• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1341-1364
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• 2023

This article introduces a method for estimating the conditional hazard function of a real-valued response variable based on a functional variable. The method uses local linear estimation of the conditional density and cumulative distribution function and is applied to a functional stationary ergodic process where the explanatory variable is in a semi-metric space and the response is a scalar value. We also examine the uniform almost complete convergence of this estimation technique.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.73-84
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• 2011

Let f, g, h, k : $\mathbb{R}^n{\rightarrow}\mathbb{C}$ be locally integrable functions. We deal with the $L^{\infty}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $${\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ $${\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ based on the concept of linear functionals on the space of smooth functions with compact support.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.54 no.7
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• pp.323-328
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• 2005

This paper is proposed maximum thrust design of slotted permanent magnet linear synchronous motor(PMLSM) using surface harmonic method(SHM) considering slot effect. The genetic a1gorithm is used for optimization. The functional are selected the maximum thrust and the minimum detent force. This time. design parameters are set as permanent magnet(PM) width. PM height and slot width. Thrust is increased from 272[N] to 295[N] and detent force is decreased from 5[N] to 2.43[N] greatly in optimum design. Therefore, thrust ripple isn't generating almost. Also, the results of 2D EMC considering slot-effect are compared with ones of experimental and finite element analysis..

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.287-301
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• 2011

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$(\ddag)\hspace{50}dk\;f\left(\frac{\sum_{j=1}^{dk}x_j}{dk}\right)=\displaystyle\sum_{j=1}^{dk}f(x_j)$$ if and only if the mapping $f$ : X ${\rightarrow}$ Y is Cauchy additive, and prove the Cauchy-Rassias stability of the functional equation ($\ddag$) in Banach modules over a unital $C^{\ast}$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^{\ast}$-algebras. As an application, we show that every almost homomorphism $h\;:\;\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h((k-1)^nuy)=h((k-1)^nu)h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and $n$ = 0,1,2,$\cdots$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^{\ast}$-algebras.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.555-574
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• 2011

It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of $CD4^+$ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number $R_0$ < 1, the HIV infection is cleared from the T-cell population and the disease dies out; if $R_0$ > 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if $R_0$ > 1. Numerical simulations are presented to illustrate the results.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.08a
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• pp.201-207
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• 1999

The automatic pinhole detection system is described. The goal of this project is to study the feasibility test of the new concept for hole detection. The developed method is able to detect almost 50$\mu\textrm{m}$ pinhole by evaluating the shining of the light as if there is pinhole in the strip. Moreover, it is possible to inspect up to the 200$\mu\textrm{m}$ inclined pinhole. The system cosists of three main functional parts: the source part of the light which is using the linear halogen lamp, the image gathering part which is using a line CCD and the image processing part. The light spot can be controlled and optimized corresponding to the situation of the strip. To eliminate back ground noise, the binary image processing method is adopted.

• Journal of Sensor Science and Technology
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• v.13 no.5
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• pp.329-334
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• 2004

Functional residual capacity (FRC) is an important diagnostic parameter measured using $N_{2}$ analyzer. Since $N_{2}$ analyzer is expensive as well as cumbersome for use of noisy vacuum pump, the FRC measurement becomes possible only in large well-equipped hospitals. The present study introduced a new $TN_{2}$ wash-out technique to measure FRC by $O_{2}/CO_{2}$ analysis, which is relatively cheaper and much simpler to apply. Slower $O_{2}$ response was compensated for high frequency to be coincided with $CO_{2}$ response, thereby enabled indirect, but accurate $N_{2}$ concentration measurement. FRC was estimated by continuous integration of expired $N_{2}$ volume obtained with air flow signal. Experiment with 3 L syringe, a standard calibration device recommended by the American Thoracic Society, demonstrated less than 1% error at 0, 1, and 2 L. Correlation coefficient was almost ideal, guaranteeing linear estimation of FRC. The present technique is inexpensive and simple to apply, thus should he of great convenience.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....