• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.419-433
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• 2013

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

• East Asian mathematical journal
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• v.34 no.3
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• pp.265-285
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• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1035-1044
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• 2021

Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.2
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• pp.67-72
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• 2005

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this paper, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition equations. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• KIEE International Transactions on Power Engineering
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• v.5A no.4
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• pp.344-349
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• 2005

In conventional small signal stability analysis, the system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of the state matrix. However, when a system contains switching elements such as FACTS equipments, it becomes a non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is performed by means of eigenvalue analysis of the system's periodic transition matrix based on the discrete system analysis method. In this paper, the RCF (Resistive Companion Form) method is used to analyze the small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of the power system, generator, controllers and FACTS equipments including switching devices should be modeled in the form of state transition equations. From this state transition matrix, eigenvalues that are mapped into unit circles can be computed precisely.

• Journal of KIISE:Software and Applications
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• v.37 no.10
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• pp.745-750
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• 2010

To effectively retrieve mathematical documents including various equations, mathaware search engines are needed. In this paper, we propose a equation retrieval system which helps users effectively search structurally similar equations. The proposed system disassembles MathML equations into three types of heterogeneous indexing terms; operators, variables, and partial structures of equations. Then, it independently indexes the disassembled terms. When a user inputs a MathML equation, the proposed system searches and ranks equations using weighted sums of three language models for the heterogeneous indexing terms. In the experiments with 244,744 MathML equations, three proposed system showed reliable performances (a P@1 of 53% in the closed test and a P@1 of 63% in the open test).

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.1007-1025
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• 2009

First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $H^{-1}$ and $L^2$ norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

• The KIPS Transactions:PartD
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• v.9D no.3
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• pp.487-494
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• 2002

In this paper, we present an equation edition system, which is designed and implemented according to the W3C MathML standard. The system can be used to edit equations for the various web-oriented applications. Various user-friendly interfaces are provided for the easy and efficient edition of equations. The edited equations can be viewed immediately with the representation modules. To improve the processing speed of equations, we upgraded functions of the conventional XML parser. The presented system will contribute to the extensive usage of equations on the web and efficient processing of XML documents with equations.

• Smart Structures and Systems
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• v.15 no.3
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• pp.897-911
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• 2015

This study presents a novel approach based on advancements in Evolutionary Computation for data-driven modeling of complex multi-dimensional memory-dependent systems. The investigated example is a benchmark coupled three-dimensional system that incorporates 6 Bouc-Wen elements, and is subjected to external excitations at three points. The proposed technique of this research adapts Genetic Programming for discovering the optimum structure of the differential equation of an auxiliary variable associated with every specific degree-of-freedom of this system that integrates the imposed effect of vibrations at all other degrees-of-freedom. After the termination of the first phase of the optimization process, a system of differential equations is formed that represent the multi-dimensional hysteretic system. Then, the parameters of this system of differential equations are optimized in the second phase using Genetic Algorithms to yield accurate response estimates globally, because the separately obtained differential equations are coupled essentially, and their true performance can be assessed only when the entire system of coupled differential equations is solved. The resultant model after the second phase of optimization is a low-order low-complexity surrogate computational model that represents the investigated three-dimensional memory-dependent system. Hence, this research presents a promising data-driven modeling technique for obtaining optimized representative models for multi-dimensional hysteretic systems that yield reasonably accurate results, and can be generalized to many problems, in various fields, ranging from engineering to economics as well as biology.