• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.47-61
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• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.217-222
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• 2003

In this paper, we consider the fuzzy differential equations (equation omitted) where F(t, x(t)) is a continuous fuzzy mapping on [0, $\infty$) ${\times}$ E$\^$n/. The purpose of this paper is to prove that the solution ${\Phi}$(t) of the fuzzy differential equations is equiasymptotically stable in the large and uniformly asymptotically stable in the large.

• Structural Engineering and Mechanics
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• 제19권4호
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

• Computers and Concrete
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• 제11권5호
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• pp.411-440
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• 2013

Large fluctuations in surface strain at the level of steel are expected in reinforced concrete flexural members at a given stage of loading due to the emergent structure (emergence of new crack patterns). This has been identified in developing deterministic constitutive models for finite element applications in Ibrahimbegovic et al. (2010). The aim of this paper is to identify a suitable probability distribution for describing the large deviations at far from equilibrium points due to emergent structures, based on phenomenological, thermodynamic and statistical considerations. Motivated by the investigations reported by Prigogine (1978) and Rubi (2008), distributions with heavy tails (namely, alpha-stable distributions) are proposed for modeling the variations in strain in reinforced concrete flexural members to account for the large fluctuations. The applicability of alpha-stable distributions at or in the neighborhood of far from equilibrium points is examined based on the results obtained from carefully planned experimental investigations, on seven reinforced concrete flexural members. It is found that alpha-stable distribution performs better than normal distribution for modeling the observed surface strains in reinforced concrete flexural members at these points.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.39-49
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• 1995

The surface hydrology of large land areas is susceptible to several preferred stable states with transitions between stable states induced by stochastic fluctuation. This comes about due to the close couping of land surface and atmospheric interaction. An interesting and important issue is the duration of residence in each mode. Mean transition times between the stable modes are analyzed for different model parameters or climatic types. In an example situation of this differential equation exhibits a bimodal probability distribution of soil moisture states. Uncertainty analysis regarding the model parameters is performed using a Monte-Carlo simulation method. The method developed in this research may reveal some important characteristics of soil moisture or precipitation over a large area, in particular, those relating to abrupt change in soil moisture or preciptation having extremely variable duration.

• The Journal of Korean Physical Therapy
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• 제29권2호
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• pp.55-61
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• 2017

Purpose: The purpose of this study was to investigate the effects of a task-oriented upper arm exercise performed in a sitting position on either an unstable support surface or a stable support surface for children with cerebral palsy. Methods: We prospectively evaluated 18 children with cerebral palsy. Eight subjects were randomly assigned to each of the stable and unstable support surface groups. We performed the upper arm exercise three times a week for 6 weeks. To confirm the effects of the intervention, the berg balance scale test, modified functional reaching test (MFRT), timed up and go test (TUG), and Jebsen-Taylor hand function test were conducted before and after the study. Results: Significant differences were observed in MFRT and TUG between the experimental and control groups (p<0.05). In the Jebsen-Taylor hand function test, there were significant differences between the groups for the items picking up small objects, stacking checkers, lifting large light objects, and lifting large heavy objects (p<0.05), but not for writing and stimulation of feeding. Significant differences were observed between the groups in items of card turning, lifting large light objects, and lifting heavy objects. Conclusion: The purpose of this study was to evaluate the effectiveness of a task-oriented upper extremity exercise program for dynamic balance and hand function performed in a sitting position with either stable or unstable support by cerebral palsy patients. There were improvements in the two groups, but performing the exercise while sitting on an unstable support surface had a greater effect on dynamic balance and hand function than exercise while sitting on a stable supporting surface. The results of this study can be used to improve the daily lives of cerebral palsy patients.

• Bulletin of the Korean Chemical Society
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• 제32권10호
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• pp.3618-3623
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• 2011

This paper presents a stable isotope chemistry of bone collagen and carbonate. Bone carbonate has the potential to provide additional isotopic information. However, it remains controversial as to whether archaeological bone carbonate retains its original biogenic signature. I used a novel application of bone density fractionation and checked the integrity of ${\delta}^{13}C_{apa}$ values using radiocarbon dating. Diagenesis in archaeological bone carbonate still remains to be resolved in extracting biogenic information. The combined use of bone density fractionation and differential dissolution method shows a large shift in the ${\delta}^{13}C_{apa}$ values. Although ${\delta}^{13}C_{apa}$ values are improved in lighter density fractions, a large percentage of contamination in bone carbonate was reported via $^{14}C$ dating compared to that noted with bone collagen.

• 대한수학회지
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• 제45권3호
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• pp.871-881
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• 2008

In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to a maximum 2-packing in G. We also show that for dominating set games corresponding to G, the core is stable if it is large, the game is extendable, or the game is exact. In fact, the core being large, the game being extendable and the game being exact are shown to be equivalent.

• Structural Engineering and Mechanics
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• 제4권5호
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• pp.529-540
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• 1996

The dynamic buckling mechanism of a single-degree-of-freedom dissipative/nondissipative gradient system is thoroughly studied, employing energy criteria. The model is chosen in such a manner, that its corresponding static response is associated with all types of distinct critical points. Under a suddenly applied load of infinite duration, it is found that dynamic buckling, occurring always through a saddle, leads to an escaped motion, which is finally attracted by remote stable equilibrium positions, belonging sometimes also to complementary paths. Moreover, although the existence of initial imperfection changes the static behaviour of the system from limit point instability to bifurcation, it is established that the proposed model is dynamically stable in the large, regardless of the values of all other parameters involved.

• Structural Engineering and Mechanics
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• 제68권3호
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• pp.377-384
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• 2018

Bi-stable structure can be stable in both its extended and coiled forms. For the un-stressed thin cylindrical shell, the strain energy expressions are deduced by using a theoretical model in terms of only two parameters. Based on the principle of minimum potential energy, the bi-stable behaviors of the cylindrical shells are investigated. The results indicate that the isotropic cylindrical shell does not have the second stable configuration and laminated cylindrical shells with symmetric or antisymmetric layup of fibers have the second stable state under some confined conditions. In the case of antisymmetric laminated cylindrical shell, the analytical expressions of the stability are derived based on the extremal principle, and the shell can achieve a compact coiled configuration without twist deformation in its second stable state. In the case of symmetric laminated cylindrical shell, the explicit solutions for the stability conditions cannot be deduced. Numerical results show that stable configuration of symmetric shell is difficult to achieve and symmetric shell has twist deformation in its second stable form. In addition, the roll-up radii of the antisymmetric laminated cylindrical shells are calculated using the finite element package ABAQUS. The results show that the value of the roll-up radii is larger from FE simulation than from theoretical analysis. By and large, the predicted roll-up radii of the cylindrical shells using ABAQUS agree well with the theoretical results.