• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.515-527
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• 1996

It has been known for mean field models that the limiting distribution reflecting the asymptotic behavior of the system is non-Gaussian at the critical state. Recently, however, Papangelow showed for the critical Curie-Weiss mean field model that there exist Gaussian structures in the asymptotic behavior of the total magnetization. We construct Gaussian structures existing in the internal fluctuation of the system for the critical case of a generalized Curie-Weiss mean field model.

• Wind and Structures
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• v.31 no.3
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• pp.217-227
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• 2020

Based on translation models, both Gaussian and non-Gaussian wind fields are generated using spectral representation method for investigating the influence of non-Gaussian characteristics and directivity effect of wind load on fatigue damage of wind turbine. Using the blade aerodynamic model and multi-body dynamics, dynamic responses are calculated. Using linear damage accumulation theory and linear crack propagation theory, crack initiation life and crack propagation life are discussed with consideration of the joint probability density distribution of the wind direction and mean wind speed in detail. The result shows that non-Gaussian characteristics of wind load have less influence on fatigue life of wind turbine in the area with smaller annual mean wind speeds. Whereas, the influence becomes significant with the increase of the annual mean wind speed. When the annual mean wind speeds are 7 m/s and 9 m/s at hub height of 90 m, the crack initiation lives under softening non-Gaussian wind decrease by 10% compared with Gaussian wind fields or at higher hub height. The study indicates that the consideration of the influence of softening non-Gaussian characteristics of wind inflows can significantly decrease the fatigue life, and, if neglected, it can result in non-conservative fatigue life estimates for the areas with higher annual mean wind speeds.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.36-51
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• 2022

We study the translation surfaces in the pseudo-Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variable.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.359-366
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• 2009

In this paper, we study a tube in a Euclidean 3-space satisfying some equation in terms of the Gaussian curvature, the mean curvature and the second Gaussian curvature.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.549-558
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• 2006

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.231-242
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• 2001

We showed in [2] that if r≤2, zero mean Gaussian of average error of the Trapezoidal rule is proportional to h/sub i//sup 2r+3/ on the interval [0,1]. In this paper, if r≥3, we show that zero mean Gaussian of average error of the Trapezoidal rule is bounded by Ch⁴/sub i/h⁴/sub j/.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.247-259
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• 2018

Factorable surfaces, i.e. graphs associated with the product of two functions of one variable, constitute a wide class of surfaces in differential geometry. Such surfaces in the pseudo-Galilean space with zero Gaussian and mean curvature were obtained in [2]. In this study, we provide new results relating to the factorable surfaces with non-zero constant Gaussian and mean curvature.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.249-266
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• 2024

In this work, we study time-like and space-like surfaces invariant by a group of translation isometries of the half-space model ℋ³₁ of the anti-de Sitter space ℍ³₁ . We determine all such surfaces with constant mean curvature and constant Gaussian curvature. We also obtain umbilical surfaces of ℋ³₁.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-477
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• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.593-611
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• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.