• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1513-1528
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• 2021

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → R_Nil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → M_Nil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.351-381
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• 2021

In this paper we introduce the notion of strong Galois H-progenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ≅ Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.

• Journal of Aerospace System Engineering
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• v.17 no.1
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• pp.24-32
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• 2023

This paper studied HART II in descending flight using rotorcraft analysis code based on geometrically exact beam (GEB) model. The present GEB model expressed by a mixed variational formulation could capture the geometrically nonlinear behavior of the blade without arbitrary assumptions. In previous results, correlation of airloads with structural moments for HART II was not as good as blade deflections. However, in present results, predictions of airloads and structural loads are fairly correlated with measured data.

• Coupled systems mechanics
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• v.11 no.6
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• pp.525-542
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• 2022

In this work we present an advanced approach to the design of small wind turbine support steel structures. To this end we use an improved version of previously developed geometrically exact beam models. Namely, three different geometrically exact beam models are used, the first two are the Reissner and the Kirchhoff beam models implementing bi-linear hardening response and the third is the Reissner beam capable of also representing connections response. All models were validated in our previous research for a static response, and in this work they are extended to dynamic response. With these advanced models, we can perform analysis of four practical solutions for the installation of small wind turbines in new or existing buildings including effects of elastoplastic response to vibration problems. The numerical simulations confirm the robustness of numerical models in analyzing vibration problems and the crucial effects of elastoplastic response in avoiding resonance phenomena.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.16 no.5
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• pp.504-515
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• 1987

This study conducts an analysis for the heat diffusion of an annular fin considering con-vection phenomena at the fin edge as well as along the fin perimeter. When the temperature of the fin base is given with an increasing exponential function, the exact series solutions of tem-perature distribution are obtained by laplace transformation in terms of dimensionless para-meters. From these solutions heat flux and fin efficiency can be obtained. These exact solu-tions converge rapidly for large values of dimensionless time, but slowly for small ones. To avoid this convergence difficulty, approximate solutions of the temperature distribution and heat flux for small values of dimensionless time are also presented. Substituting the variations of dimensionless parameters into the these exact solutions, the characteristics of these response are investigated.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.487-510
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• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.

• Coupled systems mechanics
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• v.13 no.1
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• pp.73-93
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• 2024

In this work, we propose combining an advanced optimal control algorithm with a geometrically exact beam model. For simplicity, the 2D Reissner beam model is chosen to represent large displacements and rotations. The difficulty pertains to the nonlinear nature of beam kinematics affecting the tangent stiffness matrix, making it non-constant, which compromises direct use of optimal control methods for linear problems. Thus, we seek to accommodate a time varying control using linear-quadratic regulator (LQR) algorithm with the proposed geometrically nonlinear beam model. We provide a detailed theoretical formulation and its numerical implementation in a variational format form. Several illustrative numerical examples are provided to confirm an excellent performance of the proposed methodology.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.411-421
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• 2015

This paper investigates the issue of analytic travelling wave solutions for some important coupled models of fractional order. Analytic travelling wave solutions of the considered model are found by means of the Q-function method. The results give us that the Q-function method is very simple, reliable and effective for searching analytic exact solutions of complex nonlinear partial differential equations.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.971-974
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• 2012

The facilitated diffusion effect on protein-DNA binding is studied. A rigorous theoretical approach is presented to deal with the coupling between one-dimensional and three-dimensional diffusive motions. For a simplified model, the present approach can provide numerically exact results, which are confirmed by the lattice-based Monte Carlo simulations.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2863-2866
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• 2003

In nonlinear control fields, for irregular nonlinear systems, control form which consists of approximate tracking control law and exact tracking control law and which switches between two laws has been proposed recently. In this thesis, we design new switching control law which connect approximate linearization control law and exact linearization control law by fuzzy rules for irregular nonlinear system, ball and beam system. Fuzzy switching controller designed by fuzzy concept is proved that designed scheme overcomes singularities of irregular system, improves unstability problem of switching procedure, and has more efficient control value through simulation. Stability of fuzzy control system proved by Lyapunov's stability theorems.