• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.11-27
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• 2010

Let $\Omega$ be a domain with smooth boundary in ${\mathbb{C}}^{n+1}$ and let $p{\in}{\partial}{\Omega}$. Suppose that $\Omega$ is Kobayashi hyperbolic and p is of Catlin multi-type ${\tau}=({\tau}_0,{\ldots},{\tau}_n)$. In this paper, we show that $\Omega$ admits a $C^{k}$ contraction at p with $k{\geq}\mid{\tau}\mid+1$ if and only if $\Omega$ is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial.

• Geophysics and Geophysical Exploration
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• v.5 no.3
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• pp.169-177
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• 2002

We develop the weighted-averaging finite-element method which uses four kinds of element sets. By constructing global stiffness and mass matrices for four kinds of element sets and then averaging them with weighting coefficients, we obtain a new global stiffness and mass matrix. With the optimal weighting coefficients minimizing grid dispersion and grid anisotropy, we can reduce the number of grid points required per wavelength to 4 for a $1\%$ upper limit of error. We confirm the accuracy of our weighted-averaging finite-element method through accuracy analyses for a homogeneous and a horizontal-layer model. By synthetic data example, we reconfirm that our method is more efficient for simulating a geological model than previous finite-element methods.

• Advances in aircraft and spacecraft science
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• v.8 no.4
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

• Korean Journal of Psychosomatic Medicine
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• v.31 no.2
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• pp.108-117
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• 2023

Objectives : Somatic symptom disorder (SSD) is characterized by the manifestation of a variety of physical symptoms, but little is known about differences in autonomic nervous system activity according to symptom severity, especially within patient groups. In this study, we examined differences in heart rate variability (HRV) across symptom severity in a group of SSD patients to analyze a representative marker of autonomic nervous system changes by symptoms severity. Methods : Medical records were retrospectively reviewed for patients who were diagnosed with SSD based on DSM-5 from September 18, 2020 to October 29, 2021. We applied inverse probability of treatment weighting (IPTW) methods to generate more homogeneous comparisons in HRV parameters by correcting for selection biases due to sociodemographic and clinical characteristic differences between groups. Results : There were statistically significant correlations between the somatic symptom severity and LF (nu), HF (nu), LF/HF, as well as SD1/SD2 and Alpha1/Alpha2. After IPTW estimation, the mild to moderate group was corrected to 27 (53.0%) and the severe group to 24 (47.0%), and homogeneity was achieved as the differences in demographic and clinical characteristics were not significant. The analysis of inverse probability weighted regression adjustment model showed that the severe group was associated with significantly lower RMSSD (β=-0.70, p=0.003) and pNN20 (β=-1.04, p=0.019) in the time domain and higher LF (nu) (β=0.29, p<0.001), lower HF (nu) (β=-0.29, p<0.001), higher LF/HF (β=1.41, p=0.001), and in the nonlinear domain, significant differences were tested for SampEn15 (β=-0.35, p=0.014), SD1/SD2 (β=-0.68, p<0.001), and Alpha1/Alpha2 (ß=0.43, p=0.001). Conclusions : These results suggest that differences in HRV parameters by SSD severity were showed in the time, frequency and nonlinear domains, specific parameters demonstrating significantly higher sympathetic nerve activity and reduced ability of the parasympathetic nervous system in SSD patients with severe symptoms.