• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.579-582
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• 2000

In this paper, new linearization technique for bipolar OTAs using exponential-law circuits is described. The core circuit of the proposed OTAs is the multi-TANH doublet. The OTAs have adaptively biasing current sources, which consists of the exponential-law circuits. Three types of the OTAs are presented. The linear input voltage ranges of the OTAs are almost the same as the multi-TANH triplet. Further, the OTAs have lower power dissipation than the multi-TANH triplet.

• Journal of Electrical Engineering and Technology
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• v.13 no.3
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• pp.1304-1316
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• 2018

An adaptive sliding-mode observer for speed estimation in sensorless vector controlled induction machine drives is proposed in this paper to balance the dilemma between the requirement of fast reaching transient and the chattering phenomenon reduction on the sliding-mode surface. It is well known that the sliding-mode observer (SMO) suffers from the chattering phenomenon. However, the reduction of the chattering phenomenon will lead to a slow transient process. In order to balance this dilemma, an adaptive exponential reaching law is introduced into SMO by optimizing the reaching way to the sliding-mode surface. The adaptive exponential reaching law is based on the options of an exponential term that adapts to the variations of the sliding-mode surface and system states. Moreover, the proposed sliding-mode observer considering adaptive exponential reaching law, which is called adaptive sliding-mode observer (ASMO), is capable for reducing the chattering phenomenon and decreasing the reaching time simultaneously. The stability analysis for ASMO is achieved based on Lyapunov stability theory. Simulation and experimental results both demonstrate the correctness and the effectiveness of the proposed method.

• Tunnel and Underground Space
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• v.8 no.1
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• pp.1-7
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• 1998

In order to get the information of the deformational behavior of rock masses with time in waste disposal repository, it is necessary to measure the relationships between stress and strain and time for temperature. A creep law is used in conjunction with the elastic moduli to calculate stress and displacement following waste emplacement. Exponential-time law's parameters consist of stress and temperature. In this study, thermal creep test was carried out for Whangdeung granite. The measured creep deformation behavior was well explained by exponential time law and generalized Kelvin's rheological model. Mechanicla coefficients for exponential-time creep law showed the clear tendency of temperature dependent while those for Kelvein's model didn't.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.315-321
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• 2007

We show an exponential inequality for negatively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. To obtain this result we use a truncation technique together with a block decomposition of the sums. We also identify a convergence rate for the strong law of large number.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.4
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• pp.395-401
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• 2014

Magnetic levitation systems using the attraction force of electromagnets have many constraints according to the variation of air gap and the nonlinearity of electromagnetic force and inductances. As a result of these constraints, the nonlinear control of a magnetic levitation system has been improved by the latest advanced processors and accurate measurement system which can overcome problems such as many constraints and nonlinearity. This paper concentrates on the modeling of a nonlinear magnetic levitation system and an application of an exponential reaching law based sliding mode controller using the exponential reaching law which is one of the most robust controllers against external unexpected disturbances or parameter fluctuations. Controllability of a magnetic levitation system using the sliding mode control algorithm and robustness against parameter fluctuations have been verified through the experimental results.

• Advances in nano research
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• v.14 no.4
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• pp.303-312
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• 2023

In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin's method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type-I and Type-II functionally graded cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type-I and -II clamped simply supported FG cylindrical shell with different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.

• Steel and Composite Structures
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• v.49 no.5
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• pp.547-570
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• 2023

In the present work, a comparative study has been carried out between power, exponential, and sigmoidal sandwich FGM plates for free vibration conditions under hygro-thermal conditions. Rules of mixture is used to determine effective material properties across the thickness for power-law and sigmoid sandwich FGM plates. Exponential law is used to plot effective material properties for exponentially graded sandwich FGM plates. Temperature and moisture dependent material properties were used during the analysis. Free vibration analysis is carried out using recently proposed finite element based HOZT. Present formulation satisfies interlayer transverse stress continuity conditions at interfaces and transverse shear stress-free conditions at the plate's top and bottom surfaces. The present model is free from any penalty or post-processing requirements. Several new results are reported in the present work, especially for unsymmetric sandwich FGM plates and exponential and sigmoidal sandwich FGM plates.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.553-561
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• 2015

The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.

• Korean Journal of Ecology and Environment
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• v.45 no.4
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• pp.420-443
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• 2012

An Individual-Based Model (IBM) was developed by employing natural and toxic survival rates of individuals to elucidate the community responses of benthic macroin-vertebrates to anthropogenic disturbance in the streams. Experimental models (dose-response and relative sensitivity) and mathematical models (power law and negative exponential distribution) were applied to determinate the individual survival rates due to acute toxicity in stressful conditions. A power law was additionally used to present the natural survival rate. Life events, covering movement, exposure to contaminants, death and reproduction, were simulated in the IBM at the individual level in small (1 m) and short (1 week) scales to produce species abundance distributions (SADs) at the community level in large (5 km) and long (1~2 years) scales. Consequently, the SADs, such as geometric series, log-series, and log-normal distribution, were accordingly observed at severely (Biological Monitoring Working Party (BMWP<10), intermediately (BMWP<40) and weakly (BMWP${\geq}50$) polluted sites. The results from a power law and negative exponential distribution were suitably fitted to the field data across the different levels of pollution, according to the Kolmogorov-Smirnov test. The IBMs incorporating natural and toxic survival rates in individuals were useful for presenting community responses to disturbances and could be utilized as an integrative tool to elucidate community establishment processes in benthic macroin-vertebrates in the streams.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.323-339
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• 2011

The expansion of exponential law as the law of calculation of integer numbers can be a good material for the students to experience an extended configuration which is based on an algebraic principle of the performance of equivalent forms. While current textbooks described that exponential law can be expanded from natural number to integer, rational number and real number, most teachers force students to accept intuitively that the exponential law is valid although exponent is expanded into real number. However most teachers overlook explaining the value of exponent of rational number or exponent of irrational number so most students have a lot of questions whether this value is a rational number or a irrational number. Related to students' questions, most teacher said that it is out of the current curriculum and students will learn it after going to college instead of detailed answers. In this paper, we will present several examples and the values about irrational exponents of a positive rational and irrational exponents of a positive irrational number, and study the recognition and fallacy of would-be teachers about the cases of irrational exponents of a positive rational and irrational exponents of a positive irrational number at the expansion of exponential law.