• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.551-564
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• 2001

We view Weyl structures as generalizations of Riemannian metrics and study the critical points of geometric functional which involve scalar curvature, defined on the space of Weyl structures on a closed 4-manifold. The main goal here is to provide a framework to analyze critical Weyl structures by defining functionals, discussing function spaces and writing down basic formulas for the equations of critical points.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.293-303
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• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• Journal of Korean Institute of Industrial Engineers
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• v.14 no.2
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• pp.1-10
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• 1988

We consider a vacation system in which the server takes two different types of vacations alternately. We obtain the server idle probability and derive the system size distribution and the waiting time distribution by defining supplementary variables. We show that the decomposition property works for these mixed-vacation queues. We also propose a method directly to obtain the waiting time distribution without resorting to the system equations. The T-policy is revisited and is shown that the cost is minimized when the length of vacations are the same.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2423-2425
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• 2003

This paper proposes a decision criteria for selecting the shortest path from Dubins set between the initial and final configurations of a car-like robot. The suggested scheme is a very simple and computational savings without explicitly calculating the candidate paths and having a complicated decision table. Equations for calculating the shortest path are derived in simple form with coordinate transform and defining standard forms.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.509-524
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• 2023

In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and Găvruţa stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-𝛽-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.673-692
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• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• Geomechanics and Engineering
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• v.30 no.3
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• pp.233-246
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• 2022

In this study, the city of Osijek is used as a case study area for low to medium seismicity regions with deep soil over deep geological deposits to determine horizontal PGA values. For this reason, we propose new regional attenuation equations for PGA that can simultaneously capture the effects of deep geology and local soil conditions. A micro-zoning map for the city of Osijek is constructed using the derived empirical scaling equations and compared to all prior seismic hazard estimates for the same area. The findings suggest that the deep soil atop deep geological sediments results in PGA values that are only 6 percent larger than those reported at rock soil sites atop geological rocks. Given the rarity of ground motion records for deep soils atop deep geological layers around the world, we believe this case study is a start toward defining more reliable PGA estimates for similar areas.

• Structural Engineering and Mechanics
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• v.90 no.5
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• pp.505-515
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• 2024

In this study, obtaining theoretical stress-strain curves and determining the parameters defining the equivalent rectangular stress block were aimed for 3 and 4-layered rectangular Reinforced Concrete (RC) cross-sections subjected to flexure. For these aims, the analytical stress-strain model proposed by Hognestad was chosen for the concrete grades (20 MPa≤fck≤60 MPa) used in this study. The tensile strength of the concrete was neglected and the thickness of the concrete layers in the compression zone of the concrete cross-section was taken as equal. In addition, while concrete strength was kept constant within each layer, concrete strengths belonging to separate layers were increased from the neutral axis towards the outer face of the compression zone of the concrete cross-section. After the equivalent rectangular stress block parameters were determined by numerical iterations, variations of these parameters depending on concrete strength in layers and layer numbers were obtained. Finally, some analytical equations have been proposed to predict the equivalent stress block parameters for the 3 and 4-layered RC cross-sections and validities of these proposed equations were shown by different metrics in this study.

• Advances in Energy Research
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• v.5 no.1
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• pp.31-55
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• 2017

In the present study, PV/T collector was modeled via analysis of governing equations and physics of the problem. Specifications of solar radiation were computed based on geographical characteristics of the location and the corresponding time. Temperature of the collector plate was calculated as a function of time using the energy equations and temperature behavior of the photovoltaic cell was incorporated in the model with the aid of curve fitting. Subsequently, operational range for reaching to maximal efficiency was studied using Genetic Algorithm (GA) technique. Optimization was performed by defining an objective function based on equivalent value of electrical and thermal energies. Optimal values for equipment components were determined. The optimal value of water flow rate was approximately 1 gallon per minute (gpm). The collector angle was around 50 degrees, respectively. By selecting the optimal values of parameters, efficiency of photovoltaic collector was improved about 17% at initial moments of collector operation. Efficiency increase was around 5% at steady condition. It was demonstrated that utilization of photovoltaic collector can improve efficiency of solar energy-based systems.