• Title/Summary/Keyword: the Tau method

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OPTIMAL STRATEGIES IN BIOECONOMIC DIFFERENTIAL GAMES: INSIGHTS FROM CHEBYSHEV TAU METHOD

  • Shahd H. Alkharaz;Essam El-Siedy;Eliwa M. Roushdy;Muner M. Abou Hasan
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.2
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    • pp.527-543
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    • 2024
  • In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

A Chaos Control Method by DFC Using State Prediction

  • Miyazaki, Michio;Lee, Sang-Gu;Lee, Seong-Hoon;Akizuki, Kageo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.1
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    • pp.1-6
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    • 2003
  • The Delayed Feedback Control method (DFC) proposed by Pyragas applies an input based on the difference between the current state of the system, which is generating chaos orbits, and the $\tau$-time delayed state, and stabilizes the chaos orbit into a target. In DFC, the information about a position in the state space is unnecessary if the period of the unstable periodic orbit to stabilize is known. There exists the fault that DFC cannot stabilize the unstable periodic orbit when a linearlized system around the periodic point has an odd number property. There is the chaos control method using the prediction of the $\tau$-time future state (PDFC) proposed by Ushio et al. as the method to compensate this fault. Then, we propose a method such as improving the fault of the DFC. Namely, we combine DFC and PDFC with parameter W, which indicates the balance of both methods, not to lose each advantage. Therefore, we stabilize the state into the $\tau$ periodic orbit, and ask for the ranges of Wand gain K using Jury' method, and determine the quasi-optimum pair of (W, K) using a genetic algorithm. Finally, we apply the proposed method to a discrete-time chaotic system, and show the efficiency through some examples of numerical experiments.

Mobility Management of M2M Devices with Grouping in the LTE System (LTE 시스템에서 그룹 기반 M2M 단말 이동성 관리)

  • Roh, Hee-Tae;Lee, Jang-Won
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.37B no.12
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    • pp.1119-1127
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    • 2012
  • The one of features of M2M communications, which are recently attracted attention as a future business of mobile communications, is that there is a large number of devices compared with traditional communication services. Hence, the control signal that are generated by the M2M devices may cause a significant congestion in the network and in order to solve this problem, a standardization is progressing for reducing the redundant signaling by managing M2M devices as a group in 3GPP standardization. In this paper, we propose a method of group based mobility management by managing M2M devices that have the same mobility as a group. In the proposed method, M2M devices that have the same mobility are grouped by the Mobility Management Entity (MME) and the MME elects a group header among the M2M devices in the group. Then, the group header performs the Tracking Area Update (TAU) on behalf of the group members to reduce the signaling overhead of mobility management. With the proposed method, we can achieve 80% decrease of the signaling overhead of mobility management compared with the case where each M2M device individually performs its TAU procedure.

The Accurate design of a Temperature stable Dielectric Stepped-Impedance Resonator (온도 변화에 안정한 유전체 Stepped-Impedance Resonator의 정확한 설계)

  • 임상규;김덕환안철
    • Proceedings of the IEEK Conference
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    • 1998.10a
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    • pp.625-628
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    • 1998
  • This paper presents the design method of a temperature stable stepped-impedance resonator using composite material. In this method temperature coefficient of dielectric constant $(\tau\varepsilon)$ and thermal expansion coefficient $(\alpha1)$ of dielectric material were considered. Ba(Zn1/3Nb2/3)O3 and CaZrO3 as composite material having opposite signs of temperature coefficient of dielectric constant were selected. The length of this resonator for the temperature stability of resonance frequency was calculated at 900MHz, 1.4㎓ and 1.9㎓. It was found that the ratio of the length of positive $\tau\varepsilon$ materal to the length of negative $\tau\varepsilon$ material is constant at various resonance frequencies.

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Evaluation of Nutritional Status of Inpatients with Medical Health Problems (내과 입원환자의 초기 영양상태 평가)

  • Hwang, Eun-Sook;Kim, Ju-Sung;Shin, Jae-Shin
    • The Korean Journal of Rehabilitation Nursing
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    • v.6 no.1
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    • pp.14-25
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    • 2003
  • Purpose: To investigate nutritional status of inpatients by using subjective, and objective evaluation methods and to find the relationship between them. Method: The subjects were 101 inpatients with medical health problems at a university hospital. Nutritional status was evaluated by the Subjective Global Assessment(SGA) and physical assessment including percentage of weight loss, serum albumin, hemogloin, and hematocrit. Data were analyzed using frequency, percentage, mean, Kendall's tau. Results: Grouping by the SGA, 61.4% were classified as severe malnutrition group. When applying the objective methods(physical assessment), 1.9~42.6% were diagnosed as malnutrition each item. The percentage of weight loss during previous 1~6month(${\tau}=.43{\sim}.54$, P=.0001), serum albumin(${\tau}=-.26$, P=.0003), hemoglobin of male(${\tau}=-.38$, P=.0001), and hematocrit of male(${\tau}=-.34$, P=.0001) were significantly correlated with SGA score. The coincidence rate of nutrition evaluation between the objective methods and SGA were 27.7~35.6%, 20.8%, 47.5%, 58.4% in percentage of weight loss, albumin, hemoglobin, and hematocrit. Conclusion: These findings showed a majority of inpatients were exposed to the risk of malnutrition. We recommend to evaluate inpatients' nutritional status periodically and to develop nursing intervention to solve their nutritional problems.

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Fault diagnosis based on likelihood decomposition

  • Uosaki, Katsuji;Kagawa, Tetsuo
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10b
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    • pp.272-275
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    • 1992
  • A novel fault diagnosis method based on likelihood decomposition is proposed for linear stochastic systems described by autoregressive (AR) model. Assuming that at some time instant .tau. the fault of one of the following two types is occurs: innovation fault (actuator fault); and observation fault (sensor fault), the log-likelihood function is decomposed into two components based on the observations before and after .tau., respectively, Then, the type of the fault is determined by comparing the log-likelihoods corresponding two types of faults. Numerical examples demonstrate the usefulness of the proposed diagnosis method.

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DESIGN OF SINGLE-SIDED LINEAR INDUCTION MOTOR USING FINITE ELEMENT METHOD AND SUMT (유한요소법과 SUMT를 이용한 편측식 선형유도전동기의 설계)

  • Im, Dal-Ho;Kim, Hak-Ryun;Lee, Cheol-Jik;Park, Seung-Chan
    • Proceedings of the KIEE Conference
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    • 1992.07a
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    • pp.503-505
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    • 1992
  • This paper describes the optimization of design variables of SLIM using finite element method and SUMT(Sequential Unconstrained Minimization Technique). Thrust is taken as an objective function in order to maximize thrust under constant current drive, and seven independent design variables and nine constraints are chosen. As a result, $\tau$/g(pole pitch/airgap) and $\tau$/$d_{AL}$(pole pitch/aluminum depth) of good criteria in SLIM design are determined.

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A novel approach in voltage transient technique for the measurement of electron mobility and mobility-lifetime product in CdZnTe detectors

  • Yucel, H.;Birgul, O.;Uyar, E.;Cubukcu, S.
    • Nuclear Engineering and Technology
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    • v.51 no.3
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    • pp.731-737
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    • 2019
  • In this study, a new measurement method based on voltage transients in CdZnTe detectors response to low energy photon irradiations is applied to measure the electron mobility (${\mu}_e$) and electron mobility-lifetime product $({\mu}{\tau})_e$ in a CdZnTe detector. In the proposed method, the pulse rise times are derived from low energy photon response to 59.5 keV($^{241}Am$), 88 keV($^{109}Cd$) and 122 keV($^{57}Co$) ${\gamma}-rays$ for the irradiation of the cathode surface at each detector for different bias voltages. The electron $({\mu}{\tau})_e$ product was then determined by measuring the variation in the photopeak amplitude as a function of bias voltage at a given photon energy using a pulse-height analyzer. The $({\mu}{\tau})_e$ values were found to be $(9.6{\pm}1.4){\times}10^{-3}cm^2V^{-1}$ for $1000mm^3$, $(8.4{\pm}1.6){\times}10^{-3}cm^2V^{-1}$ for $1687.5mm^3$ and $(7.6{\pm}1.1){\times}10^{-3}cm^2V^{-1}$ for $2250mm^3$ CdZnTe detectors. Those results were then compared with the literature $({\mu}{\tau})_e$ values for CdZnTe detectors. The present results indicate that, the electron mobility ${\mu}_e$ and electron $({\mu}{\tau})_e$ values in CdZnTe detectors can be measured easily by applying voltage transients response to low energy photons, utilizing a fast signal acquisition and data reduction and evaluation.

Nonlinear Analog of Autocorrelation Function (자기상관함수의 비선형 유추 해석)

  • Kim, Hyeong-Su;Yun, Yong-Nam
    • Journal of Korea Water Resources Association
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    • v.32 no.6
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    • pp.731-740
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    • 1999
  • Autocorrelation function is widely used as a tool measuring linear dependence of hydrologic time series. However, it may not be appropriate for choosing decorrelation time or delay time ${\tau}_d$ which is essential in nonlinear dynamics domain and the mutual information have recommended for measuring nonlinear dependence of time series. Furthermore, some researchers have suggested that one should not choose a fixed delay time ${\tau}_d$ but, rather, one should choose an appropriate value for the delay time window ${\tau}_d={\tau}(m-1)$, which is the total time spanned by the components of each embedded point for the analysis of chaotic dynamics. Unfortunately, the delay time window cannot be estimated using the autocorrelation function or the mutual information. Basically, the delay time window is the optimal time for independence of time series and the delay time is the first locally optimal time. In this study, we estimate general dependence of hydrologic time series using the C-C method which can estimate both the delay time and the delay time window and the results may give us whether hydrologic time series depends on its linear or nonlinear characteristics which are very important for modeling and forecasting of underlying system.

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Potential of River Bottom and Bank Erosion for River Restoration after Dam Slit in the Mountain Stream

  • Kang, Ji-Hyun;So, Kazama
    • Proceedings of the Korea Water Resources Association Conference
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    • 2011.05a
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    • pp.46-46
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    • 2011
  • Severe sediment erosion during floods occur disaster and economic losses, but general sediment erosion is basic mechanism to move sediment from upstream to downstream river. In addition, it is important process to change river form. Check dam, which is constructed in mountain stream, play a vital role such as control of sudden debris flow, but it has negative aspects to river ecosystem. Now a day, check dam of open type is an alternative plan to recover river biological diversity and ecosystem through sediment transport while maintaining the function of disaster control. The purpose of this paper is to verify sediment erosion progress of river bottom and bank as first step for river restoration after dam slit by cross-sectional shear stress and critical shear stress. Study area is upstream reach of slit check dam in mountain stream, named Wasada, in Japan. The check dam was slit with two passages in August, 2010. The transects were surveyed for four upstream cross-sections, 7.4 m, 34 m, 86 m, and 150 m distance from dam in October 2010. Sediment size was surveyed at river bottom and bank. Sediment of cobble size was found at the wetted bottom, and small size particles of sand to medium gravel composed river bank. Discharge was $2.5\;m^3/s$ and bottom slope was 0.027 m/m. Excess shear stress (${\tau}_{ex}$) was calculated for hydraulic erosion by subtracting the values of critical shear stress (${\tau}_{c}$) from the value of shear stress (${\tau}$) at river bottom and bank (${\tau}_{ex}=\tau-{\tau}_c$). Shear stress of river bottom (${\tau}_{bottom}$) was calculated using the cross-sectional shear stress, and bank shear stress (${\tau}_{bank}$) was calculated from the method of Flintham and Carling (1988). $${\tau}_{bank}={\tau}^*SF_{bank}((B+P_{bed})/(2^*P_{bank}))$$ where $SF_{bank}=1.77(P_{bed}/p_{bank}+1.5)^{-1.4}$, B is the water surface width, $P_{bed}$ and $P_{bank}$ are wetted parameter of the bed and bank. Estimated values for ${\tau}_{bottom}$ for a flow of $2.5\;m^3/s$ were lower as 25.0 (7.5 m cross-section), 25.7 (34 m), 21.3 (86 m) and 19.8 (150 m), in N/$m^2$, than critical shear stress (${\tau}_c=62.1\;N/m^2$) with cobble of 64 mm. The values were insufficient to erode cobble sediment. In contrast, even if the values of ${\tau}_{bank}$ were lower than the values for ${\tau}_{bottom}$ as 18.7 (7.5 m), 19.3 (34 m), 16.1 (86 m) and 14.7 (150 m), in N/$m^2$, excess shear stresses were calculated at the three cross-sections of 7.5 m, 34 m, and 86 m distances compare with ${\tau}_c$ is 15.5 N/$m^2$ of 16mm gravel. Bank shear stresses were sufficient for erosion of the medium gravel to sand. Therefore there is potential to erode lateral bank than downward erosion in a flow of $2.5\;m^3/s$. Undercutting of the wetted bank can causes bank scour or collapse, therefore this channel has potential to become wider at the same time. This research is about a potential of sediment erosion, and the result could not verify with real data. Therefore it need next step for verification. In addition an erosion mechanism for river restoration is not simple because discharge distribution is variable by snow-melting or rainy season, and a function for disaster control will recover by big precipitation event. Therefore it needs to consider the relationship between continuous discharge change and sediment erosion.

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