• 대한수학회보
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• 제58권6호
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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.

• 대한수학회논문집
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• 제33권2호
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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.

• 한국물환경학회지
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• 제21권4호
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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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• 제1권2호
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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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 추계학술대회 논문집
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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.

• 한국산학기술학회논문지
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• 제16권12호
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• pp.8654-8664
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• 2015

기계, 건축, 토목공학 분야 등에는 불균일 단면을 갖는 보 형태의 구조물들이 널리 사용되고 있다. 본 논문은 양단이 단순 지지된 보 구조물들의 동특성과 진동에 대한 문제를 다루며, 국부좌표를 사용한 지배방정식이 유도된다. 갤러킨의 모드합 방법으로 해가 가정되고, 고유진동수를 구하는 행렬식을 푸는 데는 이분법을 적용하였다. 유한요소법이 단지 기하학적 경계조건만을 만족시키는 허용함수를 사용하는 반면, 본 논문에서는 갤러킨의 모드합 방법을 적용하여, 지배방정식과 경계조건을 모두 만족하는 고유함수를 사용하였다. 계의 동특성을 알기위해, 네 종류의 불균일 단면을 갖는 단순 지지 보에 대해 모달 해석과 시험이 수행되었으며, 해석 결과는 실험 결과와 근사한 일치를 나타내었다.

• Computers and Concrete
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• 제19권1호
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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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• 제15권5호
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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.

• 한국음향학회지
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• 제20권5호
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• pp.83-91
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• 2001

본 논문은 수중환경에서 비교적 근거리에 위치해 있는 목표물에서 방사되는 광대역 음원신호를 취득하여 목표물의 위치를 탐지하기 위한 표적추정 (Focused) 빔 형성 기법을 제안한다. 표적추정 (Focused) 빔 형성기 기법은 배열 센서를 사용하여 구면파 형태로 입사되는 방사 신호들의 각 센서로의 상이한 전달 지연 시간 성분들을 고려하여 센서 출력 신호들을 일정 시간 구간 동안 코히어런트하게 합해 줌으로써 목표물의 위치를 판단하게 된다. 이때 견인함의 이동에 의해 배열 센서의 형태가 시간적으로 변화하게 되며, 가상의 셀들로 분리된 이미지 공간상에서 각 셀과 배열 센서간의 기하학적인 구조 분석에 의해 계산된 시간 지연 값들을 이용하여 표적추정(Focused) 빔 형성 과정을 거친 최종적인 3차원 빔 패턴 출력을 얻게 된다. 본 논문에서는 컴퓨터 시뮬레이션을 통하여 N차 다항식 (polynomial) 근사법을 이용한 실제 수차 모형 배열 형태 추정을 하였으며 생성된 가상의 수차 모형 배열을 이용하여 각각의 주파수 대역에 따른 광대역 목표물에 대한 추정 성능을 분석하여 보았다.

• 한국공간구조학회논문집
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• 제12권2호
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• pp.81-88
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• 2012

텐세그리티 구조시스템의 한 종류인 케이블 돔 시스템은 케이블과 마스트로 이루어져 있다. 이 케이블에 외부하중이 가해지지 않은 상태에서 안정된 구조물이 되기 위하여 일정의 프리텐션이 가해져야 하며 구조물은 가해진 프리텐션 하에서 자기평형응력상태에 있어야 한다. 본 연구에서는 부재의 내력 벡터의 합 원리를 기초하여 자기평형 응력모드를 구하는 새로운 방법을 제안하였으며, 자기평형응력을 유지하기 위해 필요한 응력모드를 시각화할 수 있다는 점이 기존의 논문과 비교하여 독특성을 갖는다. 본 연구에서 제안된 방법에서 사용된 기본 원리는 모든 절점에서 외부하중이 가해지지 않은 상태에서 내력벡터의 합은 0이 되어야 한다는 것이다. 제안된 방법은 CAD를 이용하여 간단히 자기 평형응력모드를 찾을 수 있으며, 예제 케이블 돔 구조물을 대상으로 각 절점에 연결된 부재들의 내력을 결정하였다. 결과 값은 역학적 계산 방법과 기존의 이론에 의해 검증하였으며 잘 일치하였다.