each cell where the target could be proximity to sensors for the coherent summation. After the coherent combining, the beam pattern can be obtained through the Focused beamforming on the image plane. Futhermore to compensate the variation of the shape of the sensor array, the paper utilizes the Nth-order polynomial approximation to estimate the shape of the sensor array obeying the water pulley modeling. Simulation results show the performance of the Focused beamforming for different frequency bands of the radiated signal.

• Journal of Korean Association for Spatial Structures
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• v.12 no.2
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• pp.81-88
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• 2012

Cable dome structures are composed of cables-masts and the cables should be in pre-tension since a structure without pre-tension is not stable. Under the pretension, self equilibrium stress state is the main characteristic of a cable dome structure. In this paper, a new method based on the basic principle of closed force polygon for equilibrium system is proposed for the determination of self-equilibrium mode of cable dome structure. The proposed method which is called geometric method has the unique characteristic of visualization of the force mode needed for maintenance of self-equilibrium. The basic theory for a self equilibrium of structure is that the summation of forces at each joint without any external load should be zero. The simplicity of the method which involves only drawing close polygon with the aid of suitable CAD software has been illustrated by means of a example. The results compared with mechanical calculation and existed method and shows good agreement.