• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1175-1199
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• 2019

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.511-527
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• 2015

For time series analysis, power transformation (especially log-transformation) is widely used for variance stabilization or normalization for stationary ARMA(p, q) model. A simple and naive back transformed forecast is obtained by taking the inverse function of expectation. However, this back transformed forecast has a bias. Under the assumption that the log-transformed data is normally distributed. The unbiased back transformed forecast can be obtained by the expectation of log-normal distribution; consequently, the property of this back transformation was studied by Granger and Newbold (1976). We investigate the sensitivity of back transformed forecasts under several different underlying distributions using simulation studies.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.107-116
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• 2012

Here, by using the symbolical method introduced by Burchnall and Chaundy, we aim at constructing certain expansion formulas for the generalized hypergeometric function $_pF_q$. In addition, using our expansion formulas for $_pF_q$, we present formulas of an analytic continuation of the Clausen hypergeometric function $_3F_2$, which are much simpler than an earlier known result. We also give some integral representations for $_3F_2$.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.6
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• pp.1037-1044
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• 2020

Since radar wind profiler (RWP) provides wind field data with high time and space resolution in all weather conditions, their verification of the accuracy and quality is essential. The simultaneous wind measurement from rawinsonde is commonly used to evaluate wind vectors from RWP. In this study, the simulation algorithm which produces the spectrum and raw time series (I/Q) data from the average values of moments is presented as a step-by-step verification method for the signal processing algorithm. The possibility of the simulation algorithm was also confirmed through comparison with the raw data of LAP-3000. The Doppler power spectrum was generated by assuming the density function of the skew-normal distribution and by using the moment values as the parameter. The simulated spectrum was generated through random numbers. In addition, the coherent averaged I/Q data was generated by random phase and inverse discrete Fourier transform, and raw I/Q data was generated through the Dirichlet distribution.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1223-1228
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• 2006

This paper presents an experimental investigation of a recently developed Kronecker Product (KP) method to determine the type, location, and intensity of structural damage from an identified state-space model of the system. Although this inverse problem appears to be highly nonlinear, the system mass, stiffness, and damping matrices are identified through a series of transformations, and with the aid of the Kronecker product, only linear operations are involved in the process. Since a state-space model can be identified directly from input-output data, an initial finite element model and/or model updating are not required. The test structure is a two-degree-of-freedom torsional system in which mass and stiffness are arbitrarily adjustable to simulate various conditions of structural damage. This simple apparatus demonstrates the capability of the damage detection method by not only identifying the location and the extent of the damage, but also differentiating the nature of the damage. The potential applicability of the KP method for structural damage identification is confirmed by laboratory test.

• Korean Journal of Community Nutrition
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• v.23 no.5
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• pp.397-410
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• 2018

Objectives: An association between dietary patterns and mental health in children has been suggested in a series of studies, yet detailed analyses of dietary patterns and their effects on ADHD (attention deficit hyperactivity disorder) are limited. Methods: We included 4569 children who had dietary intake data as part of the CHEER (Children's Health and Environmental Research) study conducted nationwide from 2005 to 2010. We assessed ADHD (Attention Deficit Hyperactivity Disorder) by the DuPaul's ADHD Rating Scales and dietary intake by a semi-quantitative food frequency questionnaire. Using intake data, we constructed five dietary patterns: "Plant foods & fish," "Sweets," "Meat & fish," "Fruits & dairy products," and "Wheat based." Results: The overall proportion of ADHD was 12.3%. Boys (17.8%) showed a higher rate of ADHD than girls (6.5%). The total intake of calories (85 kcal) and plant fat (2g) in the ADHD group was significantly higher than that of the normal group. ADHD was significantly negatively associated with dietary habits such as having breakfast and meal frequency, and positively associated with eating speed, unbalanced diet, overeating, and rice consumption. Regarding dietary patterns, the "Sweets" category was relevant to high ADHD risk (OR 1.59, 95% CI: 1.18, 2.15 for Q5 vs. Q1) in a linear relationship. An inverse, non-linear association was found between "Fruits & dairy products" and ADHD (OR 0.55, 95% CI: 0.39, 0.76 for Q4 vs. Q1). Conclusions: Our study confirms both positive and negative associations between diet and ADHD in elementary school age children. Moreover, linear or nonlinear associations between diet and ADHD draw attention to the possible threshold role of nutrients. Further studies may consider characteristics of diet in more detail to develop better intervention or management in terms of diet and health.