• Title, Summary, Keyword: Algebraic Method

### Algebraic compensator design for dynamic systems using a novel BPF transformation method (새로운 BPF 변환식을 이용한 동적 시스템의 대수적 보상기 설계)

• Ahn, P.;Kim, M.H.;Kim, J.B.;Lee, J.C.;Oh, M.H.;Ahn, D.S.
• Proceedings of the KIEE Conference
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• pp.595-597
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• 1998
• This paper deals with an algebraic compensator design for dynamic systems using a novel BPF transformation method. To obtain an algebraic compensator for the system, block pulse function's differential operation is used. Compare to unalgebraic compensator, proposed algebraic compensator is less sensitive to the measurement noise.

### A Practical Real-Time LOS Rate Estimator with Time-Varying Measurement Noise Variance (시변 측정잡음 모델을 고려한 실시간 시선각 변화율 추정필터)

• Na, Won-Sang;Lee, Jin-Ik
• Proceedings of the KIEE Conference
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• pp.2082-2084
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• 2003
• A practical real-time LOS rate estimator is proposed to handle the time-varying measurement noise statistics. To calculate the optimal Kalman gain, the algebraic transformation method is taken into account. By using the algebraic transformation, the differential algebraic Riccati equation(DARE) regarding estimation error covariance is replaced by the simple algebraic Riccati equation(ARE). The proposed LOS estimation filter gain is only a function of relative range. Consequently, the proposed method is computationally very efficient and suitable for embedded environment.

### Algebraic Reasoning Abilities of Elementary School Students and Early Algebra Instruction(1) (초등학생의 대수 추론 능력과 조기 대수(Early Algebra) 지도(1))

• Lee, Hwa Young;Chang, Kyung Yoon
• School Mathematics
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• v.14 no.4
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• pp.445-468
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• 2012
• This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

### ALGEBRAIC OPERATIONS ON FUZZY NUMBERS USING OF LINEAR FUNCTIONS

• Myung, Jae Deuk
• Korean Journal of Mathematics
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• v.11 no.1
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• pp.1-7
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• 2003
• In this paper, we introduce two types of algebraic operations on fuzzy numbers using piecewise linear functions and then show that the Zadeh implication is smaller than the Diense-Rescher implication, which is smaller than the Lukasiewicz implication. If ($f$, *) is an available pair, then $A*_mB{\leq}A*_pB{\leq}A*_jB$.

### Efficient Computations for Evaluating Extended Stochastic Petri Nets using Algebraic Operations

• Kim, Dong-Sung;Moon, Hong-Ju;Bahk, Je-Hyeong;Kwon, Wook-Hyun;Zygmunt J. Haas
• International Journal of Control, Automation, and Systems
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• v.1 no.4
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• pp.431-443
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• 2003
• This paper presents an efficient method to evaluate the performance of an extended stochastic Petri net by simple algebraic operations. The reachability graph is derived from an extended stochastic Petri net, and then converted to a timed stochastic state machine, using a semi-Markov process. The n-th moments of the performance index are derived by algebraic manipulations with each of the n-th moments of transition time and transition probability. For the derivation, three reduction rules are introduced on the transition trajectories in a well-formed regular expression. Efficient computation algorithms are provided to automate the suggested method. The presented method provides a proficient means to derive both the numerical and the symbolic solutions for the performance of an extended stochastic Petri net by simple algebraic manipulations.

### Interactive and Intuitive Physics-based Blending Surface Design for the Second Order Algebraic Implicit Surfaces

• Park, Tae-Jung;Kam, Hyeong-Ryeol;Shin, Seung-Ho;Kim, Chang-Hun
• Journal of Korea Multimedia Society
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• v.12 no.6
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• pp.842-855
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• 2009
• We present a physics-based blending method for the second order algebraic implicit surface. Unlike other traditional blending techniques, the proposed method avoids complex mathematical operations and unwanted artifacts like bulge, which have highly limited the application of the second order algebraic implicit surface as a modeling primitive in spite of lots of its excellent properties. Instead, the proposed method provides the designer with flexibility to control the shapes of the blending surface on interactive basis; the designer can check and design the shape of blending surfaces accurately by simply adjusting several physics parameter in real time, which was impossible in the traditional blending methods. In the later parts of this paper, several results are also presented.

### Tomographic Reconstruction of Two-Phase Flows

• Ko, Han-Seo;Kim, Yong-Jae
• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.571-580
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• 2003
• Tomography has been investigated to observe bubble behaviors in two-phase flows. A bubbly flow and an annular flow have been reconstructed by tomography methods such as an algebraic reconstruction technique (ART) and a multiplicative algebraic reconstruction technique (MART) . Computer synthesized phantom fields have been used to calculate asymmetric density distributions for limited cases of 3, 5, and 7 projection angles. As a result of comparison of two tomography methods, the MART method has shown a significant improvement in the reconstruction accuracy for analysis of the two-phase flows.

### Approximate voronoi diagrams for planar geometric models

• Lee, Kwan-Hee;Kim, Myung-Soo
• 제어로봇시스템학회:학술대회논문집
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• pp.1601-1606
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• 1991
• We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

### A Formulation of NDIF Method to the Algebraic Eigenvalue Problem for Efficiently Extracting Natural Frequencies of Arbitrarily Shaped Plates with the Simply Supported Boundary Condition (단순지지 경계조건을 가진 임의 형상 평판의 효율적인 고유진동수 추출을 위한 NDIF법의 대수 고유치 문제로의 정식화)

• Kang, S.W.;Kim, J.G.
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.607-613
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• 2009
• A new formulation of NDIF method to the algebraic eigenvalue problem is introduced to efficiently extract natural frequencies of arbitrarily shaped plates with the simply supported boundary condition. NDIF method, which was developed by the authors for the free vibration analysis of arbitrarily shaped membranes and plates, has the feature that it yields highly accurate natural frequencies compared with other analytical methods or numerical methods(FEM and BEM). However, NDIF method has the weak point that it needs the inefficient procedure of searching natural frequencies by plotting the values of the determinant of a system matrix in the frequency range of interest. A new formulation of NDIF method developed in the paper doesn't require the above inefficient procedure and natural frequencies can be efficiently obtained by solving the typical algebraic eigenvalue problem. Finally, the validity of the proposed method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate compared to other exact, analytical, or numerical methods.

### Automated static condensation method for local analysis of large finite element models

• Boo, Seung-Hwan;Oh, Min-Han
• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.807-816
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• 2017
• In this paper, we introduce an efficient new model reduction method, named the automated static condensation method, which is developed for the local analysis of large finite element models. The algebraic multilevel substructuring procedure is modified appropriately, and then applied to the original static condensation method. The retained substructure, which is the local finite element model to be analyzed, is defined, and then the remaining part of the global model is automatically partitioned into many omitted substructures in an algebraic perspective. For an efficient condensation procedure, a substructural tree diagram and substructural sets are established. Using these, the omitted substructures are sequentially condensed into the retained substructure to construct the reduced model. Using several large practical engineering problems, the performance of the proposed method is demonstrated in terms of its solution accuracy and computational efficiency, compared to the original static condensation method and the superelement technique.