• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.425-432
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• 2009

This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neighborhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in [1, 3-7].

• Honam Mathematical Journal
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• v.27 no.2
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• pp.317-332
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• 2005

In this paper we consider the hp-version to solve non-constant coefficients elliptic equations on a bounded, convex polygonal domain ${\Omega}$ in $R^2$. A family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties can be used for calculating the integrals. When the numerical quadrature rules $I_m{\in}G_p$ are used for computing the integrals in the stiffness matrix of the variational form we will give its variational form and derive an error estimate of ${\parallel}u-{\widetilde{u}}^h_p{\parallel}_{1,{\Omega}$.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.145-156
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• 2004

Let $D_1,\;D_2$ be convex domains in complex normed spaces $E_1,\;E_2$ respectively. When a mapping $f\;:\;D_1{\rightarrow}D_2$ is holomorphic with f(0) = 0, we obtain some results like the Schwarz lemma. Furthermore, we discuss a condition whereby f is linear or injective or isometry.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.627-639
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• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.433-444
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• 2023

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w² - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.2
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• pp.553-563
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• 1996

An algorithm for automatic mesh generation of two-dimensional arbitrary planar domain is proposed by using Delaunay triangulation algorithm. An efficient algorithm is proposed for the construction of Delaunay triangulation algorithm over convex planar domain. From the definition of boundary, boundary nodes are first defined and then interior nodes are generated ensuring the Delaunay property. These interior nodes and the boundary nodes are then linked up together to produce a valid triangular mesh for any finite element analysis. Through the various example, it is found that high-quality triangular element meshes are obtained by Delaunay algorithm, showing the robustness of the current method. The proposed mesh generation scheme has been extended to automatic remeshing, which is applicable to FE analysis including large deformation and large distortion of elements.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.813-838
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• 2011

In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.433-437
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• 2003

Quantitative Feedback Theory (QFT) is one of effective methods of robust controller design. In QFT design we can considers the phase information of the perturbed plant so it is less conservative than $H_{\infty}$ and ${\mu}$-synthesis methods and as be shown, it is more transparent than the sensitivity reduction methods mentioned . In this paper we want to overcome the major drawback of QFT method which is lack of an automatic method for loop-shaping step of the method so we focus on the following problem: Given a nominal plant and QFT bounds, synthesize a controller that achieves closed-loop stability and satisfies the QFT boundaries. The usual approach to this problem involves loop-shaping in the frequency domain by manipulating the poles and zeros of the nominal loop transfer function. This process now aided by recently developed computer aided design tools proceeds by trial and error and its success often depends heavily on the experience of the loop-shaper. Thus for the novice and First time QFT user, there is a genuine need for an automatic loop-shaping tool to generate a first-cut solution. Clearly such an automatic process must involve some sort of optimization, and while recent results on convex optimization have found fruitful applications in other areas of control theory we have tried to use LMI theory for automating the loop-shaping step of QFT design.

• ETRI Journal
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• v.43 no.1
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• pp.7-16
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• 2021

Noncontiguous orthogonal frequency division multiplexing (NC-OFDM)-based cognitive radio (CR) systems achieve highly efficient spectrum utilization by transmitting unlicensed users' data on subcarriers of licensed users' data when they are free. However, there are two disadvantages to the NC-OFDM system: out-of-band power (OBP) and a high peak-to-average power ratio (PAPR). OBP arises due to side lobes of an NC-OFDM signal in the frequency domain, and it interferes with the spectrum for unlicensed users. A high PAPR occurs due to the inverse fast Fourier transform (IFFT) block used in an NC-OFDM system, and it induces nonlinear effects in power amplifiers. In this study, we propose an algorithm called "Alternative Projections onto Convex and Non-Convex Sets" that reduces the OBP and PAPR simultaneously. The alternate projections are performed onto these sets to form an iteration, and it converges to the specified limits of in-band-power, peak amplitude, and OBP. Furthermore, simulations show that the bit error rate performance is not degraded while reducing OBP and PAPR.