• Journal of Power System Engineering
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• 제18권1호
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• pp.120-127
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• 2014

In this study, Design methods of stabilizing controller for time-delay pure singularly perturbed systems are proposed. Based on the Chang transformation and Lambert W function, we decompose the time-delayed pure singularly perturbed systems into completely decoupled subsystems and derive sufficient stability conditions for $2{\times}2$ time-delayed pure singularly perturbed systems. An illustrated example is presented to demonstrate the validity and applicability of the proposed methods.

• Bulletin of the Korean Mathematical Society
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• 제61권4호
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• pp.1121-1136
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• 2024

In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for the tilted Carathéodory function of order β and angle α (α ∈ (-π/2, π/2) and β ∈ [0, cos α)), which maps the unit disk 𝔻 into the region {w ∈ ℂ : Re{e^iαw} > β}. Using these conditions, we also derive conditions for an analytic function that maps 𝔻 into a sector defined by {w ∈ ℂ : | arg(w - γ)| < (π/2)δ}, where γ ∈ [0, 1) and δ ∈ (0, 1]. The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in 𝔻.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제27권6A호
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• pp.524-532
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• 2002

This paper reports that the Lambert W function applies to a non-iterative design of minimum mean square-error scalar quantizers for a Laplacian source. Specifically, it considers a non-iterative design algorithm for optimum quantizers for a Laplacian source; it finds that the solution of the recursive nonlinear equation in the non-iterative design is elegantly expressed in term of the principal branch of the Lambert W function in a closed form; and it proves that the non-iterative algorithm applies only to exponential or Laplacian sources. The contribution of the paper is in the reduction of the time needed for the design and the increased accuracy in resulting quantization points and thresholds, because the algorithm is non-iterative and the Lambert W function can be evaluated as accurately as desired. Also, numerical results show how optimal quantization distortion converges monotonically to the Panter-Dite constant and help derive an approximation formula for the key parameters of optimum quantizers.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Journal of the Korean Institute of Telematics and Electronics
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• 제13권4호
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• pp.1-5
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• 1976

Spectrum의 시간기복을 나타내는 시간 및 주파수의 함수 F(w,t,T) 및 W(w,t,T)를 정의하였고, 실례에 적용시켰다. Fourier변환을 f(t)와 Phasor ejwt와의 Correlation으로 정의하였고 그 변환시분이 시간마다의 성분의 합계이어서 t 시각에서의 Spectrum을 그 근거에서의 f(t)값에만 의함을 증명하였다. Two new time functions defining Time Dependent Fourier Transform F(w,t,T) and Time Dependent Spectrum Density W(w,t,T) are deduced. courier transform is defined as the correlation between the time function f(t) and phasor ejwt. Several theorems corncerning the new functions are proved in order to verify the instantaneous cause a effet of the function f(t) and the nuctuating spectrum.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.461-468
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• 2004

Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in C(z). The overlapping space $L(\varphi)$ of H(W) in C(z) is a Herglotz space with Herglotz function $\varphi(z)$ which satisfies $\varphi(z)+\varphi^＊(z^{-1})=2[1-W^{*}(z^{-1})W(z)]$. The identity ${}_{L(\varphi)}={-}_{H(W)}$ holds for every f(z) in $L(\varphi)$ and for every vector c.

• Honam Mathematical Journal
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• 제24권1호
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 한국전기전자재료학회 2002년도 하계학술대회 논문집 Vol.3 No.2
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• pp.1107-1112
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• 2002

An easy elevator originated is an opened system to compare an existing equipment, and learning efficient is high as a wiring that the sequence control circuit is on and off. The structure of an equipment to be controled from the first floor to the fifth floor is constructed by a lamp to express the function of the open-close of the door according to the cage moving, to express the mechanical actuation of the forward-reverse break and motor of load and of hand-worked control component of Push-Button S/W, L/S and Relay. In order to act of the elevator function that these components connected, designed the auto program and the sequence control circuit. Consequently the process that these(1~5steps) operated the cage with an auto program of the elevator and the sequence control circuit is controled by the step of forward and reverse that the L/S1~L/S5 of sensor adjust function let posit, by the adjustable S/W1~S/W5 of PLC testing panel and the S/W1~S/W5 which installed on the transparent acryl plate of a frame. In here, improved apparatus is the learning equipment of combined use to study the principle and the technique of the originated sequence control circuit and the auto program of PLC.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• 제16권4호
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• pp.351-357
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• 2003

An easy learning elevator originated is opened to compare the existed teaming equipment, and it had a high studied efficiency that the sequence control circuit can open and close with the wire. The structure of equipment to be controlled from the first floor to the fifth floors is demostrated by the constructive apparatus with the lamps to express the function of the open-close of the door according to the cage moving with a mechanical actuation of the forward reverse breaker and the motor of load, and the mechanical actuation of hand-operation control components of push-button S/W and L/S and relay etc. These components let connect each other in order to control of the elevator function with the auto program and the designed sequence control circuit. Consequently the cage could go and come till 1∼5 steps with an auto program of the elevator and the sequence control circuit. The sequence control circuit is controlled by the step of forward and reverse to follow as that the sensor function of L/S1 ∼ L/S5 let posit with the control switchs of S/W1 ∼ S/W5 of PLC testing panel and switchs of S/W1 ∼ S/W5 installed on the transparent acryl plate of the frame. In here, improved apparatus is the hand-auto operation combined learning equipment to study the principle and technique of the originate sequence control circuit and the auto program of PLC.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• 제18권3호
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• pp.231-239
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• 2006

An experimental investigation of a Reversible Loop Heat Pipe (RLHP) was conducted to determine the operating limits and performance characteristics as functions of the thermophysical parameters, the heat input, and the cooling intensity. Variations in both temperature and heat transport capacity were measured and analyzed in order to accurately evaluate the transient operating characteristics. In addition, the maximum heat transport as a function of the mean evaporator temperature, the ratio of heat transport to heater input power as a function of the mean evaporator temperature, and the overall thermal resistance as a function of the overall heat transport capacity were examined as well. Results indicated that the cooling intensity played an important role on the operating characteristics and performance limitation. The maximum heat transports corresponding to cooling intensity $72W/^{\circ}C$ and $290W/^{\circ}C$ were 446 W and 924 W, respectively. Also, observation of the startup characteristics indicated that the mean evaporator temperature should be maintained between $40^{\circ}C$ and $60^{\circ}C$, and overall thermal resistance were measured as $0.02^{\circ}C/W$.