• Korean Journal of Mathematics
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• 제31권3호
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• pp.243-258
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• 2023

A normalized analytic function f defined on the unit disk 𝔻 is starlike of reciprocal order α, 0 ≤ α < 1, if Re(f(z)/(zf'(z))) > α for all z ∈ 𝔻. Such functions are starlike and therefore univalent in 𝔻. Using the well-known Miller-Mocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order α. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f(z)/(zf'(z)) - 1| < 1 - α.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.247-263
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• 2023

In this article, we investigate the uniqueness problem of q-shift difference polynomial of meromorphic (entire) function with zero-order. Consequently, we prove three results with significantly generalize the results of Goutam Haldar.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.561-582
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• 2018

In this paper the growth properties of the composition of integer translated entire and meromorphic functions in terms of their (p, q)-th order are discussed and based upon that some new results are developed.

• Journal of Mechanical Science and Technology
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• 제20권10호
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• pp.1662-1669
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• 2006

Since randomness and uncertainties of design parameters are inherent, the robust design has gained an ever increasing importance in mechanical engineering. The robustness is assessed by the measure of performance variability around mean value, which is called as standard deviation. Hence, constraints in robust optimization problem can be approached as probability constraints in reliability based optimization. Then, the FOSM (first order second moment) method or the AFOSM (advanced first order second moment) method can be used to calculate the mean values and the standard deviations of functions describing constraints and object. Among two methods, AFOSM method has some advantage over FOSM method in evaluation of probability. Nevertheless, it is difficult to obtain the mean value and the standard deviation of objective function using AFOSM method, because it requires that the mean value of function is always positive. This paper presented a special technique to overcome this weakness of AFOSM method. The mean value and the standard deviation of objective function by the proposed method are reliable as shown in examples compared with results by FOSM method.

• 대한전기학회논문지
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• 제41권8호
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• pp.902-913
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• 1992

There have been several control schemes for the single input systems with unmeasurable state variables using variable structure control(VSC) theory. In the previous VSC, the systems must be represented in phase canonical form and the complete measurements for each state variable must be assumed. In order to eliminate these restrictions several VSC methods were proposed. And especially for the systems in phase canonical form with unmeasurable state variables, the reduced order switching function algorithm was proposed. But this method has many drawbacks and can not be used in the case of general form (not phase canonical form) dynamic system. Therefore this paper propose new construction method of switching fuction for the systems in phase canonical form, which reduce the restriction of reduced order switching function algorithm. And this algorithm can be realized for any state representation and adopted in the systems where not all states are available for switching function synthesis or control.

• 대한전기학회논문지
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• 제40권7호
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• pp.706-717
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• 1991

In order to remove the assumption of full state availability which is one of the major difficulties with the practical realization of variable structure control systems,a new switching function with a dynamic structure is proposed. And the control performances of the output feedback variable structure control systems with the dynamic switching function are evaluated through simulation studies. The proposed dynamic switching function is driven by small number of measured output and input variables while conventional static switching function requires full state information. Therefore, the proposition of the dynamic swiching function makes practical implementation of output feedback variable structure control scheme possible for the systems with unmeasurable state variables, high order systems and large scale systems that the conventional variable structure control schemes with static switching function cannot be applied. In the variable structure control systems with the dynamic switching function, desired control performance can be guaranteed by proper choice of design parameters such as poles of switching function dynamic equation and switching control gains even though small number of measured output and input variables are provided as shown in simulation resuls.

• 대한수학회보
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• 제38권1호
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• pp.1-6
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• 2001

We discuss the value distribution of composite entire functions including those of infinite order and estimate the number of Q-points of such functions for an entire function Q or relatively slower growth.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.93-111
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• 2010

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.79-86
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• 1999

A Boolean function generates a binary sequence which is frequently used in a stream cipher. There are number of critical concepts which a Boolean function, as a key stream generator in a stream cipher, satisfies. These are nonlinearity, correlation immunity, balancedness, SAC (strictly avalanche criterion), PC (propagation criterion) and so on. In this paper we construct an algorithm for finding the correlation immune order of a Boolean function, and check how long to find the correlation immune order of a given Boolean function in our algorithm.

• 대한전기학회논문지
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• 제31권8호
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• pp.33-38
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• 1982

This paper deals with the simplification of the transfer function in a frequency domain, viz. the integral of the squared errors between the original and the simplified model is minimized and the latter is estimated by the Walsh function. It tries to minimize the errors between the frequency responses of the two functions. This method is compared with the existing method by means of a numercal example. The frequency response of this simplified model approximates closely to that of the original model. The proposed method is simpler in analysis and easier in implementation than the existing methods. Though the Walsh function can be easily generated with the discrete values, it has errors because its zero crossings are not continuous. This method aims at the reduction of the errors in the real parts and the imaginary parts of the two functions by dividing into the more sub-intervals, and selecting the reduced-order model according to the response of the model. As a result, it can be applied for the simplification of higher order functions into lower order functions and for the design of control systems.