• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.153-159
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• 1996

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Journal of Biosystems Engineering
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• v.24 no.1
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• pp.19-24
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• 1999

Motivated by the need for developing the more efficient lighting system for light culture of strawberries in the greenhouse, this paper aims at acquiring and suggesting more concrete and scientific foundation of illuminating position, numbers of light source by investigating the types of lighting system and illumination distribution in the greenhouse for light culture of strawberries. The results of investigation and experiment are summarized as following below: 1. The types of lighting system used in the greenhouse producing strawberries were classified as 1 line and 2 lines lighting system. 2. As for the arranging types of artificial light, 2 lines lighting system, were classified as Z-type, N-type and W-type. (Refer Fig. 3) 3. The results of illumination distribution for Z-type, N-type and W-type of 2 lines illuminating system in the greenhouse with a small size tunnel measured at the height of 1.5m from the ground with 220V, 100W lamp in 6m light gap showed that maximum illuminance are 961x, 1211x, 1251x, minimum illuminance are 4.41x, 4.71x, average illuminance are 33.71x, 43.11x, 44.51x and standard deviations are 28.31x, 35.41x, 38.31x at each types. 4. Proportion of the area below optimal illuminance to floor area at the two lines illuminating system of Z-, N-, and W-type in greenhouse were appeared as 39.4%, 26.0% and 26.3%, respectively. Also proportion of the area over optimal illuminance to floor area at the two lines illuminating system of Z-, N-, W-type in greenhouse were appeared as 16.8%, 14% and 14.7%, respectively. Thus N-type was superior to the others from the view points of optimal illumination distribution and energy saving.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1349-1357
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• 2022

Let 𝒜 = (A_n)_n≥0 be an increasing sequence of rings. We say that 𝓘 = (I_n)_n≥0 is an associated sequence of ideals of 𝒜 if I₀ = A₀ and for each n ≥ 1, I_n is an ideal of A_n contained in I_n+1. We define the polynomial ring and the power series ring as follows: $I[X]\, = \,\{\, f \,=\, {\sum}_{i=0}^{n}a_iX^i\,{\in}\,A[X]\,:\,n\,{\in}\,\mathbb{N},\,a_i\,{\in}\,I_i \,\}$ and $I[[X]]\, = \,\{\, f \,=\, {\sum}_{i=0}^{+{\infty}}a_iX^i\,{\in}\,A[[X]]\,:\,a_i\,{\in}\,I_i \,\}$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.

• Proceedings of the KIEE Conference
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• 1994.07b
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• pp.1435-1438
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• 1994

The effects of Ge composition variation in $a-Si_{1-x}Ge_x:H$ alloy p-i-n solar cells on the physical properties and current density-voltage characteristics are analyzed by a new simulation modelling based on the update published experimental datas. The simulation modelling includes newly formulated density of gap density spectrum corresponding to Ge composition variation and utilizes the newly derived generation rate formulars which include the reflection coefficients and can apply to multijunction structures as well as single junction structure. The effects in $a-Si_{1-x}Ge_x:H$ single junction are analyzed through the efficiency, fill factor, open circuit voltage, short circuit current density, free carriers, trap carriers, electric field, generation rate and recombination rate. Based on the results analyzed in single junction structure, the applications to multiple junction structures are discussed and the optimal conditions reaching to a high performance are investigated.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.4
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• pp.96-101
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• 2011

The thin films of TiN have been used extensively as wear-resistant materials, for instance, such as tools of high-speed cutting, metal mold forming etc. In these days, because the thin films capable of being used more severe conditions are needed, the technologies of arc ion plating are tried to improve its characteristics. The purpose of this study is to investigate the characteristics of thin films of (Ti,Cr)N compared with those of TiN. The method of arc ion plating, which is known as showing good tight-adherence and productivity, was used. After manufacturing thin films of ($Ti_{1-x}Cr_{x}$)N (x=0~1) with change of Cr in (Ti,Cr) target, atomic concentration, structure, size of crystallite, residual stress and surface roughness of thin films on substrate were investigated. As the results, it was confirmed that Cr atomic concentrations of thin films were proportionally changed with Cr atomic concentrations of target, and thin films of ($Ti_{1-x}Cr_{x}$)N (x=0~1) showed NaCl type and CrN existed as solid solution to TiN.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Korean Journal of Materials Research
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• v.22 no.4
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• pp.185-189
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• 2012

We report plasma-assisted molecular beam epitaxy of $In_XGa_{1-X}N$ films on c-plane sapphire substrates. Prior to the growth of $In_XGa_{1-X}N$ films, GaN film was grown on the nitride c-plane sapphire substrate by two-dimensional (2D) growth mode. For the growth of GaN, Ga flux of $3.7{\times}10^{-8}$ torr as a beam equivalent pressure (BEP) and a plasma power of 150 W with a nitrogen flow rate of 0.76 sccm were fixed. The growth of 2D GaN growth was confirmed by $in-situ$ reflection high-energy electron diffraction (RHEED) by observing a streaky RHEED pattern with a strong specular spot. InN films showed lower growth rates even with the same growth conditions (same growth temperature, same plasma condition, and same BEP value of III element) than those of GaN films. It was observed that the growth rate of GaN is 1.7 times higher than that of InN, which is probably caused by the higher vapor pressure of In. For the growth of $In_xGa_{1-x}N$ films with different In compositions, total III-element flux (Ga plus In BEPs) was set to $3.7{\times}10^{-8}$ torr, which was the BEP value for the 2D growth of GaN. The In compositions of the $In_xGa_{1-x}N$ films were determined to be 28, 41, 45, and 53% based on the peak position of (0002) reflection in x-ray ${\theta}-2{\theta}$ measurements. The growth of $In_xGa_{1-x}N$ films did not show a streaky RHEED pattern but showed spotty patterns with weak streaky lines. This means that the net sticking coefficients of In and Ga, considered based on the growth rates of GaN and InN, are not the only factor governing the growth mode; another factor such as migration velocity should be considered. The sample with an In composition of 41% showed the lowest full width at half maximum value of 0.20 degree from the x-ray (0002) omega rocking curve measurements and the lowest root mean square roughness value of 0.71 nm.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.451-470
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• 2020

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition 0 = t₀ < t₁ < ⋯ < t_n < t_n+1 = T of [0, T], define X_n : C[0, T] → ℝⁿ⁺¹ by X_n(x) = (x(t₀), x(t₁), …, x(t_n)). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X_n which has a drift and does not contain the present position of paths. As applications of the formula with X_n, we evaluate the Radon-Nikodym derivatives of the functions ∫₀^T[x(t)]^mdλ(t)(m∈ℕ) and [∫₀^Tx(t)dλ(t)]² on C[0, T], where λ is a complex-valued Borel measure on [0, T]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C[0, T].

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.875-883
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• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.