• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.7-14
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• 2003

Let $P_c(z)=z^n+c$ be a complex polynomial with an integer $n{\geq}2$. We derive a criterion that the critical orbit of $P_c$ escapes to infinity and investigate its applications to the degree-n bifurcation set. The intersection of the degree-n bifurcation set with the real line as well as with a typical symmetric axis is explicitly written as a function of n. A well-defined escape-time algorithm is also included for the improved construction of the degree-n bifurcation set.

• Journal of the Korean institute of surface engineering
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• v.36 no.2
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• pp.109-115
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• 2003

Quaternary Ti-Al-Si-N films were deposited on WC-Co substrates by a hybrid deposition system of arc ion plating (AIP) method for Ti-Al source and DC magnetron sputtering technique for Si incorporation. The synthesized Ti-Al-Si-N films were revealed to be composites of solid-solution (Ti, Al, Si)N crystallites and amorphous Si3N4 by instrumental analyses. The Si addition in Ti-Al-N films affected the refinement and uniform distribution of crystallites by percolation phenomenon of amorphous silicon nitride, similarly to Si effect in TiN film. As the Si content increased up to about 9 at.%, the hardness of Ti-Al-N film steeply increased from 30 GPa to about 50 GPa. The highest microhardness value (~50 GPa) was obtained from the Ti-Al-Si-N film haying the Si content of 9 at.%, the microstructure of which was characterized by a nanocomposite of nc-(Ti,Al,Si) N/a$-Si_3$$N_4$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.2
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• pp.321-324
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• 2020

In this work, we developed a selective etching process for GaN that is a key process in p-GaN/AlGaN/GaN enhancement-mode (E-mode) power switching field-effect transistor (FET) fabrication. In order to achieve a high current density of p-GaN/AlGaN/GaN E-mode FET, the p-GaN layer beside the gate region must be selectively etched whereas the underneath AlGaN layer should be maintained. A selective etching process was implemented by oxidizing the surface of the AlGaN layer and the GaN layer by adding O2 gas to Cl2/N2 gas which is generally used for GaN etching. A selective etching process was optimized using Cl2/N2/O2 gas mixture and a high selectivity of 53:1 (= GaN/AlGaN) was achieved.

• YAKHAK HOEJI
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• v.52 no.1
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• pp.20-26
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• 2008

2-Aminothiazole ring as a bioisoster of catechol in dopamine has provided with good oral availability and lipophilic property. Selenium was reported to have an improved antioxidant ability and to reduce the loss of dopamine. 2-Aminoindan, is a rigid form of dopamine, was evaluated as a dopamine agonist with low neurotoxocity. In order to develop a novel dopamine agonist, we tried to synthesize the selenazoloaminoindan derivative that is a hybrid structure of aminoindan and aminoselenazole instead of aminothiazole. 2-Indanone-2-oxime was reduced with $TiCl_4$ and $NaBH_4$ to form 2-aminoindan, which was reacted with propionyl chloride to give 2-N-n-propionylaminoindan (2). Compound 2 was reduced with $TiCl_4$ and $NaBH_4$ to afford 2-N-n-propylaminoindan (3) and it was nitrated and reduced to form 5-amino-2-N-n-propylaminoindan (5), which was reacted with KSeCN, $Br_2$, and glacial acetic acid to give 4,6-dibromo-5- amino-2-N-n-propylaminoindan (7) instead of selenazole ring formation. Otherwise, compound 2 was nitrated and hydrogenated to form 5-amino-2-N-n-propionylaminoindan (9), which was treated with KSeCN, $Br_2$, and glacial acetic acid to give 4,6-dibromo-5-amino-2-N-n-propionylaminoindan (10). Compound 9 was cyc1ized with KSeCN and glacial acetic acid in the absence of $Br_2$ to give 6-amino-2-N-(n-propionylamino)selenazolo[4,5-f]indan (11).

• Bulletin of the Korean Chemical Society
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• v.32 no.10
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• pp.3692-3695
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• 2011

Poly(N,N'-Dichloro-N-ethyl-benzene-1,3-disulfonamide) (PCBS) and N,N,N',N'-Tetrachlorobenzene-1,3-disulfonamide (TCBDA) were found to be a mild and efficient reagent for the direct oxidative conversion of sulfur compounds to the corresponding arenesulfonyl chlorides in good to excellent yields through the oxidative chlorination. The overall process is simple, practical, and it provides convenient access to a variety of aryl or heteroarylsulfonyl chlorides. The mild reaction conditions and the broad substrate scope render this method attractive, and complementary to existing syntheses of aryl or heteroarylsulfonyl chlorides.

• Journal of the Korean Ceramic Society
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• v.56 no.1
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• pp.49-55
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• 2019

$Ti_{0.33}Al_{0.67}N/CrN$ nano-multilayers, which are known to have excellent wear resistance, were prepared using an unbalanced magnetron sputter to have various periods of 2-5 nm. $Ti_{0.33}Al_{0.67}N$ had a hexagonal structure in a single layer, but converted to a cubic structure by forming a multilayer with CrN, which has a cubic structure. Thus, $Ti_{0.33}Al_{0.67}N$ formed a superlattice in the multilayer. The $Ti_{0.33}Al_{0.67}/CrN$ multilayer with a period of 2.5 nm greatly exceeded the hardness of the $Ti_{0.33}Al_{0.67}N$ and the CrN single layer, reaching 39 GPa. According to the low angle X-ray diffraction results, the $Ti_{0.33}Al_{0.67}N/CrN$ multilayer maintained its as-coated structure to a temperature as high as $700^{\circ}C$ and exhibited hardness of 30 GPa. The thickness of the oxide layer of the $Ti_{0.33}Al_{0.67}N/CrN$ multilayered coating was less than one-tenth of those of the single layers. Thus, $Ti_{0.33}Al_{0.67}N/CrN$ multilayered coating had hardness and oxidation resistance far superior to those of its constituent single layers.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.331-346
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• 2016

The primary aim of this paper is to generalize a theorem of Hirzebruch for the complex 2-dimensional Bott manifolds, usually called Hirzebruch surfaces, to more general Bott towers of height n. To do so, we first show that all complex vector bundles of rank 2 over a Bott manifold are classified by their total Chern classes. As a consequence, in this paper we show that two Bott manifolds $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n)$ and $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n^{\prime})$ are isomorphic to each other, as Bott towers if and only if both ${\alpha}_n{\equiv}{\alpha}_n^{\prime}$ mod 2 and ${\alpha}_n^2=({\alpha}_n^{\prime})^2$ hold in the cohomology ring of $B_{n-1}({\alpha}_1,{\ldots},{\alpha}_{n-1})$ over integer coefficients. This result will complete a circle of ideas initiated in [11] by Ishida. We also give some partial affirmative remarks toward the assertion that under certain condition our main result still holds to be true for two Bott manifolds just diffeomorphic, but not necessarily isomorphic, to each other.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.8
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• pp.15-23
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• 1998

Single crystalline I $n_{x}$G $a_{1-x}$ N thin film was grwon by MOCVD on (001) sapphire substrate for the blue light emitting devices. A good quality of I $n_{0.13}$G $a_{0.87}$N/GaN heterostructure grwon above 700.deg. C was confiremed by various characterization techniques of AFM, RHEED and DC-XRD. Through PL measurement at room temperautre for the Si-Zn co-doped I $n_{x}$G $a_{a-x}$N/GaN structure grwon at 800.deg. C to obtain blue wavelength emission, 460-470 nm and 425 nm emission peak were observed, which are believed to be from donor-to-acceptor pair transition and band edge emission of In/x/G $a_{1-x}$ N, respectively. The result of PL measurement of the undoped MQW I $n_{x}$G $a_{1-x}$ N layer at low temperature confirmed that the strong MQW peak was resulted by exciton from the GAN barrier and carrier of DA pair confined into the well layer.ll layer.yer.r.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.297-305
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• 2017

Let ${\alpha}$ > 0 be a real number and $(s_{\alpha}(n))_{n{\geq}1}$ be the lexicographically greatest Sturmian word of slope ${\alpha}$. We investigate Dirichlet series of the form ${\sum}^{\infty}_{n=1}s_{\alpha}(n)n^{-s}$. To do this, a generalization of Euler's totient function is required. For a real ${\alpha}$ > 0 and a positive integer n, an arithmetic function ${\varphi}{\alpha}(n)$ is defined to be the number of positive integers m for which gcd(m, n) = 1 and 0 < m/n < ${\alpha}$. Under a condition Re(s) > 1, this paper establishes an identity ${\sum}^{\infty}_{n=1}s_{\alpha}(n)n^{-S}=1+{\sum}^{\infty}_{n=1}{\varphi}_{\alpha}(n)({\zeta}(s)-{\zeta}(s,1+n^{-1}))n^{-s}$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.875-894
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• 2017

Let $[n]=\{1,2,{\ldots},n\}$. A set ${\mathbf{A}}=\{A_1,A_2,{\ldots},A_l\}$ is a minimal cover of [n] if ${\cup}_{1{\leq}i{\leq}l}A_i=[n]$ and $$\bigcup_{{1{\leq}i{\leq}l,}\\{i{\neq}j_0}}A_i{\neq}[n]\text{ for all }j_0{\in}[l]$$. Let ${\mathcal{C}}(n)$ denote the collection of all minimal covers of [n], and write $C_n={\mid}{\mathcal{C}}(n){\mid}$. Let ${\mathbf{A}}{\in}{\mathcal{C}}(n)$. An element $u{\in}[n]$ is critical in ${\mathbf{A}}$ if it appears exactly once in ${\mathbf{A}}$. Two minimal covers ${\mathbf{A}},{\mathbf{B}}{\in}{\mathcal{C}}(n)$ are said to be restricted t-intersecting if they share at least t sets each containing an element which is critical in both ${\mathbf{A}}$ and ${\mathbf{B}}$. A family ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is said to be restricted t-intersecting if every pair of distinct elements in ${\mathcal{A}}$ are restricted t-intersecting. In this paper, we prove that there exists a constant $n_0=n_0(t)$ depending on t, such that for all $n{\geq}n_0$, if ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is restricted t-intersecting, then ${\mid}{\mathcal{A}}{\mid}{\leq}{\mathcal{C}}_{n-t}$. Moreover, the bound is attained if and only if ${\mathcal{A}}$ is isomorphic to the family ${\mathcal{D}}_0(t)$ consisting of all minimal covers which contain the singleton parts $\{1\},{\ldots},\{t\}$. A similar result also holds for restricted r-cross intersecting families of minimal covers.