• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.867-883
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• 2024

The objective of this article is to study the general set-valued nonlinear variational-hemivariational inequalities and investigate the gap function, regularized gap function and Moreau-Yosida type regularized gap functions for the general set-valued nonlinear variational-hemivariational inequalities, and also discuss the error bounds for such inequalities using the characteristic of the Clarke generalized gradient, locally Lipschitz continuity, inverse strong monotonicity and Hausdorff Lipschitz continuous mappings.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.557-573
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• 2021

In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric ₂F₁(x) function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators. Formulas (images) for compositions of such generalized fractional integrals and differential constructions with the n-times product of the generalized modified Bessel function of the second type are established. The results are obtained in terms of the generalized Lauricella function or Srivastava-Daoust hypergeometric function. Equivalent assertions for the Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential are also deduced.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.371-378
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• 2010

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Journal of Applied Reliability
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• v.15 no.1
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• pp.44-51
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• 2015

In this study, we propose reliability prediction of a satellite by function analysis. To do so, the intended functions of the satellite are derived from using function structure block diagram, and defined as main, sub, and detailed functions. Furthermore, in order to generate function and reliability structure table, reliability model rule, duty cycle, and types of switch are assigned to the classified functions. This study also establishes reliability block diagram and mathematical reliability models to schematize the relationship among the functions. The reliability of the classified function is estimated by calculating the failure rate of parts comprising them. Finally, we apply the proposed method to a small satellite as a case study. The result shows that the reliability for the detailed function and the sub function as well as the main function could be predicted quantitatively and accurately by the proposed approach.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.103-108
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• 2002

We consider an estimation of discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of a change point and jump size in variance function and then construct an estimator of entire variance function. We examine the rates of convergence of these estimators and give results on their asymptotics. Numerical work reveals that the effectiveness of change point analysis in variance function estimation is quite significant.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1213-1224
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• 2010

Using Ahlfors' covering surface method, some properties on the strong Borel direction of algebroid function of finite order are obtained. The main object of this paper is to prove existence theorem of a strong Borel direction and the existence of filling discs in such direction which briefly extends some results of meromorphic function.

• Nutrition Research and Practice
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• v.14 no.5
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• pp.490-500
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• 2020

BACKGROUND/OBJECTIVES: A cross-sectional study was undertaken to evaluate fluid intake and hydration status in association with cognitive function among 230 adolescents (10-14 years of age) in Petaling Perdana, Selangor, Malaysia. SUBJECTS/METHODS: Urine color was used to measure hydration status, while fluid intake was assessed using the 15-item beverage intake questionnaire. Cognitive function was assessed using the Wechsler Intelligence Scale for Children, Fourth Edition. RESULTS: More than half of the adolescents were mildly or moderately dehydrated (59.6%) and only one-third (33.0%) were well hydrated. Among the daily fluid types, intakes of soft drinks (r = -0.180; P = 0.006), sweetened tea (r = -0.184; P = 0.005) and total sugar-sweetened beverages (SSBs) (r = -0.199; P = 0.002) were negatively correlated with cognitive function. In terms of hydration status, cognitive function score was significantly higher (F-ratio = 4.102; P = 0.018) among hydrated adolescents (100.38 ± 12.01) than in dehydrated (92.00 ± 13.63) counterparts. Hierarchical multiple linear regression analysis, after adjusting for socio-demographic factors, showed that soft drinks (β = -0.009; P < 0.05) and sweetened tea (β = -0.019; P < 0.05) negatively predicted cognitive function (ΔR² = 0.044). When further control for sources of fluid, hydration status (β = -2.839; P < 0.05) was shown to negatively predict cognitive function (ΔR² = 0.021). The above variables contributed 20.1% of the variance in cognitive function. CONCLUSIONS: The results highlight the links between fluid intake (soft drinks, sweetened tea, total SSBs) and hydration status with cognitive function in adolescents. Interventions aimed at decreasing the consumption of SSBs and increasing hydration status through healthy fluid choices, such as water, could improve cognitive performance in adolescents.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.1-23
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• 2006

In this paper we consider an estimation of the discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of the change point in the variance function and then construct an estimator of the entire variance function. We examine the rates of convergence of these estimators and give results for their asymptotics. Numerical work reveals that using the proposed change point analysis in the variance function estimation is quite effective.

• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.81-87
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• 2000

One of the most important quantities in reliability theory is the expected number of renewals of a system during a given interval. This quantity, the renewal function, is used to determine the optimal preventive maintenance policy and to estimate the cost of a warranty. In this paper we study a parametric approach for a renewal function. The simulation study is presented to compare the relative performance of the introduced estimators of a renewal function. And we show that the proposed parametric estimator performs well.