• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.355-369
• /
• 2020

In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.

• Proceedings of the KIEE Conference
• /
• 1987.07b
• /
• pp.854-858
• /
• 1987

This paper considers impulsive noise which produce burst error in high speed(approx.160Kbps) data transmission like ISDN(Integrated Servise Digital Network) using PSTN(Public Switching Telephone Network). To begin with, we obtains the transfer function of subscriber line to calculate the variation of bandwidth when the gain of receiver is fixed and channel capacity of non-gaussian channel in upper-and lower bound, and evaluates the transmission capability. In this paper compares channel capacity bounds which obtains when probability density function of impulsive noise is Laplacian distribution function with impulsive noise generated by waveform synthesier.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.990-993
• /
• 2005

This paper presents new results on designing a robust adaptive direct controller for a class of non-linear first order systems. The designing method based on the use of dead zone in the parameters' update law. It is shown that the size of the dead zone does not depend on the upper bounds of the disturbances. That means that even if the bounds are large, the tracking error will always converge to a set of the dead zone size. However, in the ideal case, when the exogenous signal functions and the function represents un-modeled dynamics of the systems equal to zero, the proposed controller does nt mean the convergence to zero of the tracking error. Computer simulation results show the effectiveness of the controller in dealing with the stated problems.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.5
• /
• pp.479-491
• /
• 2007

This paper presents a new adaptive observer design method for a class of uncertain nonlinear systems by using spline approximation. This scheme leads to a simplified observer structure which requires only fixed number of integrations, regardless of the number of parameters to be estimated. This benefit can reduce the number of integrations of the observer filter dramatically. Moreover, the proposed adaptive observer automatically generates the required spline elements according to the varying output value and, as a result, does not requires the pre-knowledge of upper and lower bounds of the output. This is another benefit of our approach since the requirement for known output bounds have been one of the main drawbacks of practical universal approximation problems. Both of the benefits stem from the local support property, which is specific to splines.

• Proceedings of the Korean Reliability Society Conference
• /
• 2002.06a
• /
• pp.289-296
• /
• 2002

The traditional methods of evaluating the performance of a network by enumerating all possible states may quickly become computationally prohibitive, since the number of states grows exponentially as the number of components increases. In such cases, enumerating only the most probable states would provide a good approximation. In this paper, we propose a method which efficiently generates upper and lower bounds for coherent performance measures utilizing the most probable states. Compared with Yang and Kubat's method, our procedure significantly reduces the complexity and memory requirement per iteration for computing the bounds and thereby, achieves the given degree of accuracy or the coverage within a shorter time.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.407-417
• /
• 2004

It is well known that the nonlinearity of vector Boolean functions F on n-dimensional vector space $GF(2)^n$ to $GF(2)^m$ is bounded above by $2^{n-1} - 2 ^{\frac{n}{2}-1}$. In this paper we derive upper bounds and a lower bound on the nonlinearity of vector Boolean functions in terms of auto-correlations. Strengths and weaknesses of each bounds are examined. Also, we modify the notions of the sum-of-square indicator and absolute indicator for Boolean functions to the case of vector Boolean functions to measure global avalanche characteristics of vector Boolean functions. Using those indicators we compare the global avalanche characteristics of DES (Data Encryption System) and Rijndael.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.1-17
• /
• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.362-365
• /
• 2008

In the conventional fuzzy system reliability analysis, the reliabilities of the fuzzy systems and the components of fuzzy systems are represented by real values between zero and one, fuzzy numbers, vague sets, interval valued fuzzy sets, etc. This paper propose a method to represent and analyze the reliabilities of the fuzzy systems based on the internal valued vague sets defined in the universe of discourse [0, 1]. In the interval valued vague sets, the upper bounds and the lower bounds of the conventional vague sets are represented as the intervals, therefore it can allow the reliabilities of a fuzzy system to represent and analyze in a more flexible manner.

• Journal of Communications and Networks
• /
• v.4 no.2
• /
• pp.102-107
• /
• 2002

The theoretical performance of MMSE linear microdiversity combining in Rayleigh fading, additive interference channels has already been derived exactly in the literature. In the macrodiversity case the fundamental difference is that any given source may well have different average received powers at the different antennas. This makes an exact analysis more difficult and hence for the macrodiversity case we derive a bound on the mean BER and a semi-analytic upper bound on outage probabilities. Hence we provide bounds on the performance of MMSE linear microdiversity combining in Rayleigh fading with additive noise and any number of interferers with arbitrary powers.

• International Journal of Reliability and Applications
• /
• v.3 no.3
• /
• pp.133-145
• /
• 2002

The traditional methods of evaluating the performance of a network by enumerating all possible states may quickly become computationally prohibitive, since the number of states grows exponentially as the number of components increases. In such cases, enumerating only the most probable states would provide a good approximation. In this paper, we propose a method which efficiently generates upper and lower bounds for coherent performance measures utilizing the most probable states. Compared with Yang and Kubat's method, our procedure significantly reduces the complexity and memory requirement per iteration for computing the bounds and thereby, achieves the given degree of accuracy or the coverage within a shorter time.