• Title/Summary/Keyword: Linear approach

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ADAPTATION OF THE MINORANT FUNCTION FOR LINEAR PROGRAMMING

  • Leulmi, S.;Leulmi, A.
    • East Asian mathematical journal
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    • v.35 no.5
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    • pp.597-612
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    • 2019
  • In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.

Confidence Intervals for a Linear Function of Binomial Proportions Based on a Bayesian Approach (베이지안 접근에 의한 모비율 선형함수의 신뢰구간)

  • Lee, Seung-Chun
    • The Korean Journal of Applied Statistics
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    • v.20 no.2
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    • pp.257-266
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    • 2007
  • It is known that Agresti-Coull approach is an effective tool for the construction of confidence intervals for various problems related to binomial proportions. However, the Agrest-Coull approach often produces a conservative confidence interval. In this note, confidence intervals based on a Bayesian approach are proposed for a linear function of independent binomial proportions. It is shown that the Bayesian confidence interval slightly outperforms the confidence interval based on Agresti-Coull approach in average sense.

Finite Element Analysis of Magnetostrictive Linear Actuator (자왜재료를 이용한 선형 작동기의 유한요소 해석)

  • Kim, Yoon-Chang;Kim, Jae-Hwan
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.4 s.121
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    • pp.356-362
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    • 2007
  • Magnetostrictive materials have been used for linear actuators due to its large strain, large force output with moderate frequency band in the presence of magnetic field. However their performance analysis is difficult because of nonlinear material behaviors in terms of coupled strain-magnetic field dependence, nonlinear permeability, pre-stress dependence and hysteresis. This paper presents a finite element analysis technique for magnetostrictive linear actuator. To deal with coupled problems and nonlinear behaviors, a simple finite element approach is proposed, which is based on separate magnetic field calculation and displacement simulation. The finite element formulation and an in-house program development are illustrated, and a simulation model is made for a magnetostrictive linear actuator. The fabrication and performance test of the linear actuator are explained, and the performance comparison with simulation result is shown. Since this approach is simple, it can be applied for analyzing magnetostrictive underwater projectors and ultrasonic transducers.

Impact of Hand-Held Technology for Understanding Linear Equations and Graphs

  • Kwon, Oh-Nam
    • Research in Mathematical Education
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    • v.6 no.1
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    • pp.81-96
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    • 2002
  • This article describes a research project that examined the impact of hand-held technology on students' understanding linear equations and graphs in multiple representations. The results indicated that students in the graphing-approach classes were significantly better at the components of interpreting. No significant differences between the graphing-approach and traditional classes were found fur translation, modeling, and algebraic skills. Further, students in the graphing-approach classes showed significant improvements in their attitudes toward mathematics and technology, were less anxious about mathematics, and rated their class as more interesting and valuable.

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EVALUATIONS OF SOME QUADRATIC EULER SUMS

  • Si, Xin;Xu, Ce
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.489-508
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    • 2020
  • This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

Design of PD Observers in Descriptor Linear Systems

  • Wu, Ai-Guo;Duan, Guang-Ren
    • International Journal of Control, Automation, and Systems
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    • v.5 no.1
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    • pp.93-98
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    • 2007
  • A class of new observers in descriptor linear systems, proportional-derivative(PD) observers, are proposed. A parametric design approach for such observers is proposed based on a complete parametric solution to the generalized Sylvester matrix equation. The approach provides complete parameterizations for all the observer gains, gives the parametric expression for the corresponding left eigenvector matrix of the observer system matrix, realizes elimination of impulsive behaviors, and guarantees the regularity of the observer system.

Solving Linear Problems with Generalized Variable Upper Bounds

  • Yang, Kwang-Min
    • Journal of the Korean Operations Research and Management Science Society
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    • v.17 no.3
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    • pp.171-180
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    • 1992
  • This paper proposes a solution approach to linear problems with many constraints of variable upper bound (VUB) type. This type of constraints are commonly found in various scheduling type problems for which tighter bounds are essential to achieve an efficiency in enumeration. An analytical framework based on factorization is adopted to devise a solution approach to the problem and extend it for more generalized VUB problem (GVUB). This research shows why the VUB type constraints are amenable to the factorization and gives a unified approach to generalized upper bound(GUB) problems, VUB problems and GVUB problems. Implementation issues are also included.

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Nonlinear Soil-Structure Interaction Analysis Considering Complicated Soil Profile (복잡한 지반 형상을 고려한 비선형 지반-구조물상호작용 해석)

  • Park, Jang-Ho
    • Journal of the Korean Society of Safety
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    • v.26 no.1
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    • pp.36-42
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    • 2011
  • This paper presents a nonlinear soil-structure interaction analysis approach, which can consider precisely characteristics of structures, complicated soil profiles and nonlinear characteristics of soil. Although many methods have been developed to deal with the soil-structure interaction effects in past years, most of them are nearly unpractical since it is difficult to model complicated characteristics of structure and soil precisely. The presented approach overcomes the difficulties by adopting an maligned mesh generation approach and multi-linear model. The applicability of the proposed approach is validated and the effects of complicated characteristics of structure and soil on soil-structure interaction are investigated through the numerical example by the proposed nonlinear soil-structure interaction analysis approach.

An improved Kalman filter for joint estimation of structural states and unknown loadings

  • He, Jia;Zhang, Xiaoxiong;Dai, Naxin
    • Smart Structures and Systems
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    • v.24 no.2
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    • pp.209-221
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    • 2019
  • The classical Kalman filter (KF) provides a practical and efficient way for state estimation. It is, however, not applicable when the external excitations applied to the structures are unknown. Moreover, it is known the classical KF is only suitable for linear systems and can't handle the nonlinear cases. The aim of this paper is to extend the classical KF approach to circumvent the aforementioned limitations for the joint estimation of structural states and the unknown inputs. On the basis of the scheme of the classical KF, analytical recursive solution of an improved KF approach is derived and presented. A revised form of observation equation is obtained basing on a projection matrix. The structural states and the unknown inputs are then simultaneously estimated with limited measurements in linear or nonlinear systems. The efficiency and accuracy of the proposed approach is verified via a five-story shear building, a simply supported beam, and three sorts of nonlinear hysteretic structures. The shaking table tests of a five-story building structure are also employed for the validation of the robustness of the proposed approach. Numerical and experimental results show that the proposed approach can not only satisfactorily estimate structural states, but also identify unknown loadings with acceptable accuracy for both linear and nonlinear systems.

A simple and rapid approach to modeling chromium breakthrough in fixed bed adsorber

  • Chu, Khim Hoong
    • Advances in environmental research
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    • v.7 no.1
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    • pp.29-37
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    • 2018
  • A simple mathematical model for predicting fixed bed adsorption dynamics is described. The model is characterized by a linear adsorption isotherm and a linear driving force expression for mass transfer. Its analytic solution can be approximated with an algebraic equation in closed form which is easily evaluated by spreadsheet computation. To demonstrate one application of the fixed bed model, a previously published adsorption system is used as a case study in this work. The adsorption system examined here describes chromium breakthrough in a fixed bed adsorber packed with imidazole functionalized adsorbent particles and is characterized by a nonlinear adsorption isotherm. However, the equilibrium behavior of the fixed bed adsorber is in essence governed by a linear adsorption isotherm due to the use of a low influent chromium concentration. It is shown that chromium breakthrough is predicted reasonably well by the fixed bed model. The model's parameters can be easily extracted from independent batch experiments. The proposed modeling approach is very simple and rapid, and only Excel is used for computation.