• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.439-449
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• 2021

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if G is a finitely generated virtually nilpotent group and there exists g ∈ G such that if Tg is expansive and has the shadowing property, then T is topologically stable.

• Journal of electromagnetic engineering and science
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• v.3 no.1
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• pp.39-44
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• 2003

An unconditionally stable compact 2D Alternating-Direction Implicit (ADI) FDTD method for calculating dispersion characteristics of waveguide structures is proposed. The numerical stability and numerical dispersion relation of the proposed method are also presented and discussed. Numerical wavelengths for the dominant and higher order modes in a hollow waveguide are obtained from numerical simulations and compared with those from the analytical dispersion relation. The numerical results show that the proposed scheme has the potential to successfully analyze a class of waveguides having locally fine geometry with reduced numerical costs.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1901-1904
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• 2003

MPC or model predictive control is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global aymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.529-546
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• 2011

A deterministic tuberculosis model for theoretically assessing the potential impact of the combined effects of case detection in the presence of treatment is formulated. The qualitative features of its equilibria are analyzed and it is found that the disease-free equilibrium may not be globally asymptotically stable when the reproduction number is less than unity. This disease threshold number is further used to assess the impact of active TB case finding alone and in conjunction with treatment. A critical threshold parameter ${\Theta}$ say for which case detection will have a positive impact is derived. Using the Centre Manifold theory, the model may exhibit the phenomenon of backward bifurcation (coexistence of a locally stable endemic equilibrium with a stable disease-free equilibrium) when the reproduction number is less than unity. It is shown that the possibility of backward bifurcation occurring decreases with increase case detection. Graphical representations suggest that increase in case finding accompanied by treatment of detected TB cases, result in a marked decrease of TB cases (both latent and active TB).

• Journal of Gastric Cancer
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• v.4 no.1
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• pp.7-14
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• 2004

Purpose: The purpose of this study was to evaluate the treatment result of surgical resection after preoperative chemotherapy in inoperable gastric cancer patients. Materials and Methods: We analyzed 18 gastric cancer patients who underwent gastric resection after preoperative chemotherapy because they showed some clinical response to chemotherapy (15 with distant metastasis and 3 with locally advanced lesions). The mean postoperative follow-up period was $15.3\pm15.5$ ($1\∼56$) months. Results: In 15 patients with distant metastasis, 2 ($13.3\%$) showed complete response (CR), 10 ($66.7\%$) partial response (PR), 2 ($13.3\%$) stable disease (SD), and 1 ($6.7\%$) progressive disease (PD). The clinical response rate was $80.0\%$ Five subtotal gastrectomies, 4 total gastrectomies, and 6 extended total gastrectomies were performed. Two cases of CR were alive without recurrence for 4 and 26 months, respectively. Mean survival period in PR case was 37.7 months, but 2 cases of SD and 1 case of PD died after 11.7, 17.9, and 0.9 months, respectively. Postoperative survival was significantly associated with the response to chemotherapy (P<0.01). The mean survival period of the 10 patients with a complete resection was 44.1 months, which was significantly better than that of the 5 patients with an incomplete resection (9.8 months, P=0.03). Among 3 patients with locally advanced gastric cancer, 2 cases showed PR to chemotherapy, and complete resection was possible only by gastrectomy for those patients. Conclusion: In some selected cases, surgical resection was achievable after preoperative chemotherapy for patients with inoperable metastatic or locally advanced gastric cancer.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.1-25
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• 2013

In this paper we have developed a mathematical model of alcohol abuse. It consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined. Sensitivity analysis of $R_0$ identifies ${\beta}_1$, the transmission coefficient from moderate and occasional drinker to heavy drinker, as the most useful parameter to target for the reduction of $R_0$. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0$ < 1. It is found that, when $R_0$ = 1, a backward bifurcation can occur and when $R_0$ > 1, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE. Our aim of this analysis is to identify the parameters of interest for further study with a view for informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.747-767
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• 2013

In this paper we have constructed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined and sensitivity analysis of $R_0$ indicates that ${\beta}1$ (the transmission coefficient from moderate and occasional drinker to heavy drinker) is the most useful parameter for preventing drinking habit. Stability analysis of the model is made using the basic reproduction number. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0&lt;1$. It is found that, when $R_0=1$, a backward bifurcation can occur and when $R_0&gt;1$, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE under some conditions. Our important analytical findings are illustrated through computer simulation. Epidemiological implications of our analytical findings are addressed critically.

• Proceedings of the KIEE Conference
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• 2008.04a
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• pp.51-52
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• 2008

In this paper, we propose two control schemes. The first control scheme is an adaptive passivity-based excitation control which regulates the terminal voltage to its reference. This controller is obtained through two steps: firstly, a simple direct adaptive passivation controller is designed for the power system with parametric uncertainties; then a linear PI controller is applied to converge the terminal voltage to its reference. The second control scheme is a linear governor control which consists of the frequency and the mechanical power. It is shown that the internal dynamics are locally stable with controllable damping. In the end, the boundness of all electrical variables, the frequency, the mechanical power, and the convergence of the terminal voltage to its reference can be achieved by these control schemes.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.789-830
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• 2003

By forming completions of families of noncommutative polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncommutative analogue of the functional calculus for elements of commutative $C^{*}$-algebras and von Neumann algebras. These notions give a precise meaning to $C^{*}$-algebras defined by generator and relations and we show how they relate to many parts of operator and operator algebra theory.