• The Journal of the Acoustical Society of Korea
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• v.16 no.3E
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• pp.62-68
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• 1997

In this paper, a modified adaptive sign (MAS) algorithm based on a mixed norm error criterion is proposed. The mixed norm error criterion of be minimized is constructed as a combined convex function of the mean-absolute error and the mean-absolute error to the third power. A convergence analysis of the MAS algorithm is also presented. Under a set of mild assumptions, a set of nonlinear evolution equations that characterizes the statistical mean and mean-squared behavior of the algorithm is derived. Computed simulations are carried out to verify the validity of our derivations.

• East Asian mathematical journal
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• v.14 no.2
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• pp.421-427
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• 1998

In this paper we provide sufficient conditions which ensure the strong consistency of $L_p$-norm estimation in nonlinear regression model when the probability distribution of the errors term is symmetric about zero. The least absolute deviation and least square estimation are discussed as special cases of the proposed estimation.

• Economic and Environmental Geology
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• v.28 no.4
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• pp.433-438
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• 1995

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.583-590
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• 2008

In this article, we focuss on. sequences of polynomials with {$\pm1$} coefficients constructed by recursive argument that is known as Rudin-Shapiro polynomials. The asymptotic behavior of these polynomials defines as the ratio of their 2q-norm with 2-norm to be dominated by some number depending on q or "the best" by an absolute constant. In this work we first show the conjecture holds for some finite numbers of m and then introduce a technique that give the result for any positive odd integer m whenever it holds for all pervious even numbers.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.118-123
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• 2007

A robust objective function in the frequency domain is applied to the acoustic full waveform inversion. The proposed objective function is defined as $l_1$-norm of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to a number of factors such as parameterization, initial model, noise and so on. The numerical tests were performed for checking the sensitivity to attenuation and several noises. For the comparison with other objective functions, the conventional least-squares method and the logarithmic method were tested under the same condition. The synthetic data examples show that the proposed algorithm is more robust than the well-known methods.

• The korean journal of orthodontics
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• v.18 no.1 s.25
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• pp.127-139
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• 1988

Esthetic is one of the prime goal of the orthodontic treatment. It is represented by the word of harmony or balance. There is no absolute esthetic norm but it is important to study about it in orthodontic and orthognatic surgical treatment planning. The purpose of this study is to obtain the norm of Korean female adolescents who were candidates of 1986, 1987 Miss Korea Beauty Contest. The 77 individual samples were selected and studied by cephalometric analysis. Obtained results were as follows: 1 Korean esthetic norm was obtained. 2. Simple correlation coefficient was obtained between each measurements. 3. Holdaway ratio of Korean beauty was 3.3 : 1. 4. To compare with caucasian, profile of Korean beauty had less prominant nose, more prominant lip and deeper sulcus depth.

• The Journal of the Acoustical Society of Korea
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• v.14 no.6
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• pp.62-67
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• 1995

In this paper, the features extraction of reflected ultrasonic signals from various type of defects existing in Al metal has been studied by digital signal processing. Since the reflected signals from various type of the defects are ambiguous in features distinction from effects of noise, Wiener filtering using AR (auto-regressive) technique and least-absolute-values norm method has been used in features extraction and comparison of signals. In this experiment, three types of the defect in aluminum specimen have been considered: a flat cut, an angular cut, a circular hole. And the reflected signal have been measured by pulse-echo methods. In the result of digital signal processing of the reflected signal, it has been found that the features extraction method have been effective for classification of the reflected signals from various defects.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.151-157
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• 2003

OLS로 알려진 기존의 주절 방법은 변수수의 증가에 따라 다중공선성(Multicollinearity)의 문제와 더불어 해석력(Interpretability)이 떨어지는 문제를 가지게 된다. 본 연구에서는 파라미터의 절대값의 크기(L1-Norm)에 제약을 줌으로써 이와 같은 OLS의 문제를 해결할 수 있는 동시에, 잔차의 제곱합대신 절대오차를 사용하는 Least Absolute Value(LAV) 방법을 사용함으로써 이상치에 로버스트한 결과를 주는 방법론을 제안한다. 또한. 본 연구에서 제안하는 방법이 선형계획법에 의해 모델처럼 될 수 있는 특성으로 인해 제약조건이 있는 이차 형태의 최적화 문제보다 수행 속도면에서 뛰어난 결과를 주는 것을 수치예제을 통해 보인다.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.417-430
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• 2013

Let X be a Banach space and ${\psi}$ a continuous convex function on ${\Delta}_{K+1}$ satisfying certain conditions. Let $(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}$ be the ${\psi}$-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-$l^N_1$-ness of Banach spaces using ${\psi}$-direct sums.

• Animal Bioscience
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• v.37 no.1
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• pp.16-27
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• 2024

Objective: The objective of this study was to investigate the effect of heat stress on the growth traits and genetic parameters of Thai native chickens. Methods: A total of 16,487 records for growth traits of Thai native chickens between 2017 and 2022 were used in this study. Data included the body weight at birth, body weight at 4, 8, and 12 weeks of age (BW0, BW4, BW8, BW12), average daily gain during 0 to 4, 4 to 8, and 8 to 12 weeks of age (ADG0-4, ADG4-8, ADG8-12), absolute growth rate at birth, at 4, 8, and 12 weeks of age (AGR0, AGR4, AGR8, AGR12). The repeatability test day model used the reaction-norm procedure to analyze the threshold point of heat stress, rate of decline of growth traits, and genetic parameters. Results: At temperature and humidity index (THI) of 76, Thai native chickens began to lose their growth traits, which was the onset of heat stress in this study. The estimated heritability, genetic correlation between animal and heat stress effect, and correlations between the intercept and slope of the permanent environmental effects were 0.27, -0.85, and -0.83 for BW, 0.17, -0.81, and -0.95 for ADG, 0.25, -0.61, and -0.83 for AGR, respectively. Male chickens are more affected by heat stress than female chickens with a greater reduction of BW, ADG, and AGR, values equal to -9.30, -0.23, -15.21 (in males) and -6.04, -0.21, -10.10 (in females) gram per 1 level increase of THI from the THI of 76. Conclusion: The influence of thermal stress had a strong effect on the decline in growth traits and genetic parameters in Thai native chickens. This study indicated that genetic models used in conjunction with THI data are an effective method for the analysis and assessment of the effects of heat stress on the growth traits and genetics of native chickens.