• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.75-81
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• 2002

Lipschitz stability and Lipschitz ø$_{o}$ - equistability of the functional differential equation x'= B(x)f(t, x, $x_{t}$), $x_{to}$ =$\theta$$_{o}$ are discussed. Sufficient conditions are given using the comparison with the corresponding scalar equation.ion.n.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.303-323
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• 2016

For a canonical threefold X, it is known that $p_n$ does not vanish for a sufficiently large n, where $p_n=h^0(X,\mathcal{O}_X(nK_X))$. We have shown that $p_n$ does not vanish for at least one n in {6, 8, 10}. Assuming an additional condition $p_2{\geq}1$ or $p_3{\geq}1$, we have shown that $p_{12}{\geq}2$ and $p_n{\geq}2$ for $n{\geq}14$ with one possible exceptional case. We have also found some inequalities between ${\chi}(\mathcal{O}_X)$ and $K^3_X$.

• Proceedings of the Materials Research Society of Korea Conference
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• 1996.11a
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• pp.140-140
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• 1996

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.513-518
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• 2003

In this paper, we have proved a theorem on Hausdorff summability of Fourier series which generalizes various known results. We prove that if $${\int}_{o}^{t}\;{\mid}{\phi}(u){\mid}\;du=o(t)\;as\;t{\rightarrow}0\; and\;\lim_{n{\rightarrow}{\infty}}{\int}^{\eta}_{{\pi}/n}{\frac{{\mid}{\phi}(t)-{\phi}(t+{\pi}/n){\mid}}{t}}dt=o(n)$$ where 0 < ${\eta}$ < 1, then the Fourier series is (H, ${\mu}_n$) summable to s at t = x where the sequence ${\mu}_n$ is given by ${\mu}_n={\int}^1_0x^n{\chi}(x)\;dx\;n=0,1,2\;and\;K_n(t)=\limits\sum_{{\nu}=0}^n(\array {n\\{\nu}})({\Delta}^{{n}-{\nu}}{\mu}_{\nu}){\frac{sin{\nu}t}{t}}$.

• Corrosion Science and Technology
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• v.9 no.2
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• pp.81-86
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• 2010

The mechanisms of selective oxidation of intercritically annealed CMnAl TRIP steels in a Continuous Galvanizing Line (GCL) were studied by cross-sectional observation of the surface and sub-surface regions by means of High Resolution Transmission Electron Microscopy (HR-TEM). The selective oxidation and nitriding of an intercritically annealed CMnAl TRIP steel in a controlled dew point 10%$H_2+N_2$ atmosphere resulted in the formation of c-xMnO.$MnO_2$ (1${\leq}$x<3) and c-xMnO.$Al_2O_3$ ($x{\geq}1$) particles on the steel surface. Single crystal c-xMnO.$SiO_2$ ($2{\leq}x{\leq}4$) oxide particles were also observed on the surface. A thin film of crystalline c-xMnO.$SiO_2$ (2${\leq}$x<3) and c-xMnO.$Al_2O_3$ ($x{\geq}1$) was present between these particles. In the sub-surface region, internal oxidation, nitriding and intermetallic compound formation were observed. In the first region, large crystalline c-xMnO.$SiO_2$ ($1{\geq}x{\geq}2$) and c-xMnO.$Al_2O_3$ ($x{\geq}1$) oxides particles were present. In the second region, c-AlN particles were observed, and in a third region, small $MnAl_x$ (x>1) intermetallic compound particles were observed.

• Journal of the Korean Ceramic Society
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• v.31 no.12
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• pp.1577-1587
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• 1994

TiO2 thin films with the substitution of oxygen with nitrogen were deposited on silicon substrate by metalorganic chemical vapor deposition (MOCVD) using Ti(OCH(CH3)2)4 (titanium tetraisopropoxide, TTIP) and N2O as source materials. X-ray diffraction (XRD) results indicated that the crystal structure of the deposited thin films was anatase TiO2 with only (101) plane observed at the deposition temperatures of 36$0^{\circ}C$ and 38$0^{\circ}C$, and with (101) and (200) plane at above 40$0^{\circ}C$. Raman spectroscopic results indicated that the crystal structure was anatase TiO2 in accordance with the XRD results without any rutile, fcc TiN, or hcp TiN structure. No fundamental difference was observed with temperature increase, but the peak intensity at 194.5 cm-1 increased with strong intensity at 143.0 cm-1 for all samples. The crystalline size of the films varied from 49.2 nm to 63.9 nm with increasing temperature as determined by slow-scan XRD experiments. The refractive index of the films increased from 2.40 to 2.55 as temperature increased. X-ray photoelectron spectroscopy (XPS) study showed only Ti 2s, Ti 2p, C 1s, O 1s and O 2s peaks at the surface of the film. The composition of the surface was estimated to be TiO1.98 from the quatitative analysis. In the bulk of the film Ti 2s, Ti 2p, O 1s, O 2s, N 1s and N 2s were detected, and Ti-N bonding was observed due to the substitution of oxygen with nitrogen. A satellite structure was observed in the Ti 2p due to the Ti-N bonding, and the composition of titanium nitride was determined to be about TiN1.0 from the position of the binding energy of Ti-N 2p3/2 and the quatitative analysis. The spectrum of Ti 2p energy level could be the sum of a 4, 5, or 6 Gaussian curve reconstruction, and the case of the sum of the 6 Gaussian curve reconstruction was physically most meaningful. From the results of Auger electron spectroscopy (AES), it was known that the composition was not varied significantly throughout the whole thickness of the film, and silicon oxide was not observed at the interface between the film and the substrate. The composition of the film was possible (TiO2)1-x.(TiN)x or TiO2-2xNx and in this experimental condition x was found to be about 0.21-0.16.

• Korean Journal of Materials Research
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• v.7 no.2
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• pp.102-106
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• 1997

Micro gas sensors including thin film catal) tic type require stress-free memhrancs for etch stop of Si anisotropic etching and sublayer of sensing elements hecause stress is one of the main factors affecting breakdown of thin membranes. This paper reports the effects of deposition conditions on stress and refractive index of $SiN_{x}/SiO_{x}/(NON)$ films deposited by low pressure c11ernic;rl vapor deposition(L, t'CVI)) 2nd reactve sputtering. In the case of I.PCVI1, the stresses of $SiN_{x}$ and NON films arc $7.6{\times}10^{8}dyne/cm^2$ and $3.3{\times}10^{8}dyne/cm^2$, respectibely, and the refractive indices are 3.05 and 152, respectively. In the cxse oi the sputtered SiN, , compressi\e stress decreased in magnitude and then turned to tensility as increasing proc, ess pressure by lmtorr to 30mtorr and cicreasmg applied power density by $2.74W/cm^2$ to $1.10W/cm^2$. The hest value of film stress obt;~ined under condition of lOmtorr and $1.37W/cm^2$ in this' experiment was $1.2{\times}10^{9}dyne/cm^2$ cnnipressive. The refr~ict~ve index decreased from 2 05 to 1 89 as decreasing applied power density by lnitorr to 3Orntorr and increasing process pressure hy $2.74W/cm^2$ to $1.10W/cm^2$. Stresses of films deposited by both LPCVL) and sputtering decreased as incre;lsing temperature and showed plastic behavior as decreasing temperature.

• Proceedings of the Korean Vacuum Society Conference
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• 1993.07a
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• pp.87-88
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• 1993

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.49 no.1
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• pp.1-7
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• 2000

The SNOSFET memory devices with ultrathin ONO(tunnel oxide-nitride-blocking oxide) gate dielectric were fabricated using n-well CMOS process and investigated its characteristics. The thicknesses of tunnel oxide, nitride and blocking oxide were $23{\AA},\; 53{\AA}\; and\; 33{\AA}$, respectively. Auger analysis shows that the ONO layer is made up of $SiO_2(upper layer of blocking oxide)/O-rich\; SiO_x\N\_y$. It clearly shows that the converting layer with $SiO_x\N\_y(lower layer of blocking oxide)/N-rich SiO_x\N\_y(nitride)/O-rich SiO_x\N\_y(tunnel oxide)$. It clearly shows that the converting layer with $SiO_x\N\_y$ phase exists near the interface between the blocking oxide and nitride. The programming condition of +8 V, 20 ms, -8 V, 50 ms is determined and data retention over 10 years is obtained. Under the condition of 8 V programming, it was confirmed that the modified Fowler-Nordheim tunneling id dominant charge transport mechanism. The programmed threshold voltage is distributed less than 0.1 V so that the reading error of memory stated can be minimized. An $8\times8$ NAND type flash EEPROM with SONOSFET memory cell was designed and simulated with the extracted SPICE parameters. The sufficient read cell current was obtained and the upper limit of $V_{TH}$ for write state was over 2V.

• Particle and aerosol research
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• v.6 no.4
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• pp.165-172
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• 2010

Titania is widely used as an effective photocatalyst for the photodegradation of environmental pollutants in air. In this study, novel N-doped $ZrO_2/TiO_2$ photocatalysts were synthesized via sol-gel method and characterized by UV-Vis spectrophotometer, transmission electron microscope, and X-ray diffractometer. N-doped $ZrO_2/TiO_2$ photocatalysts were nano-sized with an average particle size of about 20 nm. The XRD pattern of N-doped $ZrO_2/TiO_2$ photocatalysts showed both anatase and rutile phases. The photocatalytic activity of N-doped $ZrO_2/TiO_2$ photocatalysts was evaluated by degradation of NO under UV and visible light irradiation at various parameters such as amount of photocatalyst, concentration of NO, and intensity of light. The photocatalytic activity of N-doped $ZrO_2/TiO_2$ photocatalysts was effective for the enhancement of the degradation of NO and higher than that of $TiO_2$ photocatlysts under UV and visible light irradiation.