• 제목/요약/키워드: Exponential formula

검색결과 76건 처리시간 0.02초

Weibull 신호원에 최적인 양자기의 지지역에 관한 연구 (On the Support Region of a Minimum Mean-Square Error Scalar Quantizer for a Weibull Source)

  • 임실규;나상신
    • 한국통신학회논문지
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    • 제29권1C호
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    • pp.129-139
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    • 2004
  • 이 논문은 최소평균제곱오차의 의미에서 Weibull 신호원에 최적인 홑양자기의 지지역에 관한 연구이다. 양자기의 지지역은 최외곽 양자경계값으로 정해지는 구간으로, 이는 양자기의 왜곡양의 결정에 중요한 영향을 미치므로 이에 대한 연구를 시작하였다. 이 논문에 제시된 연구결과는 다음과 같다. 첫째, Weibull 분포에 최적인 양자기의 최외곽 경계값의 근사식을 유도하였다. 둘째, Weibull 신호원의 중요한 형태인 레일리 분포와 지수 분포의 경우에 최적 양자기를 설계하여, 유도된 근사식을 실제값과 비교하여, 근사식의 정확도를 평가하였다. 양자기 지지역 왼쪽 끝경계값의 근사식은, 레일리와 지수 분포 각각의 경우에 양자점이 128과 256 이상일 때 실제값과 약 1% 이내의 오차를 갖으며, 오른쪽 끝경계값 근사식도 각각 양자점이 512와 32 이상일 때 약 1% 이내의 오차를 갗는 것으로 판명되었다. 또, 양자점의 개수가 증가하면 공식의 정확도가 높아졌다. 결론적으로 경계값, 근사식은 매우 높은 정확도를 갖는 것으로 사료된다. 따라서, 이 논문의 기여점은, Weibull 분포에 최적인 양자기의 지지역을 정확하게 표현할 수 있는 구체적인 공식을 유도·제시한 것이다. 이 공식은 Weibull 신호원에 최적인 양자기의 성능분석과 양자기 불일치 연구에 귀중하게 사용될 수 있을 것으로 사료된다.

무방향 네트워크의 2-터미날 신뢰성 계산을 위한 $K^4$-chain 축소 ($K^4$-chain Reductions for Computing 2-terminal Reliability in an Undirected Network)

  • 홍정식
    • 한국경영과학회지
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    • 제21권3호
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    • pp.215-225
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    • 1996
  • For an undirected stochastic network G, the 2-terminal reliability of G, R(G) is the probability that the specific two nodes (called as terminal nodes) are connected in G. A. typical network reliability problem is to compute R(G). It has been shown that the computation problem of R(G) is NP-hard. So, any algorithm to compute R(G) has a runngin time which is exponential in the size of G. If by some means, the problem size, G is reduced, it can result in immense savings. The means to reduce the size of the problem are the reliability preserving reductions and graph decompositions. We introduce a net set of reliability preserving reductions : the $K^{4}$ (complete graph of 4-nodes)-chain reductions. The total number of the different $K^{4}$ types in R(G), is 6. We present the reduction formula for each $K^{4}$ type. But in computing R(G), it is possible that homeomorphic graphs from $K^{4}$ occur. We devide the homemorphic graphs from $K^{4}$ into 3 types. We develop the reliability preserving reductions for s types, and show that the remaining one is divided into two subgraphs which can be reduced by $K^{4}$-chain reductions 7 polygon-to-chain reductions.

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Asymptotic Analyses of a Statistical Multiplexor with Heterogeneous ATM Sources

  • Lee, Hyong-Woo;Mark, Jon-Wei
    • Journal of Electrical Engineering and information Science
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    • 제2권3호
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    • pp.29-40
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    • 1997
  • Two asymptotic analyses of the queue length distribution at a statistical multiplexor supporting heterogeneous exponential on-off sources are considered. The first analysis is performed by approximating the cell generation rates as a multi-dimensional Ornstein-Uhlenbeck process and then applying the Benes queueing formula. In the second analysis, w state with a system of linear equations derived from the exact expressions of the dominant eigenvalue of the matrix governing the queue length distribution. Assuming that there are a large number of sources, we obtain asymptotic approximations to the dominant eigenvalue. Based on the analyses, we define a traffic descriptor to include the mean and the variance of the cell generation rate and a burstiness measure. A simple expression for the quality of service (QoS) in cell loss rate is derived in terms of the traffic descriptor parameters and the multiplexor parameters (output link capacity and buffer size). The result is then used to quantify the factors determining the required capacity of a call taking the statistical multiplexing gain into consideration. As an application of the analyses, we can use the required capacity calculation for simple yet effective connection admission control(CAC) algorithms.

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Evaluation of vertical dynamic characteristics of cantilevered tall structures

  • Li, Q.S.;Xu, J.Y.;Li, G.Q.
    • Structural Engineering and Mechanics
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    • 제11권4호
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    • pp.357-372
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    • 2001
  • In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations, exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz method is also applied to determine the natural frequencies and mode shapes in the vertical direction for cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this paper are simple and convenient for engineering applications. Numerical example shows that the fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the proposed methods are in good agreement with the corresponding measured data. It is also shown that the selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall buildings.

극소치유량에 대한 적정분포형의 설정과 확률갈수량의 산정 (Probability Funetion of Best Fit to Distribution of Extremal Minimum Flow and Estimation of Probable Drought Flow)

  • 김지학;이순탁
    • 물과 미래
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    • 제8권1호
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    • pp.80-88
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    • 1975
  • In this paper the authors established the best fit distribution function by applying the concept of probabiaity to the annual minimum flow of nine areas along the Nakdong river basin which is one of the largest Korean rivers and calculated the probable minimum flow suitable to those distribution function. Lastly, the authors tried to establish the best method to estimate the probable minimun flow by comparing some frequency analysis methods. The results obtained are as follows (1) It was considered that the extremal distribution type III was the most suitable one in the distributional types as a result of the comparision with Exponential distribution, Log-Normal distribution, Extremal distribution type-III and so on. (2) It was found that the formula of extremal distribution type-II for the estimation of probable minimum flow gave the best result in deciding the probable minimum flow of the Nakdong river basin. Therfore, it is recommended that the probable minimum flow should be estimated by using the extremal distribution type-III method. (3) It could be understood that in the probable minimum flow the average non-excessive probability appeared to be $Po{\fallingdotseq}1-\frac{1}{2T}$ and gave the same values of the probable variable without any difference in the various methods of plotting technique.

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Evolution of dynamic mechanical properties of heated granite subjected to rapid cooling

  • Yin, Tubing;Zhang, Shuaishuai;Li, Xibing;Bai, Lv
    • Geomechanics and Engineering
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    • 제16권5호
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    • pp.483-493
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    • 2018
  • Experimental study of the deterioration of high-temperature rock subjected to rapid cooling is essential for thermal engineering applications. To evaluate the influence of thermal shock on heated granite with different temperatures, laboratory tests were conducted to record the changes in the physical properties of granite specimens and the dynamic mechanical characteristics of granite after rapid cooling were experimentally investigated by using a split Hopkinson pressure bar (SHPB). The results indicate that there are threshold temperatures ($500-600^{\circ}C$) for variations in density, porosity, and P-wave velocity of granite with increasing treatment temperature. The stress-strain curves of $500-1000^{\circ}C$ show the brittle-plastic transition of tested granite specimens. It was also found that in the temperature range of $200-400^{\circ}C$, the through-cracks induced by rapid cooling have a decisive influence on the failure pattern of rock specimens under dynamic load. Moreover, the increase of crack density due to higher treatment temperature will result in the dilution of thermal shock effect for the rocks at temperatures above $500^{\circ}C$. Eventually, a fitting formula was established to relate the dynamic peak strength of pretreated granite to the crack density, which is the exponential function.

Experimental study on seepage characteristics of large size rock specimens under three-dimensional stress

  • Sun, Wenbin;Xue, Yanchao;Yin, Liming;Zhang, Junming
    • Geomechanics and Engineering
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    • 제18권6호
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    • pp.567-574
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    • 2019
  • In order to study the effect of stress and water pressure on the permeability of fractured rock mass under three-dimensional stress conditions, a single fracture triaxial stress-seepage coupling model was established; By using the stress-seepage coupling true triaxial test system, large-scale rock specimens were taken as the research object to carry out the coupling test of stress and seepage, the fitting formula of permeability coefficient was obtained. The influence of three-dimensional stress and water pressure on the permeability coefficient of fractured rock mass was discussed. The results show that the three-dimensional stress and water pressure have a significant effect on the fracture permeability coefficient, showing a negative exponential relationship. Under certain water pressure conditions, the permeability coefficient decreases with the increase of the three-dimensional stress, and the normal principal stress plays a dominant role in the permeability. Under certain stress conditions, the permeability coefficient increases when the water pressure increases. Further analysis shows that when the gob floor rock mass is changed from high stress to unloading state, the seepage characteristics of the cracked channels will be evidently strengthened.

Equilibrium and Non-equilibrium Molecular Dynamics Simulations of Thermal Transport Coefficients of Liquid Argon

  • Chang Bae Moon;Gyeong Keun Moon;Song Hi Lee
    • Bulletin of the Korean Chemical Society
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    • 제12권3호
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    • pp.309-315
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    • 1991
  • The thermal transport coefficients-the self-diffusion coefficient, shear viscosity, and thermal conductivity-of liquid argon at 94.4 K and 1 atm are calculated by non-equilibrium molecular dynamics (NEMD) simulations of a Lennard-Jones potential and compared with those obtained from Green-Kubo relations using equilibrium molecular dynamics (EMD) simulations and with experimental data. The time-correlation functions-the velocity, pressure, and heat flux auto-correlation functions-of liquid argon obtained from the EMD simulations show well-behaved smooth curves which are not oscillating and decaying fast around 1.5 ps. The calculated self-diffusion coefficient from our NEMD simulation is found to be approximately 40% higher than the experimental result. The Lagrange extrapolated shear viscosity is in good agreement with the experimental result and the asymptotic formula of the calculated shear viscosities seems to be an exponential form rather than the square-root form predicted by other NEMD studies of shear viscosity. The agreement for thermal conductivity between the simulation results (NEMD and EMD) and the experimental result is within statistical error. In conclusion, through our NEMD and EMD simulations, the overall agreement is quite good, which means that the Green-Kubo relations and the NEMD algorithms of thermal transport coefficients for simple liquids are valid.

The Relationship Between the Water Color and the Transparency in the Seas Around Korea

  • Hahn, Sangbok
    • 한국해양학회지
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    • 제3권2호
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    • pp.55-62
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    • 1968
  • The distributions of average water color and the transparency in the seas around Korea show two patterns: the one is the East Sea and the South Ses, the other is the Yellow Sea. In the East Sea and the South Sea, the water colors C$\sub$E/ in Forel scales change from green to greenish blue with distance x in miles from the seashore, an average color is bluish green, 3.7 in Forel scales, and the relationship is given by C$\sub$E/ = 5e$\^$-0.056.root.x; an average transparency is 15m and the transparency T$\sub$E/ shows following formula with distance x, E$\sub$E/=0.9.root.x+10. In the Yellow Sea, the water color C$\sub$Y/ changes from green yellow to bluish green with distance, an average color is light green, 5.6 in Forel scales, and the relationship is given by C$\sub$Y/= 8.5e$\^$-0.086.root.x; an average transparency is 7m, the farther it is from the seashore, the deeper transparency T$\sub$Y/ is as following, T$\sub$Y/=1.2 .root.x+1. Along the seashore, the transparency T$\sub$Y/ is only 10% that of the East Sea and the South Sea. The distributions of the water color and the transparency by depth change in values within the continental shelf. The water color in Forel scales decreases with the distance from the seashore and depth; the transparency increases with the distance and depth. They are caused by suspended particles, especially suspended clay, and it is the major factor in the change in color and transparency, particularly in the Yellow Sea. In September, the sea water is the clearest in the seas around Korea, transparency shows the maximum and water color the minimum in forel scales. The water color shows green yellow when transparency is 1m, green at 10m, and greenish blue at 20m. the relationship between the water color and the transparency shows an exponential distribution as following, C=9e$\^$-kT/, k=0.0625m$\^$-1/. This formula agrees with calculated formulas between the water color and the transparency from the emprircal formulas C$\sub$E/ and T$\sub$E/, C$\sub$Y/ and T$\sub$Y.

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3차원 유한요소해석에 의한 얕은 기초의 지지력 특성 (Bearing Capacity Characteristics of Shallow Foundation by Three Dimension FEM)

  • 박춘식;김종환
    • 한국지반공학회논문집
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    • 제35권3호
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    • pp.17-24
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    • 2019
  • 본 연구는 지반 위 얕은 기초의 지지력에 대한 특성을 파악하기 위하여 지반 조건, 기초 크기, 기초 형상 등의 다양한 조건에 대하여 3차원 유한요소해석을 수행하여 기존의 지지력 이론과 비교 검토하였다. 유한요소해석 결과 극한지지력은 기초크기에 따라 지지력이 거듭제곱이나 로그 식으로 차츰 수렴하였고, 지반강도가 증가할수록 지지력 증가가 커지지 않는 직선적인 변화를 보였다. 기존 지지력 이론과 비교한 결과 순수모래는 지지력 비($q_{FEA}/q_{theory}$)가 Terzaghi식의 결과와 가장 유사하였다. 순수점토는 약 0.4~0.6, 일반토사는 0.3~1.3 정도로 산정되었고, 지반강도가 증가할수록 지지력 비가 감소하면서 1.0 이하로 나타났다. 기초 크기에 따른 지지력을 1.0m 기초의 지지력으로 정규화시킨 지지력 비($q_u/q_{u(1.0)}$)는 순수모래에서 ${\phi}=25^{\circ}$, $30^{\circ}$, $35^{\circ}$일 때 이론식의 35%, 15%, 5% 정도로 산정되었고, 순수점토는 크기 효과가 없었으며, 일반토사는 지반강도가 작은 경우에 순수모래의 이론식에 대해 약 10% 이하로 나타났다. 지반강도 증가에 따른 지지력 비는 내부마찰각의 영향이 큰 것으로 나타났다. 기초형상별 지지력 비에 따른 형상계수는 기초형상에 따라 다르게 나타났고, 원형기초는 1.5, 정사각형 기초는 1.3, 직사각형 기초와 연속 기초는 1.1~1.0의 형상계수를 나타내었다.