• 제목/요약/키워드: Matrix Exponential

검색결과 132건 처리시간 0.04초

효율적인 D-클래스 계산을 위한 알고리즘 (Algorithm for Efficient D-Class Computation)

  • 한재일
    • 한국IT서비스학회지
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    • 제6권1호
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    • pp.151-158
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    • 2007
  • D-class computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and search for equivalent $n{\times}n$ Boolean matrices according to a specific equivalence relation. It is easy to see that even multiplying all $n{\times}n$ Boolean matrices with themselves shows exponential time complexity and D-Class computation was left an unsolved problem due to its computational complexity. The vector-based multiplication theory shows that the multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices can be done much more efficiently. However, D-Class computation requires computation of equivalent classes in addition to the efficient multiplication. The paper discusses a theory and an algorithm for efficient D-class computation, and shows execution results of the algorithm.

샘플치 $H{\infty}$ 문제: 최악의 외란의 폐경로 표현을 통한 이산화 기법 적용 (The Sampled-Data $H{\infty}$ Problem: Applying the Discretization Method via a Closed-Loop Expression of Worst-Case Disturbance)

  • 조도현;박진홍
    • 한국컴퓨터산업학회논문지
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    • 제2권7호
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    • pp.967-974
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    • 2001
  • 리프팅 기법을 사용하지 않고 최악의 경우에 대한 등가 이산화 절차를 통하여 샘플치 $H{\infty}$ 문제를 다루었다. 이산 문제 특성화를 유도하기 위해서 표준 선형 2차 이론의 결과를 이용하였다. 제안한 방법은 한 번의 행렬 지수함수 풀이만을 필요로 하므로 리프팅 기법에 비해 매우 간단하지만, 리프팅 기법을 사용하여 구한 샘플치 $H{\infty}$ 최적 제어기와의 성능차이가 거의 없었다. 또한, 제안한 방법을 도립진자 모델에 적용하였다

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Numerical Calculation of Vibrational Transition Probability for the Forced Morse Oscillator by Use of the Anharmonic Boson Operators

  • 이창순;김유항
    • Bulletin of the Korean Chemical Society
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    • 제22권7호
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    • pp.721-726
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    • 2001
  • The vibrational transition probability expressions for the forced Morse oscillator have been derived using the commutation relations of the anharmonic Boson operators. The formulation is based on the collinear collision model with the exponential repulsive potential in the framework of semiclassical collision dynamics. The sample calculation results for H2+ He collision system, where the anharmonicity is large, are in excellent agreement with those from an exact, numerical quantum mechanical study by Clark and Dickinson, using the reactance matrix. Our results, however, are markedly different from those of Ree, Kim and Shin's in which they approximate the commutation operator I。 as unity, the harmonic oscillator limit. We have concluded that the quantum number dependence in I。 must be retained to get accurate vibrational transition probabilities for the Morse oscillator.

Fisher Information and the Kullback-Leibler Distance in Concomitants of Generalized Order Statistics Under Iterated FGM family

  • Barakat, Haroon Mohammed;Husseiny, Islam Abdullah
    • Kyungpook Mathematical Journal
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    • 제62권2호
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    • pp.389-405
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    • 2022
  • We study the Fisher Information (FI) of m-generalized order statistics (m-GOSs) and their concomitants about the shape-parameter vector of the Iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate distribution. We carry out a computational study and show how the FI matrix (FIM) helps in finding information contained in singly or multiply censored bivariate samples from the IFGM. We also run numerical computations about the FIM for the sub-models of order statistics (OSs) and sequential order statistics (SOSs). We evaluate FI about the mean and the shape-parameter of exponential and power distributions, respectively. Finally, we investigate the Kullback-Leibler distance in concomitants of m-GOSs.

Thermo-mechanical response of size-dependent piezoelectric materials in thermo-viscoelasticity theory

  • Ezzat, Magdy A.;Al-Muhiameed, Zeid I.A.
    • Steel and Composite Structures
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    • 제45권4호
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    • pp.535-546
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    • 2022
  • The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam

  • Zerrouki, Rachid;Karas, Abdelkader;Zidour, Mohamed;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • 제78권2호
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    • pp.117-124
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    • 2021
  • This work focused on the novel numerical tool for the bending responses of carbon nanotube reinforced composites (CNTRC) beams. The higher order shear deformation beam theory (HSDT) is used to determine strain-displacement relationships. A new exponential function was introduced into the carbon nanotube (CNT) volume fraction equation to show the effect of the CNT distribution on the CNTRC beams through displacements and stresses. To determine the mechanical properties of CNTRCs, the rule of the mixture was employed by assuming that the single-walled carbon nanotubes (SWCNTs)are aligned and distributed in the matrix. The governing equations were derived by Hamilton's principle, and the mathematical models presented in this work are numerically provided to verify the accuracy of the present theory. The effects of aspect ratio (l/d), CNT volume fraction (Vcnt), and the order of exponent (n) on the displacement and stresses are presented and discussed in detail. Based on the analytical results. It turns out that the increase of the exponent degree (n) makes the X-beam stiffer and the exponential CNTs distribution plays an indispensable role to improve the mechanical properties of the CNTRC beams.

부산시 좌천동 단열암반층에서 자연구배 추적자시험을 이용한 수리분산특성 연구 (Characteristics of Hydrodynamic Dispersion Using a Natural Gradient Tracer Test in a Fractured Rock at the Jwacheon-dong, Busan City)

  • 정상용;강동환;김병우
    • 지질공학
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    • 제16권3호
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    • pp.245-254
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    • 2006
  • 부산시 좌천동의 단열암반층에서 자연구배 추적자시험으로 브롬이온농도를 관측하여 심도별 단열발달 상태에 따른 수리분산특성을 비교하였으며, 단열암반층의 유효공극율과 종분산지수를 추정하였다. 수직적인 수리분산특성의 차이는 브롬이온의 농도이력곡선, 관측심도별 브롬이온농도와 시간에 대한 선형회귀분석 및 관측지점별 수리단열특성을 이용하여 규명되었다. 관측공 내 지표면하 18 m(RQD 13%, 평균절리간격 2 cm, TCR 100%) 지점이 주입지점에서의 이격거리가 짧고 단열이 더욱 발달되어 있었기 때문에 25 m(RQD 41%, 평균절리간격 7 cm, TCR 100%) 지점보다 추적자가 빨리 도달하였으며, 초기농도와 최고농도가 더 높게 나타났다. 최고농도도달 전후의 농도변화에 의하면 추적자가 최고농도도달시까지는 주로 1차 단열을 통해 이송되었고, 최고농도도달 이후에는 2차 단열을 통해 이송되거나 기질확산에 의한 수리 분산이 진행되었다. 선형회귀분석에 의한 지표면하 18 m 지점에서 브롬이온농도의 증가/감소 기울기는 3.46/-1.57이며 지표면하 25 m 지점에서는 3.19/-0.47로서 파쇄가 더 심한 지표면하 18 m 지점에서의 용질이송이 빠르게 진행됨을 알 수 있었다. 농도이력곡선에서 브롬이온의 농도증가 형태는 가우시안함수로 나타나고, 농도감소 형태는 기질확산에 의한 꼬리효과(tailing effect)로 인해 지수함수로 나타났다. CATTI 코드를 이용하여 추정한 단열암반층의 유효공극율은 10.5%, 종분산지수는 0.85 m이었다.

Dose-dependent effects of a microbial phytase on phosphorus digestibility of common feedstuffs in pigs

  • Almeida, Ferdinando N.;Vazquez-Anon, Mercedes;Escobar, Jeffery
    • Asian-Australasian Journal of Animal Sciences
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    • 제30권7호
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    • pp.985-993
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    • 2017
  • Objective: The objective of this study was to evaluate increasing doses of a novel microbial phytase (Cibenza Phytaverse, Novus International, St. Charles, MO, USA) on standardized total tract digestibility (STTD) of P in canola meal (CM), corn, corn-derived distiller's dried grains with solubles (DDGS), rice bran (RB), sorghum, soybean meal (SBM), sunflower meal (SFM), and wheat. Methods: Two cohorts of 36 pigs each (initial body weight = $78.5{\pm}3.7kg$) were randomly assigned to 2 rooms, each housing 36 pigs, and then allotted to 6 diets with 6 replicates per diet in a randomized complete block design. Test ingredient was the only dietary source of P and diets contained 6 concentrations of phytase (0, 125, 250, 500, 1,000, or 2,000 phytase units [FTU]/kg) with 0.4% of $TiO_2$ as a digestibility marker. Feeding schedule for each ingredient was 5 d acclimation, 5 d fecal collection, and 4 d washout. The STTD of P increased (linear or exponential $p{\leq}0.001$) with the inclusion of phytase for all ingredients. Results: Basal STTD of P was 37.6% for CM, 37.6% for corn, 68.6% for DDGS, 10.3% for RB, 41.2% for sorghum, 36.7% for SBM, 26.2% for SFM, and 55.1% for wheat. The efficiency of this novel phytase to hydrolyze phytate is best described with a broken-line model for corn, an exponential model for CM, RB, SBM, SFM, and wheat, and a linear model for DDGS and sorghum. Based on best-fit model the phytase dose (FTU/kg) needed for highest STTD of P (%), respectively, was 735 for 64.3% in CM, 550 for 69.4% in corn, 160 for 55.5% in SBM, 1,219 for 57.8% in SFM, and 881 for 64.0% in wheat, whereas a maximum response was not obtained for sorghum, DDGS and RB within the evaluated phytase range of 0 to 2,000 FTU/kg. These differences in the phytase concentration needed to maximize the STTD of P clearly indicate that the enzyme does not have the same hydrolysis efficiency among the evaluated ingredients. Conclusion: Variations in enzyme efficacy to release P from phytate in various feedstuffs need to be taken into consideration when determining the matrix value for phytase in a mixed diet, which likely depends on the type and inclusion concentration of ingredients used in mixed diets for pigs. The use of a fixed P matrix value across different diet types for a given phytase concentration is discouraged as it may result in inaccurate diet formulation.

로그 모델을 사용한 반강접 철골 골조의 탄성 해석 (Elastic Analysis of Steel Frame with Semi-rigid Connections using the Log Model)

  • 이상섭;문태섭
    • 한국강구조학회 논문집
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    • 제12권5호통권48호
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    • pp.527-535
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    • 2000
  • 철골 구조물의 접합부는 전통적으로 강접 혹은 단순 접합으로 이상화하여 설계되어 졌으나 많은 연구를 통해 이러한 모델링이 불합리할 수 있음이 밝혀져 왔다. 골조의 정확한 해석을 위해 부재의 2차효과($P-{\delta}$효과) 및 구조물 전체의 2차효과($P-{\Delta}$효과)의 고려가 필수적이고, 무엇보다도 접합부의 고유한 강성을 부여하는 것이 중요하다. 즉 실험을 통해 얻은 접합부의 모멘트-회전각을 골조 해석시 있는 그대로 반영할 수 있어야 한다. 이러기 위해 모멘트-회전각을 표현할 수 있는 단일 수식의 개발이 필요하며 지금까지 다양한 수식이 개발되어 보고되고 있다. 본 논문은 기하학적효과 및 접합부 강성을 고려할 수 있도록 이론을 통해 유도한 접합부의 강성행렬에 모멘트-회전각 관계를 표현하는 수정지수 함수 모델, 멱함수 모델 그리고 제안한 로그함수 모델을 사용하여 골조 해석을 실시하고, 그 결과를 통해 유도된 강성행렬의 적용가능성을 알아보고, 제안한 로그함수의 유효성을 밝히고자 한다.

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고검화도의 폴리(비닐 알코올)/디메틸설폭사이드 용액에서의 점성도 특성과 탐침입자의 확산 (Probe Diffusion and Viscosity Properties in Dimethyl Sulfoxide Solution of Poly(vinyl alcohol) with High Degree of Hydrolysis)

  • 엄효상;박일현
    • 폴리머
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    • 제34권5호
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    • pp.415-423
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    • 2010
  • 고검화도(98%이상)의 폴리(비닐 알코올)(PVA)를 디메틸설폭사이드(DMSO) 용매에 녹인 뒤 PVA 준희박 용액 대에서 농도 $C{\simeq}0.14\;g/mL$까지 점성도를 측정하였으며, 이 시스템을 매트릭스로 하여 폴리스티렌(PS) 라텍스 입자의 확산운동 지연을 동적 광산란법으로 조사하였다. PVA/DMSO계의 점성도를 고유점성도 $[{\eta}]$로 스케일된 환산농도 $C[{\eta}]$에 대하여 도시하였을 때 C$[{\eta}]$ >2에서는 분자량 의존성이 강하게 나타났으며, 그 원인은 PVA 용액 내에 존재하는 불균일 영역때문인 것으로 추정하였다. 그러나 매트릭스 내에서 탐침입자의 확산운동은 모든 측정농도에서 단일모드로 관찰되었고, 용액상 및 용매상에서의 확산계수의 비인 D/Do를 $C[{\eta}]$로 도시할 때 전체 농도 범위에서 분자량 의존성은 전혀 나타나지 않았으나 신장지수함수의 적용 한계는 C$[{\eta}]$ >2.5인 것으로 관찰되었다.