• 대한수학회지
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• 제59권5호
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• pp.869-890
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• 2022

We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case.

• 대한수학회지
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• 제59권3호
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• East Asian mathematical journal
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• 제25권1호
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• pp.11-26
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• 2009

In this paper, the concepts of compatible mappings of types (A) and (P) are introduced in an induced metric space, two common xed point theorems for two pairs of compatible mappings of types (A) and (P) in an induced complete metric space are established. As their applications, the existence and uniqueness results of common solution for a system of functional equations arising in dynamic programming are discussed.

• 대한수학회논문집
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• 제36권3호
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.229-241
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• 2007

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.501-515
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• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.

• 대한간호학회지
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• 제40권3호
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• pp.411-422
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• 2010

Purpose: In the present study, an analysis of the life of adolescents with complex congenital heart disease (CHD) was done using grounded theory. Consideration was given to the socio-cultural context of Korea. Methods: After approval from the institutional review board of Y hospital, 12 patients ranging in age from 14 to 35 were recruited. Data were gathered using in-depth interviews. Theoretical sampling was performed until the concepts were saturated. Results: The results confirmed the life of adolescents with complex CHD as a 'journey to finding uniqueness of oneself as a person with CHD'. The life consisted of 3 stages. In the crisis stage, participants had a feeling of threat to self-existence, and made an effort to be the same as others. In the self-recognition stage, participants who had sufficient role-performance built self-esteem while those who did not fell into self-accusation. In the self-establishment stage, participants who reached sufficiency in independence and knowledge planned the future, whereas those who did not conformed to the realities of life. Conclusion: The results of present study provide help in understanding the experiences of adolescents with CHD and provide a basis for developing nursing intervention strategies for these patients.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.749-759
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• 2024

In this manuscript, we formulate the notion of Ω(H, θ)-contraction on a self mapping f : W → W, this contraction based on the concept of Ω-distance mappings equipped on G-metric spaces together with the concept of H-simulation functions and the class of Θ-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.

• ETRI Journal
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• 제36권1호
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• pp.31-41
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• 2014

The heterogeneous network (HetNet) has been discussed in detail in the Long-Term Evolution (LTE) and LTE Advanced standards. However, the standardization of High-Speed Packet Access HetNet (HSPA HetNet) launched by 3GPP is pushing at full steam. Interference coordination (IC), which is responsible for dealing with the interference in the system, remains a subject worthy of investigation in regard to HSPA HetNet. In this paper, considering the network framework of HSPA HetNet, we propose a quasi-distributed IC (QDIC) scheme to lower the interference level in the co-channel HSPA HetNet. Our QDIC scheme is constructed as slightly different energy-efficient non-cooperative games in the downlink (DL) and uplink (UL) scenarios, respectively. The existence and uniqueness of the equilibrium for these games are first revealed. Then, we derive the closed-form best responses of these games. A feasible implementation is finally developed to achieve our QDIC scheme in the practical DL and UL. Simulation results show the notable benefits of our scheme, which can indeed control the interference level and enhance the system performance.