• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.487-509
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• 2018

The Truncated Moment Problem (TMP) entails finding a positive Borel measure to represent all moments in a finite sequence as an integral; once the sequence admits one or more such measures, it is known that at least one of the measures must be finitely atomic with positive densities (equivalently, a linear combination of Dirac point masses with positive coefficients). On the contrary, there are more general moment problems for which we aim to find a "signed" measure to represent a sequence; that is, the measure may have some negative densities. This type of problem is referred to as the General Truncated Moment Problem (GTMP). The Jordan Decomposition Theorem states that any (signed) measure can be written as a difference of two positive measures, and hence, in the view of this theorem, we are able to apply results for TMP to study GTMP. In this note we observe differences between TMP and GTMP; for example, we cannot have an analogous to the Flat Extension Theorem for GTMP. We then present concrete solutions to lower-degree problems.

• Journal of Korea Water Resources Association
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• v.55 no.7
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• pp.545-556
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• 2022

It is recommended to use long-term hydrometeorological data for more than the service life of the hydraulic structures and water resource planning. For the purpose of expanding rainfall data, stochastic simulation models, such as Modified Bartlett-Lewis Rectangular Pulse (BLRP) and Neyman-Scott Rectangular Pulse (NSRP) models, have been widely used. The optimal parameters of the model can be estimated by repeatedly comparing the statistical moments defined through a combination of parameters of the probability distribution in the optimization context. However, parameter estimation using relatively small observed rainfall statistics corresponds to an ill-posed problem, leading to an increase in uncertainty in the parameter estimation process. In addition, as shown in previous studies, extreme values are underestimated because objective functions are typically defined by the first and second statistical moments (i.e., mean and variance). In this regard, this study estimated the parameters of the NSRP model using the objective function with the third moment and compared it with the existing approach based on the first and second moments in terms of estimation of extreme rainfall. It was found that the first and second moments did not show a significant difference depending on whether or not the skewness was considered in the objective function. However, the proposed model showed significantly improved performance in terms of estimation of design rainfalls.

• Special Issue of the Society of Naval Architects of Korea
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• 2008.09a
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• pp.46-53
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• 2008

Recently, the synthetic material stern tube bush has been applied by ship owner's requirement because the synthetic material has a merit. That is to say, when stern tube seal is damaged and sea water comes into stern tube, it can work without problem because of water lubricating property. However, the material also has a demerit of temperature rise problem when some factors meets on synthetic material, for example, not sufficient lubrication oil supply and not proper shaft alignment and so on. As known in the world, the RAILKO bush is rampant for synthetic material by some ship owner because of the above mentioned reason. However, the bush has several accidents on large container vessel. Unfortunately or fortunately our yard has a chance to apply the RAILKO bush owing to requirement of specific ship owner. Therefore, it is much more required to approach the accurate shaft alignment analysis. In line with this reason, we had a shaft alignment calculation considering hull deformation and hull flexibility (hull stiffness). Also, in the calculation, we had considered dynamic condition which is reflected he propeller thrust forces and moments and oil film stiffness on the shaft alignment calculation. According to he shaft alignment calculation, bearing slope was applied on the tern tube bush and was measured. The RAILKO bush should be applied the running in procedure according to maker's recommendation for performing the oil film on the bush surface. Finally, the vessels were delivered successfully without any problem with AILKO bush as shown on his paper.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.725-728
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• 2005

The scattering problem of the randomly rough surface is examined by the method of moments(MoM), small perturbation method (SPM), integral equation method (IEM) and the semi-empirical polarimetic model. To apply the numerical technique of the MoM to microwave scattering from a rough surface, at first, many independent randomly rough surfaces with a rms height and a correlation length are generated with Gaussian random deviate. Then, an efficient Monte Carlo simulation technique is applied to estimate the scattering coefficients of the surfaces.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.19-32
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• 2005

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.3
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• pp.532-538
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• 1997

Exactly aclculated antenna factors are requeired for determining EMI levels in an actual radiated emission test. In this paper, the antenna factors of short dipole antennas above the ground plane are calculated theoretically for the antenna with Roberts balun specified ANSI C63.5 regulation. Also treated is a half-wavelength dipole antenna with Roberts balun to compare the antenna factors with those of resonant dipole antenna. In formulationof antenna factors the antenna is treated as the boundary value problem of Maxwells equations and is analyzed by the Galerkins method of moments. The balun is treated using circuit theory based on power transmission mismatch.

• Journal of Astronomy and Space Sciences
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• v.1 no.1
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• pp.5-21
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• 1984

The airflow along the surface of a launch vehicle together with base flow of clustered nozzles cause problems which may affect the stability or efficiency of the entire vehicle. The problem may occur when the vehicle is on the launching pad or even during flight. As for such problems, local steady-state loads, overall steady-state loads, buffet, ground wind loads, base heating and rocket-nozzle hinge moments are examined here specifically.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.323-333
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• 1994

In this paper we present some approximation theorems related to the problem of finding optimal densities with prescribed moments. The implementation of the approximation theorems is to be done in some examples.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.2
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• pp.163-168
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• 2011

Robust optimization or reliability-based design optimization are some of the methodologies that are employed to take into account the uncertainties of a system at the design stage. For applying such methodologies to solve industrial problems, accurate and efficient methods for estimating statistical moments and failure probability are required, and further, the results of sensitivity analysis, which is needed for searching direction during the optimization process, should also be accurate. The aim of this study is to employ the function approximation moment method into the sensitivity analysis formulation, which is expressed as an integral form, to verify the accuracy of the sensitivity results, and to solve a typical problem of reliability-based design optimization. These results are compared with those of other moment methods, and the feasibility of the function approximation moment method is verified. The sensitivity analysis formula with integral form is the efficient formulation for evaluating sensitivity because any additional function calculation is not needed provided the failure probability or statistical moments are calculated.

• Smart Structures and Systems
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• v.29 no.2
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• pp.267-278
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• 2022

Pre-stressed concrete circular spun piles are widely used in various infrastructure projects around the world and offer an economical deep foundation system with consistent and superior quality compared to cast in-situ and other concrete piles. Conventional methods for measuring the lateral response of piles have been limited to conventional instrumentation, such as electrical based gauges and pressure transducers. The problem with existing technology is that the sensors are not able to assist in recording the lateral stiffness changes of the pile which varies along the length depending on the distribution of the flexural moments and appearance of tensile cracks. This paper describes a full-scale bending test of a 1-m diameter spun pile of 30 m long and instrumented using advanced fibre optic distributed sensor, known as Brillouin Optical Time Domain Analysis (BOTDA). Optical fibre sensors were embedded inside the concrete during the manufacturing stage and attached on the concrete surface in order to measure the pile's full-length flexural behaviour under the prescribed serviceability and ultimate limit state. The relationship between moments-deflections and bending moments-curvatures are examined with respect to the lateral forces. Tensile cracks were measured and compared with the peak strains observed from BOTDA data which corroborated very well. By analysing the moment-curvature response of the pile, the structure can be represented by two bending stiffness parameters, namely the pre-yield (EI) and post-yield (EI_cr), where the cracks reduce the stiffness property by 89%. The pile deflection profile can be attained from optical fibre data through closed-form solutions, which generally matched with the displacements recorded by Linear Voltage Displacement Transducers (LVDTs).