• Title/Summary/Keyword: P-1근사

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A Study on the Similitude of member Behavior for Small-Scale Modeling of Reinforced Concrete Structure (철근콘크리트 축소모델의 부재거동 상사성에 관한 연구)

  • 이한선;장진혁
    • Magazine of the Korea Concrete Institute
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    • v.8 no.3
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    • pp.177-185
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    • 1996
  • Four types of experiments were performed to check the similitude of member behavior between prototype and 1 /10 scale models : (1) Test of slender columns with P-$\Delta$ effect, (2) Test of short columns with and without confinement steel, (3) Test of simple beams without stirrups, and (4) 'T-beam test. Based on the results of experiments, the conclusions were made as follows : (1) The P-$\Delta$ effect of slender columns can be almost exactly represented by 1/10 scale model. (2) The effect of confinement on short columns by the hoop steel can be also roughly simulated by 1/10 scale model. (3) The failure modes of simple beams without stirrups are brittle shear failures in prototype whereas those of 1/10 scale models are the ductile yielding of tension steel followed by large diagonal tension cracking and compressive concrete failure. (4) The behaviors of prototype and 1/10 scale model in T-beams appear very similar.

Dislocation in Semi-infinite Half Plane Subject to Adhesive Complete Contact with Square Wedge: Part II - Approximation and Application of Corrective Functions (직각 쐐기와 응착접촉 하는 반무한 평판 내 전위: 제2부 - 보정 함수의 근사 및 응용)

  • Kim, Hyung-Kyu
    • Tribology and Lubricants
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    • v.38 no.3
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    • pp.84-92
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    • 2022
  • In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, Fkij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that Fxxx(ŷ) = Fxyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as Fkij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λI=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of Fkij, i.e.(1 - λI) and p, Log|Fkij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

Low Power 31.6 pJ/step Successive Approximation Direct Capacitance-to-Digital Converter (저전력 31.6 pJ/step 축차 근사형 용량-디지털 직접 변환 IC)

  • Ko, Youngwoon;Kim, Hyungsup;Moon, Youngjin;Lee, Byuncheol;Ko, Hyoungho
    • Journal of Sensor Science and Technology
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    • v.27 no.2
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    • pp.93-98
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    • 2018
  • In this paper, an energy-efficient 11.49-bit successive approximation register (SAR) capacitance-to-digital converter (CDC) for capacitive sensors with a figure of merit (FoM) of 31.6 pJ/conversion-step is presented. The CDC employs a SAR algorithm to obtain low power consumption and a simplified structure. The proposed circuit uses a capacitive sensing amplifier (CSA) and a dynamic latch comparator to achieve parasitic capacitance-insensitive operation. The CSA adopts a correlated double sampling (CDS) technique to reduce flicker (1/f) noise to achieve low-noise characteristics. The SAR algorithm is implemented in dual operating mode, using an 8-bit coarse programmable capacitor array in the capacitance-domain and an 8-bit R-2R digital-to-analog converter (DAC) in the charge-domain. The proposed CDC achieves a wide input capacitance range of 29.4 pF and a high resolution of 0.449 fF. The CDC is fabricated in a $0.18-{\mu}m$ 1P6M complementary metal-oxide-semiconductor (CMOS) process with an active area of 0.55 mm2. The total power consumption of the CDC is $86.4{\mu}W$ with a 1.8-V supply. The SAR CDC achieves a measured 11.49-bit resolution within a conversion time of 1.025 ms and an energy-efficiency FoM of 31.6 pJ/step.

Ab Initio Studies on Hydrogen-Bonded Dimers of Fluoromethanes with Ammonia and Water (플루오르화메탄들과 암모니아 및 물과의 수소결합 이량체들에 관한 Ab Initio 연구)

  • Soon-Ki Lee;Seung-Hoon Kim
    • Journal of the Korean Chemical Society
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    • v.37 no.4
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    • pp.408-415
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    • 1993
  • Systematic ab initio SCF calculations have been performed on the hydrogen-bonded dimers of fluoromethanes involving $CH_4,\;CH_3F,\;CH_2F_2\;and\;CHF_3$ with ammonia and water applying basis sets of 9s5p/5s and 9s5p1d/5p1d. Various ground state properties of these stable dimeric complexes have been evaluated. We compared these with corresponding properties of isolated monomers. We report equilibrium geometries, stabilization energies, dipole moments and force constants of intermolecular bonds. The effects arising as a consequence of the non-additive behavior of hydrogen bonding in chain-like oligomers are discussed. Systematic, methodical errors due to the use of the SCF approximation and the basis set dependence of the computed results are pointed out.

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A Variable Latency Goldschmidt's Floating Point Number Divider (가변 시간 골드스미트 부동소수점 나눗셈기)

  • Kim Sung-Gi;Song Hong-Bok;Cho Gyeong-Yeon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.9 no.2
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    • pp.380-389
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    • 2005
  • The Goldschmidt iterative algorithm for a floating point divide calculates it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's divide algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To calculate a floating point divide '$\frac{N}{F}$', multifly '$T=\frac{1}{F}+e_t$' to the denominator and the nominator, then it becomes ’$\frac{TN}{TF}=\frac{N_0}{F_0}$'. And the algorithm repeats the following operations: ’$R_i=(2-e_r-F_i),\;N_{i+1}=N_i{\ast}R_i,\;F_{i+1}=F_i{\ast}R_i$, i$\in${0,1,...n-1}'. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than ‘$e_r=2^{-p}$'. The value of p is 29 for the single precision floating point, and 59 for the double precision floating point. Let ’$F_i=1+e_i$', there is $F_{i+1}=1-e_{i+1},\;e_{i+1}',\;where\;e_{i+1}, If '$[F_i-1]<2^{\frac{-p+3}{2}}$ is true, ’$e_{i+1}<16e_r$' is less than the smallest number which is representable by floating point number. So, ‘$N_{i+1}$ is approximate to ‘$\frac{N}{F}$'. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables ($T=\frac{1}{F}+e_t$) with varying sizes. 1'he superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a divider. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc

A Variable Latency Goldschmidt's Floating Point Number Square Root Computation (가변 시간 골드스미트 부동소수점 제곱근 계산기)

  • Kim, Sung-Gi;Song, Hong-Bok;Cho, Gyeong-Yeon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.9 no.1
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    • pp.188-198
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    • 2005
  • The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

A Variable Latency Newton-Raphson's Floating Point Number Reciprocal Square Root Computation (가변 시간 뉴톤-랍손 부동소수점 역수 제곱근 계산기)

  • Kim Sung-Gi;Cho Gyeong-Yeon
    • The KIPS Transactions:PartA
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    • v.12A no.5 s.95
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    • pp.413-420
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    • 2005
  • The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. The bits to the right of p fractional bits in intermediate multiplication results are truncated and this truncation error is less than '$e_r=2^{-p}$'. The value of p is 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications Per an operation is derived from many reciprocal square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

A Variable Latency Newton-Raphson's Floating Point Number Reciprocal Computation (가변 시간 뉴톤-랍손 부동소수점 역수 계산기)

  • Kim Sung-Gi;Cho Gyeong-Yeon
    • The KIPS Transactions:PartA
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    • v.12A no.2 s.92
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    • pp.95-102
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    • 2005
  • The Newton-Raphson iterative algorithm for finding a floating point reciprocal which is widely used for a floating point division, calculates the reciprocal by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the reciprocal of a floating point number F, the algorithm repeats the following operations: '$'X_{i+1}=X=X_i*(2-e_r-F*X_i),\;i\in\{0,\;1,\;2,...n-1\}'$ with the initial value $'X_0=\frac{1}{F}{\pm}e_0'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 27 for the single precision floating point, and 57 for the double precision floating point. Let $'X_i=\frac{1}{F}+e_i{'}$, these is $'X_{i+1}=\frac{1}{F}-e_{i+1},\;where\;{'}e_{i+1}, is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to $'\frac{1}{F}{'}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables $(X_0=\frac{1}{F}{\pm}e_0)$ with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal unit. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia scientific computing, etc.

Application of microprocessor to control of spot welding processes (마이크로프로세서를 이용한 점용접 공정제어)

  • 조형석
    • Journal of the korean Society of Automotive Engineers
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    • v.5 no.3
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    • pp.24-32
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    • 1983
  • 전기 동저항 제어실험을 통해 다음과 같은 결론을 얻었다. (1) 점용접 과정에서 동 저항이 용접질(용접강도)을 잘 나타내 준다. 1) 동저항 곡선의 peak가 발생하는 시간이 이르면 일반적으로 늦게 나타난 것보다 용접질이 좋다. (단, expulsion이 발생하지 않을 때까지). 2) peak에서의 저항값과 용접시간 끝에서의 저항값 차이가 클수록 일반적으로 용접질이 좋다. (2) 한 동 저항곡선에 다른 동 저항곡선을 맞추려는 제어를 할 때는 다음과 같은 관계가 있다. 1) P-control로는 동저항을 추적하는 효과를 충분히 얻을 수 없고 적분제어기를 추가한 PI-control을 하면 잘 추적한다. 2) 용접질의 관점으로 볼 때 원하는 용접강도를 얻으려고 PI제어를 하면 그 용접 평균강도에 아주 근사한 강도를 얻을 수 있다.

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The Influence of Extreme Value in Binomial Confidence Interval (이항 신뢰구간에서 극단값의 영향)

  • Ryu, Jea-Bok
    • Communications for Statistical Applications and Methods
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    • v.18 no.5
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    • pp.615-623
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    • 2011
  • Several methods are used in interval estimation for binomial proportion; however the coverage probabilities of most confidence intervals depart from the confidence level when the binomial population proportion closes to 0 or 1 due to the extreme value. Vollset (1993), Agresti and Coull (1998), Newcombe (1998), and Brown et al. (2001) suggested methods to adjust the extreme value. This paper discusses the influence of extreme value in a binomial confidence interval through the numerical comparison of 6 confidence intervals.