• 대한수학회논문집
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• 제34권3호
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• pp.841-854
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• 2019

In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $S^{\delta}[{\alpha}]$, $0{\leq}{\alpha}<1$, $-{\infty}<{\delta}<{\infty}$ which has been introduced and studied by Kumar [17] (see also [20], [21], [22], [23]). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bound for the Bloch's constant for all functions in that family.

• 대한수학회논문집
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• 제37권2호
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.

• Journal of Power Electronics
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• 제5권2호
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• pp.109-119
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• 2005

This paper deals with the performance analysis of static compensator (STATCOM) based voltage regulator for self­excited induction generators (SEIGs) supplying balanced/unbalanced and linear/ non-linear loads. In practice, most of the loads are linear. But the presence of non-linear loads in some applications injects harmonics into the generating system. Because an SEIG is a weak isolated system, these harmonics have a great effect on its performance. Additionally, SEIG's offer poor voltage regulation and require an adjustable reactive power source to maintain a constant terminal voltage under a varying load. A three-phase insulated gate bipolar transistor (IGBT) based current controlled voltage source inverter (CC- VSI) known as STATCOM is used for harmonic elimination. It also provides the required reactive power an SEIG needs to maintain a constant terminal voltage under varying loads. A dynamic model of an SEIG-STATCOM system with the ability to simulate varying loads has been developed using a stationary d-q axes reference frame. This enables us to predict the behavior of the system under transient conditions. The simulated results show that by using a STATCOM based voltage regulator the SEIG terminal voltage can be maintained constant and free from harmonics under linear/non linear and balanced/unbalanced loads.

• 전기의세계
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• 제26권4호
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• pp.41-53
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• 1977

With the equivalent series circuit analyzed aby revolving field theory and drawn by using the equivalent circuit constant ratios in capacitor motor with windings not in quadrature having space harmonics in its magnetic field (the above ratios are the equivalent circuit constants for the fundamental flux to the magnetizing reactance of the circuit), the equation for the alternating torque with twice line freequency in the motor is directly derived, and the alternating torque is measured with the self-made stator vibration angle amplitude measuring apparatus that is composed of a pickup, filter, photoelectric pickoff etc. The measured values satisfactorily compared with computed values. The properties of the alternating torque characteristics for respective harmonic fluxes and the r5esultant alternating torque characteristic, the effects of the alternating torque characteristics for respective harmonic fluxes on the resultant alternating torque characteristic, the effects of the variation in the motor constants and the equivalent circuit constant ratios for the fundamental flux on the alternating torque characteristics for respective harmonic fluxes and the resultant alternating torque characteristic, are made clear, applying the equation. There exist the optimum values of the motor constants and the equivalent circuit constant ratios for the fundamental flux for decreasing the alternating torque, and the value could be determined in design by the method presented in this paper.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.109-129
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• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• 대한수학회지
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• 제49권5호
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• pp.977-991
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• 2012

Let (M,F) and (M',F') be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F' is nonpositive, then any transversally harmonic map ${\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ${\phi}$ is transversally constant.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.369-374
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• 2016

In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+{\bar{f_x(z)}}$ under the integral operator $I_f(z)={\int_{o}^{z}}{\frac{f_1(u)}{u}}du+{\bar{{\int_{o}^{z}}{\frac{f_x(u)}{u}}}}$ and obtain the sharp constant ${\frac{{\sqrt[4]{6}}-{\sqrt[]{15}}}{9}}$, which generalized the result corresponding to the class of analytic functions given by Nash.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2014년도 제46회 동계 정기학술대회 초록집
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• pp.199.1-199.1
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• 2014

In nonlinear optics, the properties of nonlinear optical responses such as polarization and nonlinear analysis of the nonlinear surfaces were investigated using the jellium model by optical second harmonic generation. The nonlinear response of the Al metal surfaces were calculated using TDLDA. Band structure, lattice constant and bulk modulus of the Al metal were investigated. Effective potential and electron density were compared by changing different.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1461-1466
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• 2010

aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K < 0 and (N, $\bar{b}$) is a complete Riemannian manifold with sectional curvature bounded above by a constant $\mu$ > 0. Let u : $M{\times}[0,\;{\infty}]{\rightarrow}B_{\tau}(p)$ is a heat equation for harmonic map. We estimate the energy density of u.

• Journal of Power Electronics
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• 제14권1호
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• pp.175-182
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• 2014

Tracking harmonic current quickly and precisely is one of the keys to designing active power filters (APF). In the past, the current state feedback decoupling PI control was an effective means for three-phase systems in the current control of constant voltage constant frequency inverters and high frequency PWM reversible rectifiers. This paper analyzes in detail the limitation of the conventional PI conditioner in the APF application field and presents a novel PI control method. Canceling the delay of one sampling period and the misadjustment for tracking the harmonic current is the key problem of this PI control. In this PI control, the predictive output current value is obtained by a state observer. The delay of one sampling period is remedied in this digital control system by the state observer. The predictive harmonic command current value is obtained by a repetitive predictor synchronously. The repetitive predictor can achieve better predictions of the harmonic current. By this means, the misadjustment of the conventional PI control for tracking the harmonic current is cancelled. The experiment results with a three-level NPC APF indicate that the steady-state accuracy and dynamic response of this method are satisfying when the proposed control scheme is implemented.