• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.619-628
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• 2023

In this paper, the fractional order time-varying linear dynamical systems are investigated by using a residual power series method. A residual power series method (RPSM) is constructed for this problem. The exact solution is obtained by the Laplace transform method and the analytical solution is calculated via the residual power series method (RPSM). As an application, some examples are tested to show the accuracy and efficacy of the proposed methods. The obtained result showed that the proposed methods are effective and accurate for this type of problem.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.127-133
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• 2012

It is well known that if the ${\beta}$-expansion of any nonnegative integer is finite, then ${\beta}$ is a Pisot or Salem number. We prove here that $\mathbb{F}_q((x^{-1}))$, the ${\beta}$-expansion of the polynomial part of ${\beta}$ is finite if and only if ${\beta}$ is a Pisot series. Consequently we give an other proof of Scheiche theorem about finiteness property in $\mathbb{F}_q((x^{-1}))$. Finally we show that if the base ${\beta}$ is a Pisot series, then there is a bound of the length of the fractional part of ${\beta}$-expansion of any polynomial P in $\mathbb{F}_q[x]$.

• Journal of Power Electronics
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• v.16 no.5
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• pp.1629-1638
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• 2016

Differential power processing (DPP) systems are among the most effective architectures for photovoltaic (PV) power systems because they are highly efficient as a result of their distributed local maximum power point tracking ability, which allows the fractional processing of the total generated power. However, DPP systems require a high-efficiency, high step-up/down bidirectional converter with broad operating ranges and galvanic isolation. This study proposes a single, magnetic, high-efficiency, high step-up/down bidirectional DC-DC converter. The proposed converter is composed of a bidirectional flyback and a bidirectional isolated switched-capacitor cell, which are competitively cheap. The output terminals of the flyback converter and switched-capacitor cell are connected in series to obtain the voltage step-up. In the reverse power flow, the converter reciprocally operates with high efficiency across a broad operating range because it uses hard switching instead of soft switching. The proposed topology achieves a genuine on-off interleaved energy transfer at the transformer core and windings, thus providing an excellent utilization ratio. The dynamic characteristics of the converter are analyzed for the controller design. Finally, a 240 W hardware prototype is constructed to demonstrate the operation of the bidirectional converter under a current feedback control loop. To improve the efficiency of a PV system, the maximum power point tracking method is applied to the proposed converter.

• Proceedings of the KIEE Conference
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• 2003.04a
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• pp.224-227
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• 2003

Single phase induction motor(SPIM) is one of the most widely used type of low power AC motors in the world, especially for domestic or commercial applications where a three phase power supply is not available. Fractional horse power of the SPIM have no starting torque their own. So there are several ways of starting SPIMS. The most common type is the starting capacitor installed in series with the auxiliary winding to increase the starting torque. Also, the auxiliary winding is disconnected once the speed of the motor reaches 70 to 80 [%] of the rated speed. In the conventional systems, this function is conducted by a centrifugal switch. But the mechanical centrifugal switch has many problems such as switch malfunction. This paper presents the starter design of SPIM capacitor starting switch using microcontroller.

• Smart Structures and Systems
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• v.22 no.1
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• pp.81-94
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• 2018

Automatic Generation Control (AGC) has functionally controlled the interchange power flow in order to suppress the dynamic oscillations of frequency and tie-line power deviations as a perturbation occurs in the interconnected multi-area power system. Furthermore, Flexible AC Transmission Systems (FACTS) can effectively assist AGC to more enhance the dynamic stability of power system. So, Static Synchronous Series Compensator (SSSC), one of the well-known FACTS devices, is here applied to accurately control and regulate the load frequency of multi-area multi-source interconnected power system. The research and efforts made in this regard have caused to introduce the Fractional Order Proportional Integral Derivative (FOPID) based SSSC, to alleviate both the most significant issues in multi-area interconnected power systems i.e., frequency and tie-line power deviations. Due to multi-objective nature of aforementioned problem, suppression of the frequency and tie-line power deviations is formularized in the form of a multi-object problem. Considering the high performance of Multi Objective Bees Algorithm (MOBA) in solution of the non-linear objectives, it has been utilized to appropriately unravel the optimization problem. To verify and validate the dynamic performance of self-defined FOPID-SSSC, it has been thoroughly evaluated in three different multi-area interconnected power systems. Meanwhile, the dynamic performance of FOPID-SSSC has been accurately compared with a conventional controller based SSSC while the power systems are affected by different Step Load Perturbations (SLPs). Eventually, the simulation results of all three power systems have transparently demonstrated the dynamic performance of FOPID-SSSC to significantly suppress the frequency and tie-line power deviations as compared to conventional controller based SSSC.

• Proceedings of the KIEE Conference
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• 2002.11d
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• pp.267-270
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• 2002

Fractional horse power single phase induction motors have no starting torque their own. So there are several ways of starting single phase induction motors. The most common type is the starting capacitor installed in series with the auxiliary winding to increase the starting torque. Also, the auxiliary winding is disconnected once the speed of the motor reaches 70 to 80 [%] of the rated speed. In the conventional systems, this function is conducted by a centrifugal switch. But the mechanical centrifugal switch has many problems such as switch malfunction. This paper presents the new methods of electronic starting switch by inductor to overcome these shortcomings of centrifugal switch.

• The Transactions of the Korean Institute of Power Electronics
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• v.6 no.2
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• pp.132-140
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• 2001

A universal motor is a small dc series machine motor that is designed to operate from an ac machine. The characteristics of universal motors are high no-load and staring torque. Because of the high operating speed, the size of these motors for a given hp rating is typically smaller that other fractional hp ac machine, making it ideal for hand-held tools and appliances where weight, compactness, and speed are importance factors. A phase-angle control with AC drive system gains a high popularity due to their simple implementation, but contains the disadvantage of their poor input power factor, subharmonic current. Pulse width modulation control with DC drive systems increase the power factor as without delay phase angle. This paper analyzed the subharmonic characteristics of the phase angle control system that is controlled by zero voltage crossing similar to traditional method, and the dc chopper system that is used PWM.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.195-200
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• 1998

Since the neural network was introduced, significant progress has been made on data handling and learning algorithms. Currently, the most popular learning algorithm in neural network training is feed forward error back-propagation (FFEBP) algorithm. Aside from the success of the FFEBP algorithm, polynomial neural networks (PNN) learning has been proposed as a new learning method. The PNN learning is a self-organizing process designed to determine an appropriate set of Ivakhnenko polynomials that allow the activation of many neurons to achieve a desired state of activation that mimics a given set of sampled patterns. These neurons are interconnected in such a way that the knowledge is stored in Ivakhnenko coefficients. In this paper, the PNN model has been developed using the plasma enhanced chemical vapor deposition (PECVD) experimental data. To characterize the PECVD process using PNN, SiO$_2$films deposited under varying conditions were analyzed using fractional factorial experimental design with three center points. Parameters varied in these experiments included substrate temperature, pressure, RF power, silane flow rate and nitrous oxide flow rate. Approximately five microns of SiO$_2$were deposited on (100) silicon wafers in a Plasma-Therm 700 series PECVD system at 13.56 MHz.

• Journal of Distribution Science
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• v.14 no.1
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• pp.93-102
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• 2016

Purpose - The purpose of paper is studying the static and dynamic side for long-term memory storage properties, and increase the explanatory power regarding the long-term memory process by looking at the long-term storage attributes, Korea Composite Stock Price Index. The reason for the use of GPH statistic is to derive the modified statistic Korea's stock market, and to research a process of long-term memory. Research design, data, and methodology - Level shifts were subjected to be an empirical analysis by applying the GPH method. It has been modified by taking into account the daily log return of the Korea Composite Stock Price Index a. The Data, used for the stock market to analyze whether deciding the action by the long-term memory process, yield daily stock price index of the Korea Composite Stock Price Index and the rate of return a log. The studies were proceeded with long-term memory and long-term semiparametric method in deriving the long-term memory estimators. Chapter 2 examines the leading research, and Chapter 3 describes the long-term memory processes and estimation methods. GPH statistics induced modifications of statistics and discussed Whittle statistic. Chapter 4 used Korea Composite Stock Price Index to estimate the long-term memory process parameters. Chapter 6 presents the conclusions and implications. Results - If the price of the time series is generated by the abnormal process, it may be located in long-term memory by a time series. However, test results by price fixed GPH method is not followed by long-term memory process or fractional differential process. In the case of the time-series level shift, the present test method for a long-term memory processes has a considerable amount of bias, and there exists a structural change in the stock distribution market. This structural change has implications in level shift. Stratum level shift assays are not considered as shifted strata. They exist distinctly in the stock secondary market as bias, and are presented in the test statistic of non-long-term memory process. It also generates an error as a long-term memory that could lead to false results. Conclusions - Changes in long-term memory characteristics associated with level shift present the following two suggestions. One, if any impact outside is flowed for a long period of time, we can know that the long-term memory processes have characteristic of the average return gradually. When the investor makes an investment, the same reasoning applies to him in the light of the characteristics of the long-term memory. It is suggested that when investors make decisions on investment, it is necessary to consider the characters of the long-term storage in reference with causing investors to increase the uncertainty and potential. The other one is the thing which must be considered variously according to time-series. The research for price-earnings ratio and investment risk should be composed of the long-term memory characters, and it would have more predictability.