• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.5
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• pp.94-100
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• 1994

The junction failure mechanism of W plugs has not been fully understood while the selective W deposition has been widely used for plugging interconnection lines. In this paper, the thermal stability and junction failure mechanism of sub-micron contacts using selective CVD-W plugs were intensively studied with the metal lines of AISiCu, Ti/AISiCu and TiN/AISiCu. The experimental results showed that the contact chain resistance and leakage current in the AISiCu and Ti/AISiCu metallizations were significantly degraded after annealing. From the SEM analysis, it was found that the junction spiking, due to the Al atoms diffusion along the porous interface between selective CVD-W and contactside wall, caused the junction failure. In constast, there was no degradation of the contact resistance and junction leakage current in TiN/AISiCu metal structu-re. It is believed that the TiN barrier layer could prevent AI(Ti) atoms Fromdiffusing. Therefore, TiN barrier between W plug and Al should be used to impro-ve the thermal stability of sub-micron contacts using the selective CVD-W plugs.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.49-58
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• 2005

In this paper we observe the structure of the roots of q-Bernoulli polynomials, ${\beta}_n(w,h{\mid}q)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of ${\beta}_n(w,h{\mid}q)$ for $-{\frac{1}{5}},-{\frac{1}{2}}$. Finally, we give a table for numbers of real and complex zeros of ${\beta}_n(w,h{\mid}q)$.

• Journal of Ocean Engineering and Technology
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• v.3 no.2
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• pp.535-535
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• 1989

• Journal of Ocean Engineering and Technology
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• v.4 no.2
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• pp.172-172
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• 1990

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.993-1003
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• 2012

The family of graphs $\hat{W}_{4n}$ is defined by taking the simple whee graph $W_{n+1}$ with $n$ rim vertices and then adding three extra vertices on every rim edge of the wheel. In this paper, the critical group of this whole family of graphs is investigated.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.233-238
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• 1999

Kawamoto generalized the Witt algebra using F[${X_1}^{\pm1},....{X_n}^{\pm1}$] instead of F[x1,…, xn]. We construct the generalized Witt algebra $W_{g,h,n}$ by using additive mappings g, h from a set of integers into a field F of characteristic zero. We show that the Lie algebra $W_{g,h,n}$ is simple if a g and h are injective, and also the Lie algebra $W_{g,h,n}$ has no ad-digonalizable elements.

• Electrical & Electronic Materials
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• v.8 no.3
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• pp.272-277
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• 1995

We report the properties of optically pumped stimulated emission at room temperature (RT) from column-III nitride semiconductors of GaN, AlGaN/GaN double heterostructure (DH) and AlGaN/GaInN DH which prepared on a sapphire substrate using an AIN buffer-layer by the nietalorganic vapor phase epitaxy (MOVPE) method. The peak wavelength of the stimulated emission at RT from AIGaN/GaN DH is 369nm and the threshold of excitation pumping power density (P$\_$th/) is about 84kW/cm$\^$2/, and they from AlGaN/GaInN DH are 402nm and 130kW/cm$\^$2/ at the pumping power density of 200kW/cm$\^$2/, respectively. The P$\_$th/ of AIGaN/GaN and AlGaN/GaInN DHs are lower than the single layers of GaN and GaInN due to optical confinement within the active layers of GaN and GaInN, respectively.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.509-525
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• 2014

Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.