• Title/Summary/Keyword: $e^N$-Method

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CONVERGENCE OF NEWTON'S METHOD FOR SOLVING A NONLINEAR MATRIX EQUATION

  • Meng, Jie;Lee, Hyun-Jung;Kim, Hyun-Min
    • East Asian mathematical journal
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    • v.32 no.1
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    • pp.13-25
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    • 2016
  • We consider the nonlinear matrix equation $X^p+AX^qB+CXD+E=0$, where p and q are positive integers, A, B and E are $n{\times}n$ nonnegative matrices, C and D are arbitrary $n{\times}n$ real matrices. A sufficient condition for the existence of the elementwise minimal nonnegative solution is derived. The monotone convergence of Newton's method for solving the equation is considered. Several numerical examples to show the efficiency of the proposed Newton's method are presented.

Crystalline Properties of GaN Layers Grown on PSS and AlN Buffered PSS by HVPE Method (HVPE법을 이용하여 PSS와 AlN Buffered PSS 위에 성장시킨 GaN 박막의 결정 특성)

  • Lee, Won Jun;Park, Mi Seon;Lee, Won Jae;Kim, Il Su;Choi, Young Jun;Lee, Hae Yong
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.31 no.6
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    • pp.386-391
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    • 2018
  • An epitaxial GaN layer was grown on a cone-shape-patterned sapphire substrate (PSS) (Sample A) and an AlN-buffered PSS (Sample B) with two growth steps under the same process conditions by employing the hydride vapor phase epitaxy (HVPE) method. We have investigated the characteristics of the GaN layer grown on two kinds of substrates at each growth step. The cross-sectional SEM image of the GaN layer grown on the two types of substrates showed growth states of GaN layers formed during the 1st and 2nd growth steps with different growth durations. Dislocation density was obtained by calculation using the FWHM value of the rocking curve for (002) and (102). Sample A showed 2.62+08E and 6.66+08E and sample B exhibited 5.74+07E and 1.65+08E for two different planes. The red shift was observed is photoluminescence (PL) analysis and Raman spectroscopy results. GaN layers grown on AlN-buffered PSS exhibited better optical and crystallographic properties than GaN layers grown on PSS.

A study of the Insulation Characteristic in $SF_6-N_2$ Mixture Gases ($SF_6-N_2$ 혼합기체의 절연특성에 관한 연구)

  • Ha, Sung-Chul;Song, Byoung-Doo
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.11b
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    • pp.613-616
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    • 2001
  • This SF6 gas is widely used in industrial of insulation field. In this paper, N2 is mixed to improve pure SF6 gas characteristics. Electron transport coefficients in SF6-N2 mixture gases are simulated in range of E/N values from 70 to 400 [Td] at 300K and 1 Torr by using Boltzmann equation method. The results of this method, which are like electron drift velocity, ionization coefficient, attachment coefficient, effective ionization coefficient, and critical EIN, can be important data to present characteristic of gas for insulation. Specially critical E/N is a data to evaluate insulation strength of a gas and is presented in this paper for various mixture ratios of SF6-N2 mixture gases.?⨀␍?܀㘱〮㜳㬓M敤楣楮攠慮搠桥污瑨

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A Study on Minimizing Position Error in Hyperbolic Fix Determination. (쌍곡면항법에 있어서 편위오차이 최소화에 관한 연구)

  • 김우숙;김동일;정세모
    • Journal of the Korean Institute of Navigation
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    • v.14 no.2
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    • pp.1-14
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    • 1990
  • The Radio Navigation System(R. N. S.) has been progressed consistantly with the development of electric-electronic engineering techniques since the R. D. E had been developed in 1910. The R. N. S. mostly depends on either Hyperbolic Navigation System(H. N. S.) or Spherical Navigation System(S. N. S.) in the ocean, and on Rectangular Navigation System (R. N. S.) in the air near the airport or an a combinations of the above systems in both area. Another effective R. N. S may be the Ellipse-Hyperbola Navigation System(E-H N. S.), which is proposed and named such in this paper. The equations calculating GDOP are derived and the GDOP values are calculated in the case of H. N. S., S. N. S, and E-H. N. S., respectively, for the specified case that four transmitting stations are arranged on the apex of a square, Then the GDOP diagrams of above navigation systems are presented for qualitative comparison in this paper. To measure the distances from the receiver to the stations in S. N. S., and/or the sum of distances to two stations in E-H N. S., the time synchronization between the transmitter clocks and the receiver clock is a major premise. The author has proposed the algorithm for getting this synchronmization utilizing the by S. N. S. or E-H N. S while GDOPs of those are relatively good. Even though clock synchronization error is a voidable due to the fix error used, the simulated results shows that the position accuracy of S. N. S. and E-H N. S. by the proposed method is far upgraded compared with that determined by H. N. S. directly, as far as the outer region of transmitter arrangement is concerned.

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Low Temperature Preparation and Photocatalytic Activity of TiO{2-x}Nx (TiO{2-x}Nx의 저온제조 및 광화학적 특성)

  • Jung, Dong-Woon
    • Journal of the Korean Chemical Society
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    • v.54 no.1
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    • pp.120-124
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    • 2010
  • $TiO_2$ and N-substituted $TiO_{2-x}N_x$ were synthesized by using precipitation method. $TiO_{2-x}N_x$ compound absorbed whole UV light as well as long wavelength of visible light (400 - 700 nm) because of the change of band gap from 3.2 eV to 1.77 eV. Results obtained revealed that $TiO_{2-x}N_x$ showed higher activity than pure $TiO_2$ or P-25 for visible-photocatalytic degradation of 1,4-dichlorobenzene.

A NOTE ON E. CARTAN'S METHOD OF EQUIVALENCE AND LOCAL INVARIANTS FOR ISOMETRIC EMBEDDINGS OF RIEMANNIAN MANIFOLDS

  • Han, Chong-Kyu;Yoo, Jae-Nyun
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.771-790
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    • 1997
  • By using the method of equivalence of E. Cartan we calculate the local scalar invariants for Riemannian 2-maniolds. We define also a notion of local invariants for submanifolds in $R^{n + d}, n \geq 2, d \geq 1$, in terms of the symmetry of the local isometric embedding equations of Riemannian n-manifolds into $R^{n + d}$. We show that the local invariants obtained by the Cartan's method are the intrinsic expressions of the local invariants in our sense in the casees of surfaces in $R^3$.

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Fabrication and Properties of AIN/SiC Structures using Reactive RF Magnetron Sputtering Method (반응성 RF 마그네트론 스퍼터링 법을 이용한 AIN/SiC 구조의 제작 및 특성)

  • Kim, Yong-Seong;Kim, Kwang-Ho
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.18 no.11
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    • pp.977-982
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    • 2005
  • Al/AlN/n-type 6H-SiC (0001) MIS structures were prepared by AlN layers on vicinal 6H-SiC(0001) substrates with reactive RF magnetron sputtering method. The AlN films were annealed at $900^{\circ}C$, $N_2$ atmosphere lot 1 minutes showed the best result. With XRD analysis, AlN(0002) peak was clearly found. The typical dielectric constant value of the AlN film in the MIS capacitors was obtained as 8.4 from photo C-V. Also, the gate leakage current density of the MlS capacitor was $10^{-10}\;A/cm^2$ order within the electric field of 1.8 MV/cm. Finally, the amount of interface trap densities, $D_{it}$, was evaluated as $5.3\times10^{10}\;eV^{-1}cm^{-2}$ at (Ec-0.85) eV.

The Measurements of the Activity Coefficients by E.M.F. Method and A Study of the Hydration (E. M. F.法에 依한 活性度係數의 測定과 Ion水和에 對한 考察)

  • Sakong, Yell;Hwang, Jung-Euy
    • Journal of the Korean Chemical Society
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    • v.6 no.2
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    • pp.113-116
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    • 1962
  • In this study we have measured the activity coefficients of NaCl in solution by E.M.F. method, depending upon MacInnes' equation at 25 dog. The cell (electrodes) is same as MacInnes' except the cock which was designed by ourselves as figure 1.Additionally, we have calculated the hydration number of NaCl from the activity coefficients using Robinson's equation and ionic hydration number according to our new formula $\frac{n_M{^+}+0.8}{n_A{^-}-0.1}=n_{MA}$, which was mentioned our former thesis.We also have calculated the hydration number of some salts from the ionic hydration number using upper formula and have got reasonable series match with other's value.As the results of our studying, we conclude it as follow;1) Liquid junction potential depend only on the bulk concentration of the both solution.2) The formula $\frac{n_M{^+}+0.8}{{n_A{^-}}-0.1}=n_{MA}$ is reasonable one in deducing to ionic hydration number.3) From upper relation, we can calculate the hydration number of unknown salts from it's ionic hydration numbers.

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Evaluation of Undrained Shear Strength of Busan New-port Clay by DMT (DMT를 이용한 부산신항 점토의 비배수 전단강도 추정)

  • Hong, Sung-Jin;Shin, Dong-Hyun;Kim, Dong-Hee;Jung, Sang-Jin;Lee, Woo-Jin
    • Journal of the Korean Geotechnical Society
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    • v.23 no.7
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    • pp.87-98
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    • 2007
  • A series of dilatometer test, field vane test, and $CK_0U$ triaxial test were performed for clayey soils of Busan new port site to develop the relationships between undrained shear strength and the DMT results. Normalized undrained shear strength is turned out to be $S_{u(CKU)}/{\sigma}'_v=0.30{\sim}0.35\;for\;CK_0U$ triaxial test and ${\mu}S_{u(VST)}/{\sigma}'_v=0.20{\sim}0.22$ for vane shear test. By comparing the undrained shear strength estimated from DMT indices with the results measured by in-situ vane test or $CK_0U$ triaxial test, two methods to predict the undrained shear strength from DMT results are suggested. One is based on the relationship between $S_u/{\sigma}'_v$ and horizontal stress index (KD) while another method comes from $N_c-I_D$ and $N_c-E_D$ correlation. It was observed that the method based on $N_c-I_D\;or\;N_c-E_D$ relation shows slightly better accuracy than the one based on $K_D$ although all of the methods suggested in this study provided comparable values of predicted undrained shear strength. Since the definitions of $I_D\;and\;E_D$ contain $p_1-p_0$, in which soil condition is reflected, it is believed that the prediction method using $N_c$ is capable of taking a material type into consideration.

Temporal and Spatial Variability of Precipitation and Evaporation over the Tropical Ocean

  • Yoo, Jung-Moon;Lee, Hyun-A
    • Journal of the Korean earth science society
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    • v.24 no.1
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    • pp.22-29
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    • 2003
  • Temporal and spatial variability of precipitation (P), evaporation (E), and moisture balance (P-E; precipitation minus evaporation) has been investigated over the tropical ocean during the period from January 1998 to July 2001. Our data were analyzed by the EOF method using the satellite P and E observations made by the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) and the Special Sensor Microwave/Imager (SSM/I). This analysis has been performed for two three-year periods as follow; The first period which includes the El Ni${\tilde{n}}$o in early 1998 ranges from January 1998 to December 2000, and the second period which includes the La Ni${\tilde{n}}$o events in the early 1999 and 2000 (without El Ni${\tilde{n}}$o) ranges from August 1998 to July 2001. The areas of maxima and high variability in the precipitation and in the P-E were displaced from the tropical western Pacific and the ITCZ during the La Ni${\tilde{n}}$o to the tropical middle Pacific during the El Ni${\tilde{n}}$o, consistent with those in previous P studies. Their variations near the Korean Peninsula seem to exhibit a weakly positive correlation with that in the tropical Pacific during the El Ni${\tilde{n}}$o. The evaporation, out of phase with the precipitation, was reduced in the tropical western Pacific due to humid condition in boreal summer, but intensified in the Kuroshio and Gulf currents due to windy condition in winter. The P-E variability was determined mainly by the precipitation of which the variability was more localized but higher by 2-3 times than that of evaporation. Except for the ITCZ (0-10$^{\circ}$N), evaporation was found to dominate precipitation by ${\sim}$2 mm/day over the tropical Pacific. Annual and seasonal variations of P, E, and P-E were discussed.