• Title/Summary/Keyword: Theta function

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Transient Response Analysis of the Trigonometric Distributed RC Circuit (삼각함수형 RC분포회로의 과도응답해석)

  • 김덕진
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.4 no.4
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    • pp.13-18
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    • 1967
  • Since all the poles of the open circuit voltage transfer function of the trigonometric, linear, passive RC circuits exist on the negative real axis of s-plane, its transient response to the unit step input is monotonic. This satisfies the necessary conditions for the applicability of Elmore's method which had been developed originally for the transient analysis of lumped circuit in computing the rise time and delay time of the trigonometric distributed RC circuits. This paper describes the computing method of rise and delay times of the trigonometric distributed RC circuit. The analysis shows that the transient response of this kind circuit depends only upon the time constant and distance angle $\theta$. As $\theta$ is increased, the rise and delay titles are increased non-linearly.

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Chemical solution derived hydroxyapatite films on Si substrates (화학 용액법으로 Si 기판 위에 제조한 하이드록시아파타이트 박막에 관한 연구)

  • 송종은;류현욱;신종윤;김병훈;김윤호;임용무
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.9 no.6
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    • pp.570-573
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    • 1999
  • Hydroxyapatite films were prepared on Si(100) substrates by using a sol-gel method with calcium nitrate and phosphoric acid as starting materials. Precursor sols were spin-coated onto the substrates and prefired at $500^{\circ}C$ for 10 min in air. Formation of the hydroxypatite structure was confirmed in the sample annealed at $500^{\circ}C$ by the X-ray diffraction $\theta$-2$\theta$ scans and a tricalcium phosphate phase was observed in the samples annealed at both temperature regions of $500^{\circ}C$~$700^{\circ}C$ and $900^{\circ}C$. From the results of Fourier transform infrared spectroscopy, the change of a carbon content and improvement of crystallinity have been discussed as a function of increase of annealing temperature.

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Design of ultraprecision hi-directional actuator for nm using a permanent magnet and electromagnet (영구 자석과 전자석의 상호작용을 이용한 초정밀 양방향 구동기 설계)

  • Kim Ki-Hyun;Gweon Dae-Gab
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.9 s.174
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    • pp.147-154
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    • 2005
  • A precision hi-directional actuator for a high precision leveling system with $Z{\Theta}_x{\Theta}_y$ motions is proposed and designed in this paper. The actuator is composed of a force generation structure, a guide mechanism, and a symmetric structure. At first, its driving force is generated by a change of flux in air gaps by permanent and changeable flux. The permanent flux is generated by a permanent magnet. The changeable flux is created by variable current flowing through coil. The combination of permanent and changeable flux makes various flux densities in air gaps between moving part and fixed yokes. And then, the difference between flux densities in lower and upper gaps creates forces fur the $bi-direction({\pm}z)$ motion. The guide mechanism of this actuator is composed of two circular plates and one shaft. Reducing motions generated by forces except z-motion, these circular plates endow the actuator with high stiffness for fast settling time. And the function of the shaft is to transfer motion to an object. At last, total body has a symmetric structure to be stable on thermal error. The actuator is designed by MAXWELL 2D and ProMECHANICA. The designed actuator is evaluated by 8nm laser doppler vibrometer, dynamic signal analyzer, and simple PID controller.

On Generalized Integral Operator Based on Salagean Operator

  • Al-Kharsani, Huda Abdullah
    • Kyungpook Mathematical Journal
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    • v.48 no.3
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    • pp.359-366
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    • 2008
  • Let A(p) be the class of functions $f\;:\;z^p\;+\;\sum\limits_{j=1}^{\infty}a_jz^{p+j}$ analytic in the open unit disc E. Let, for any integer n > -p, $f_{n+p-1}(z)\;=\;z^p+\sum\limits_{j=1}^{\infty}(p+j)^{n+p-1}z^{p+j}$. We define $f_{n+p-1}^{(-1)}(z)$ by using convolution * as $f_{n+p-1}\;*\;f_{n+p-1}^{-1}=\frac{z^p}{(1-z)^{n+p}$. A function p, analytic in E with p(0) = 1, is in the class $P_k(\rho)$ if ${\int}_0^{2\pi}\|\frac{Re\;p(z)-\rho}{p-\rho}\|\;d\theta\;\leq\;k{\pi}$, where $z=re^{i\theta}$, $k\;\geq\;2$ and $0\;{\leq}\;\rho\;{\leq}\;p$. We use the class $P_k(\rho)$ to introduce a new class of multivalent analytic functions and define an integral operator $L_{n+p-1}(f)\;\;=\;f_{n+p-1}^{-1}\;*\;f$ for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.

Electrical Characteristics of ZnO Piezo-electric Thin film for SAW filter (SAW 필터용 ZnO 압전 박막의 전기적 특성)

  • Lee, Dong-Yoon;Yoon, Seok-Jin
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.18 no.10
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    • pp.909-916
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    • 2005
  • The structural and electrical property of RF magnetron sputtered ZnO thin film have been studied as a function of RF power, substrate temperature, oxygen/argon gas ratio and film thickness at constant sputtering power, sputtering working pressure and target-substrate distance. To analyze a crystallo-graphic properties of the films, $\theta$/2$\theta$ mode X-ray diffraction, SEM, and AFM analyses. C-axis preferred orientation, resistivity and surface roughness highly depended on oxygen/argon gas ratio. The resistivity of ZnO thin film(6000 ${\AA}$) rapidly increased with increasing oxygen ratio and the resistivity value of $9 {\ast} 10^7 {\Omega}cm$ was obtained at a working pressure of 10 mTorr with the same oxygen/argon gas ratio. The surface roughness was also improved with increasing oxygen ratio and the ZnO films deposited with the same oxygen/argon gas ratio showed the excellent roughness value of 28.7 ${\AA}$. With increase of the substrate temperature, The C-axis preferred orientation of ZnO thin film increases and the resistivity decreases due to deviation from the stoichiometric ZnO due to oxygen deficiency.

JACOBI'S THETA FUNCTIONS AND THE NUMBER OF REPRESENTATIONS OF A POSITIVE INTEGER AS A SUM OF FOUR TRIANGULAR NUMBERS

  • Kim, Aeran
    • Honam Mathematical Journal
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    • v.38 no.4
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    • pp.753-782
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    • 2016
  • In this paper we deduce the number of representations of a positive integer n by each of the six triangular forms as $${\frac{1}{2}}x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{1}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+3x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+3x_3(x_3+1)+3x_4(x_4+1).$$

The Effects of Fuel Pellet Eccentricity on Fuel Rod Thermal Performance (핵연료의 편심이 연료봉 열적 성능에 미치는 영향)

  • Suh Young-Keun;Sohn Dong-Seong
    • Nuclear Engineering and Technology
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    • v.20 no.3
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    • pp.189-196
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    • 1988
  • This study investigates the effect of fuel pellet eccentricity on fuel rod thermal performance under the steady state condition. The governing equations in the fuel pellet and the cladding region are set up in 2-dimensional cylindrical coordinate (r, $\theta$) and are solved by finite element method. The angular-dependent heat transfer coefficient in the gap region is used in order to account for the asymmetry of gap width. Material propeties are used as a function of temperature and volumetric heat generation as a function of radial position. The results show the increase of maximum local heat flux at the cladding outer surface and the decrease of maximum and average fuel temperatures due to eccentricity. The former is expected to affect the uncertainties in the minimum DNBR calculation. The latter two are expected to reduce the possibility of fuel melting and the fuel stored energy. Also, the fuel pellet eccentricity introduces asymmetry in fuel pellet temperature and movement of the location of maximum fuel pellet temperature.

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The Study of Cognitive Functional Difference and EEG Spectrum Difference among Sasang Constitutions (사상체질에 따른 뇌파, 학습능력 차이에 관한 연구)

  • Kim, Seok-Hwan;Choi, Kang-Wook;Lee, Sang-Ryong;Jung, In-Chul
    • Journal of Oriental Neuropsychiatry
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    • v.18 no.2
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    • pp.89-100
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    • 2007
  • Objective : The purpose of this study is to examine relationship between cognitive function and sasang constitution by analyzing EEG status of company workers in Cheon-An. Method : 59 company workers were tested with cognitive assessment EEG program and questionaire for the Sasang Constitution Classification II. They were assorted by Sasang Constitutions, and we analyzed its correlation with cognitive assessment score and EEG data. Results : 1. According to mean active EEG rhythm of Alpha. H-Beta, Gamma wave, there were no significant difference among Sasang Constitution. 2. According to mean success, error, concentration, response, workload and left/right brain activity score, there were no significant difference among Sasang Constitution. 3. According to mean active EEG rhythm of Theta, SMR, M-Beta wave, Soyangin(少陽人)'s value was significantly higher than that of Taeumin(太陰人) 4. According to mean cognitive strenghth score, Soyangin(少陽人)'s value was significantly higher than that of Taeumin(太陰人). Conclusion : In conclusion, Sasang Constitutional difference has no relevance with cognitive abilities However, Soyangin(少陽人) showed higher mean active EEG rhythm of Theta, SMR, M-Beta wave than that of Taeumin(太陰人). In addition, Soyangin(少陽人) also showed higher mean cognitive strenghth score than that of Taeumin(太陰人).

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Some Theorems Connecting the Unified Fractional Integral Operators and the Laplace Transform

  • Soni, R. C.;Singh, Deepika
    • Kyungpook Mathematical Journal
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    • v.45 no.2
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    • pp.153-159
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    • 2005
  • In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.

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SAMELSON PRODUCTS IN FUNCTION SPACES

  • GATSINZI, JEAN-BAPTISTE;KWASHIRA, RUGARE
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1297-1303
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    • 2015
  • We study Samelson products on models of function spaces. Given a map $f:X{\rightarrow}Y$ between 1-connected spaces and its Quillen model ${\mathbb{L}}(f):{\mathbb{L}}(V){\rightarrow}{\mathbb{L}}(W)$, there is an isomorphism of graded vector spaces ${\Theta}:H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W))){\rightarrow}H_*({\mathbb{L}}(W){\oplus}Der({\mathbb{L}}(V),{\mathbb{L}}(W)))$. We define a Samelson product on $H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W)))$.