• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.885-892
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• 2010

In this paper we study the structures and properties of a single cycle T-finction, whose theory has been lately proposed by Klimov and Shamir. Any cryptographic system based on T-functions may be insecure. Some of the TSC-series stream ciphers have been successfully attacked by some attacks. So it is important to analyze every aspect of a single cycle T-function. We study some properties on a single cycle T-function and we show some examples are single cycle T-functions by these properties, whose proof is easier than existing methods.

• 한국해양학회지
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• v.28 no.3
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• pp.192-201
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• 1993

To reduce tsunami hazards, it is necessary to develope the methods which can simulate tsunami wave signals of coastal areas. In the present paper, it is attempted t use Sign Method for analyzing and simulating recorded tsunami signals. A tsunami record Y(t) can be represented as the convolution integral of a source evolution function E(t') and a wave propagation function K(t-t') Y(t)=.int. E(t')K(t-t')dt' A source function contains the peculiarities of a tsunami generator. A wave function is a kind of transfer function which contains the characteristics of a wave propagation path. The source functions and the wave function and the wave functions of 9 Korean coast points and 6 Japan coast points are estimated, and the tsunami wave signals are simulated by the convolution integrals of the source functions and the wave functions. According to the results of analysis, the Sign Method is an effective method for simulating tsunami wave signals of Korean coast points which are located far from tsunami source areas. Furthermore, if the source function of a neighboring point ad the wave function of an another tsunami are given, unrecorded tsunami wave also can be estimated.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.463-487
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• 2019

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q, t)L-th order and relative (p, q, t)L-th type of entire and meromorphic function with respect to another entire function.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.453-462
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• 2005

We derive the influence function on t statistic and find its feature; the influence function on t statistic has two forms depending on the value of ${\mu}_0$. Sample influence functions are used to verify the validity of the derived influence function. We use random samples from normal distribution to show the validity of the function. The simulation study proves that the obtained influence function is very accurate to in estimating changes in t statistic when an observation is added or deleted.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.69-91
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• 2022

In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p, q, t)L-th order, relative (p, q, t)L-th type and relative (p, q, t)L-th weak type and that of Wronskian generated by one of the factors.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.93-111
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• 1993

Let ${X(t) : t \geq 0}$ be a real-valued stochastics process with stationary independent increments. In this paper, under the condition of stochastic compactness, we obtain appropriate function $\alpha(t)$ and random function $\beta(t)$ such that for some positive finite constant C, lim sup${X(t) - \alpha(t)}/\beta(t) = C$ a.s. both as t tends to zero and infinity.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.7
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• pp.615-623
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• 2008

This paper proposes an $H_{\infty}$ controller design method for Takagi-Sugeno (T-S) fuzzy systems using a fuzzy basis-function-dependent Lyapunov function. Sufficient conditions for the guaranteed $H_{\infty}$ performance of the T-S fuzzy control system are given in terms of linear matrix inequalities (LMIs). These LMI conditions are further used for a convex optimization problem in which the $H_{\infty}-norm$ of the closed-loop system is to be minimized. To facilitate the basis-function-dependent Lyapunov function approach and thus improve the closed-loop system performance, additional decision variables are introduced in the optimization problem, which provide an additional degree-of-freedom and thus can enlarge the solution space of the problem. Numerical examples show the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.327-345
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• 2009

In this paper, we define generalized Fourier-Hermite functionals on a function space $C_{a,b}[0,\;T]$ to obtain a complete orthonormal set in $L_2(C_{a,b}[0,\;T])$ where $C_{a,b}[0,\;T]$ is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in $L_2(C_{a,b}[0,\;T])$ has a generalized Fourier-Wiener function space transform ${\cal{F}}_{\sqrt{2},i}(F)$ also belonging to $L_2(C_{a,b}[0,\;T])$.

• Journal of Internet of Things and Convergence
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• v.8 no.5
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• pp.127-132
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• 2022

As the IoT technology is more developed, it is more important for the accuracy of IoT data. Since the IoT data supports a different formats and protocols, it is often happened that the IoT system is failed or the incorrect data is generated with the unreliable IoT devices(sensor, actuator). Because the abnormality of IoT device or the user situation is not detected correctly, this problem makes the user to be unsatisfied with the IoT system. This study proposes the decision methodology of IoT data consistency whether the IoT data is generated in normal range or not by using the mathematical functions('gradient descent function' and 'linear regression function'). It may be concluded that the gradient function method is suitable for the IoT data which the 'increasing velocity' is related with the next generated pattern(eg. sensor devices), the linear regression function method is suitable for the IoT data which the 'the difference from linear regression function' is related with the next generated pattern in case the data has a linear pattern(eg. water meter, electric meter).