• 대한수학회보
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• 제44권3호
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• pp.569-587
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• 2007

In this paper, we establish the generalized Hyers-Ulam-Rassias stability of the Pexider type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ and its general solution.

• 한국세라믹학회지
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• 제31권12호
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• pp.1570-1576
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• 1994

Effect of Na2O/SiO2 molar ratio, calcining temperature and addition of NaCl were investigated on the hydrothermal formation of X-type zeolite from the natural mordenite, which is a kind of rock deposited abundantly in kuryong po. Pulverized mordenite was first mixed with NaOH or NaOH-NaCl solution, and crystallized under hydrothermal condition at 90~10$0^{\circ}C$ for 10 hrs. Optimum condition for synthesis of the X-type zeolite were \circled1 the ratio Na2O/SiO2, NaCl/Al2O3 and H2O/Na2O:0.68, 11.4 and 40, respectively, \circled2 calcining temperature of starting materials: 90$0^{\circ}C$, \circled3 aging time: 48 hrs. and \circled4 crystallization temperature: 10$0^{\circ}C$. The yield of X-type zeolite under the optimum condition was about 55~60%, and the major crystallized X-type zeolite was faujasite phase. Zeolite of then type X was crystallized when NaCl was added to treating solution with in the limit 14.25 of NaCl/Al2O3 molar ratio. As the calcination temperature (from 50$0^{\circ}C$ to 95$0^{\circ}C$) of starting materials increases, yield of zeolite x increase.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.113-128
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• 2014

Consider a class of p(x)-Kirchhoff type equations of the form $$\left\{-M\left({\int}_{\Omega}\;\frac{1}{p(x)}{\mid}{\nabla}u{\mid}^{p(x)}\;dx\right)\;div\;({\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)={\lambda}V(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u=0\;on\;{\partial}{\Omega},$$ where p(x), $q(x){\in}C({\bar{\Omega}})$ with 1 < $p^-\;:=inf_{\Omega}\;p(x){\leq}p^+\;:=sup_{\Omega}p(x)$ < N, $M:{\mathbb{R}}^+{\rightarrow}{\mathbb{R}}^+$ is a continuous function that may be degenerate at zero, ${\lambda}$ is a positive parameter. Using variational method, we obtain some existence and multiplicity results for such problem in two cases when the weight function V (x) may change sign or not.

• 충청수학회지
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• 제32권3호
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• pp.337-347
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• 2019

In this paper, we investigate the generalized Hyers-Ulam stability of the quadratic and quartic type functional equations $$f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)-2f(kx)\\{\hfill{67}}+2k^2f(x)+2(k^2-1)f(y)=0,\\f(x+5y)-5f(x+4y)+10f(x+3y)-10f(x+2y)+5f(x+y)\\{\hfill{67}}-f(-x)=0,\\f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)\\{\hfill{67}}-{\frac{k^2(k^2-1)}{6}}[f(2x)-4f(x)]+2(k^2-1)f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.

• 한국자기학회:학술대회 개요집
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• 한국자기학회 1998년도 춘계연구발표회 논문개요집
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• pp.74-75
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• 1998

• 호남수학학술지
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• 제29권4호
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• pp.543-554
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• 2007

In this paper, we prove the stability of a mixed type functional equation f( -x + y + z) + f(x - y + z) + f(x + y - z) = f(x - y) + f(y - z) + f(z - x) + f.(x) + f(y) + f(z).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권1호
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• pp.51-60
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• 2020

In this note, we investigate the Hyers-Ulam stability and the hyperstability of the Pexider type functional equation g(x + y + xy) = g(x) + f(y) + xf(y) + yg(x).

• 한국자기학회:학술대회 개요집
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• 한국자기학회 1991년도 추계연구발표회 논문개요집
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• pp.64-64
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• 1991

• Journal of Magnetics
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• 제1권1호
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• pp.19-23
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• 1996

In the present study, the $Sm_2Fe_{17}N_x$-type interstitial materials have been prepared by reaction between Nb-free or Nb-containing $Sm_2Fe_{17}$-type alloy and $N_2$ gas. Nitrogenation behaviour of the $Sm_2Fe_{17}N_x$-type material and disproportionation characteristics of the nitrogenated materials have been studied by means of differential thermal analysis (DTA) and thermopiezic analysis (TPA). Magnetic properties of the produced $Sm_2Fe_{17}N_x$-type interstitial materials were characterised in vibrating sample magnetometer (VSM) or thermomagnetic analyser (TMA). Epoxy-bonded or Zn-bonded $Sm_2Fe_{17}N_x$-type magnets were prepared, and their magnetic properties were investigated. It has been found that nitrogenation kinetics of the Sm2Fe17Nx-type alloy is improved significantly by the Nb-substitution for Fe in the alloy. The Nb-substitution is also found to enhance thermal stability of the $Sm_2Fe_{17}N_x$-type interstitial material. Hard magnetic properties of the interstitial materials produced from Nb-free orNb-containing alloy is high enough (intrinsic coercivity : over 7 kOe) for application as bonded permanent magnets. The good hard magnetic properties of the interstitial material are maintained in the epoxy-bonded magnet. Intrinsic coercivity of the Zn-bonded magnets is improved significantly as post-bonding annealing time increases.

• 전력전자학회논문지
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• 제4권1호
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• pp.66-72
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• 1999

본 논문은 고주파 공진형 PWM 인버터식 X-선 장치의 인버터에 단상과 3상 전파정류방식 및 PSU 전원을 연결시켰을 때 나타나는 단시간 출력특성에 대해 분석하였다. X-선의 선질은 X-선관에 입력되는 DC 전압 파형에 의존한다. DC 출력전압 파형은 DC 전압전원의 고조파 왜곡에 의해 영향을 받는다. 이러한 관전압 파형의 왜곡은 X-선 출력의 직선성, 재현성 및 출력선질을 저하시킨다. 따라서 본 논문에서는 DC 출력전압 파형과 세 가지 형식의 DC 입력전원 형식에 따른 출력선량을 비교하였고 이에 따른 실험결과를 검토하였다.