• 대한수학회논문집
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• 제34권3호
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• pp.863-879
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• 2019

In this paper we study the Myers' theorem for orientable Riemannian hypersurfaces under some restrictions on the mean curvature, the second-order mean curvature, or the divergence of the shape operator and give some estimates for the diameter of such hypersurfaces.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• 대한기계학회논문집B
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• 제24권2호
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• pp.224-232
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• 2000

Four turbulent $k-{\varepsilon}$ models (i.e., standard model, modified models with streamline curvature modification and/or preferential dissipation modification) are applied in order to analyze the turbulent flow of wall-attaching offset jet. For numerical convergence, this paper develops a method of slowly increasing the convective effect induced by skew-velocity in skew-upwind scheme (hereafter called Partial Skewupwind Scheme). Even though the method was simple, it was efficient in view of convergent speed, computer memory storage, programming, etc. The numerical results of all models show good prediction in first order calculations (i.e., reattachment length, mean velocity, pressure), while they show some deviations in ·second order (i.e., kinetic energy and its dissipation rate). Like the previous results obtained by upwind scheme, the streamline curvature modification results in better prediction, while the preferential dissipation modification does not.

• 대한수학회논문집
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• 제29권1호
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• pp.141-153
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• 2014

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집B
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• pp.579-584
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• 2000

Algebraic Reynolds Stress (ARS) model is applied in order to analyze the turbulent flow of wall-attaching offset jet and to evaluate the model's predictability. The applied numerical schemes are upwind scheme and skew-upwind scheme. The numerical results show good prediction in first order calculations (i.e., reattachment length, mean velocity, pressure), while they show slight deviations in second order (i.e., kinetic energy and turbulence intensity). By comparison with the previous results using $k-{\varepsilon}$ model, ARS model predicts better than the standard $k-{\varepsilon}$ model, however, predicts slightly worse than the $k-{\varepsilon}$ model including the streamline curvature modification. Additionally this study can reconfirm that skew-upwind scheme has approximately 25% improved predictability than upwind scheme.

• 대한기계학회논문집B
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• 제24권12호
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• pp.1615-1624
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• 2000

Algebraic Reynolds Stree (ARS) model is applied in order to analyze the turbulent flow of wall-attaching offset jet and to evaluate the predictability of model. The applied numerical schemes are the upwind scheme and the skew-upwind scheme. The numerical results show a good prediction in the first order calculations(i.e., reattachment length, mean velocity, pressure), however, slight deviations in the second order(i.e., kinetic energy and turbulence intensity). Comparing with the previous results using the k-$\varepsilon$ model, the ARS model predicts better than the standard k-$\varepsilon$ model, however, slightly worse than the k-$\varepsilon$ model including the streamline curvature modification. Additionallay this study can reconfirm that the skew-upwind scheme has approximately 25% improved predictability than the upwind scheme.

• 대한기계학회논문집
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• 제9권4호
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• pp.403-413
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• 1985

본 논문에서는 수직벽 하류에 형성되는 박이 전단층의 발전과 재부착 그리고 재발전 경계층에 대해 평균 속도, 벽면의 압력 분포, 난류 강도, 레이놀즈 전단 압력 및 아직 수직벽에 대해서는 보고된바 없는 난류 떨림 속도 성분들의 3승곱 통계치를 측정하여 난류 구조의 변화를 분석하고 이를 수치적 계산 모델개발의 자 료로 제공하고자 함이 이 연구의 목적이다.

• Smart Structures and Systems
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• 제9권6호
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• 한국도로학회논문집
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• 제17권5호
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• pp.47-56
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• 2015

PURPOSES: The purpose of this study is to estimate the impact of variable message signage (VMS) on traffic safety as a function of road curve radius using statistical methods. METHODS: In order to analyze the impact of VMS installations on traffic safety, travel speed, lateral distance, and geometric data relating to road curvature in each study area was acquired and analyzed for the impact of providing VMS information on driver performance and traffic safety using statistical methods including student t-test, Mann-Whitney test, and the Anderson-Darling test for estimating traffic safety hazard zone in each lane. RESULTS: As a result of analyzing driver performance characteristics before and after providing VMS information, it was determined that by providing VMS information, mean travel speed is deceased and vehicles are driven with increased precision, following the centerline in the first and second lanes. Also the results of analyzing traffic safety impacts of VMS indicate that traffic safety performance factors in the first lane of the Gapyeong section can, on average, increase in the left and right side of the lane by 19.22% and 68.98%, respectively, and in the case of the second lane, safety impacts, on average, can increase in both sides by 100%. For the Hongcheon section, traffic safety impacts in the first lane, on average, can increase along the left and right sides of the lane by 32.31% and 47.18%, and within the second lane, traffic safety can be increased along the left and right side of the lane by 10.97% and -0.01%, respectively. CONCLUSIONS: Based on the results of this study, the impact on traffic safety obtained by providing VMS information for road sections with smaller curve radii is greater than can be obtained for road sections with larger curve radii.