• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.3
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• pp.243-250
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• 2009

The adjoint variable method can reduce computation time and save computer resources because it can selectively provide the sensitivity information for the positions that designers wish to measure. However, the adjoint variable method commonly employs exact analytical differentiation with respect to the design variables. It can be cumbersome to precisely differentiate every given type of finite element. This trouble can be overcome only if the numerical differentiation scheme can replace this exact manner of differentiation. But, the numerical differentiation scheme causes of severe inaccuracy due to the perturbation size dilemma. For assuring the accurate sensitivity without any dependency of perturbation size, this paper employs a complex variable that has been mainly used for computational fluid dynamics problems. The adjoint variable method combined with complex variables is applied to obtain the shape and size sensitivity for structural optimization. Numerical examples demonstrate that the proposed method can predict stable sensitivity results and that its accuracy is remarkably superior to traditional sensitivity evaluation methods.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.899-907
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• 2001

Complex variable methods are used to solve the first and the second fundamental problems for infinite plate with two holes having arbitrary shapes which are conformally mapped on the domain outside of the unit circle by means of rational mapping function. Some applications are investigated and some special cases are derived.

• Journal of the Institute of Convergence Signal Processing
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• v.12 no.2
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• pp.128-132
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• 2011

Least mean square adaptive algorithms have played important role in radar, sonar, speech processing, and mobile communication. In mobile communication area, the convergence rate of a LMS algorithm is quite important. However, LMS algorithms have slow and non-uniform convergence rate problem For overcoming these shortcomings, various variable step LMS adaptive algorithms have been studied in recent years. Most of these recent LMS algorithms have used complex variable step methods to get a rapid convergence. But complex variable step methods need a high computational complexity. Therefore, the main merits such as the simplicity and the robustness in a LMS algorithm can be eroded. The proposed deterministic variable step LMS algorithm is based upon a simple deterministic function for the step update so that the simplicity of the proposed algorithm is obtained and the fast convergence is still maintainable.

• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.277-298
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• 2010

The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

• Bulletin of the Korean Chemical Society
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• v.24 no.8
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• pp.1111-1118
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• 2003

We present one-color nonlinear wavepacket interferometry (WPI) signal calculations for a system of two electronic levels and one vibrational degree of freedom. We consider two cases, a displaced harmonic oscillator system, which can be treated analytically, and a model photodissociative system, whose WPI signal must be calculated by numerical wavepacket propagation. We show how signals obtained with different combinations of intrapulse-pair phase shifts can be combined to isolate the complex-valued overlap between a given onepulse target wavepacket and a variable three-pulse reference wavepacket. We demonstrate that with a range of inter- and intrapulse-pair delays the complex overlaps and variable reference states can be used to reconstruct the target wavepacket. We compare our results with previous methods for vibronic state reconstruction based on linear WPI and discuss further generalizations of our method.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.371-383
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• 2019

Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.11 s.242
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• pp.1527-1533
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• 2005

Three methods for design sensitivity analysis such as finite difference method(FDM), direct differentiation method(DDM) and adjoint variable method(AVM) are well known. FDM and DDM for design sensitivity analysis cost too much when the number of design variables is too large. An AVM is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation. Because the adjoint equation is independent of the number of design variables, an AVM is efficient for when number of design variables is too large. In this study, AVM has been extended to the eigenproblem of damped systems whose eigenvlaues and eigenvectors are complex numbers. Moreover, this method is implemented into a commercial finite element analysis program by means of the semi-analytical method to show applicability of the developed method into practical structural problems. The proposed_method is compared with FDM and verified its accuracy for analytical and practical cases.

• Journal of Electrical Engineering and Technology
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• v.12 no.4
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• pp.1600-1604
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• 2017

A new Complex Image Method based on Genetic Algorithm (GA) is proposed to calculate the Green's functions of CPW (coplanar waveguide)-type microwave components and antennas. The closed-forms of the spectral-domain integrals are obtained by the GA, avoiding the conventional procedures of the tedious linear algebra and the sampling conditions sensitive to the complex-variable sampling paths adopted in the Prony's and GPOF methods. The proposed method is compared with the numerical Sommerfeld Integral, which results in good agreement.

• FOCUS: LIFE SCIENCE
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• no.1
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• pp.9.1-9.5
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• 2024

Method development for complex low molecular mass (LMM) samples using reversed-phase (RP) separation conditions presents significant challenges due to the presence of many unknown analytes over wide concentration ranges. This guide aims to optimize method parameters-column length (L), temperature (T), flow rate (F), and final mobile phase conditions (Øfinal)-to maximize separation peak capacity. Validated by prior research, this protocol benefits laboratories dealing with metabolomics, natural products, and contaminant screening. This practical guide provides a structured approach to maximizing peak capacity for complex LMM separations. It complements computational optimization strategies and offers a step-by-step method development process. The Snyder-Dolan test is highlighted as essential for determining the need for gradient or isocratic elution and guiding column length decisions. The decision tree framework helps analysts prioritize variable optimization to develop effective separation methods for complex samples.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.443-449
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• 2017

Estimation of population proportion like the distribution rate of LED TV and the prevalence of a disease are often estimated based on survey sample data. Population proportion is generally considered as a special form of population mean. In complex sampling like stratified multistage sampling with unequal probability sampling, the denominator of mean may be random variable and it is estimated like ratio estimator. In this research, we examined the estimation of distribution rate based on stratified multistage sampling, and determined some numerical outcomes using stratified random sample data with about 25% of missing observations. In the data used for this research, the survey weight was determined by deterministic way. So, the weights are not random variable, and the population distribution rate and its variance estimator can be estimated like population mean estimation. When the weights are not random variable, if one estimates the variance of proportion estimator using ratio method, then the variances may be inflated. Therefore, in estimating variance for population proportion, we need to examine the structure of data and survey design before making any decision for estimation methods.