• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.31A no.8
• /
• pp.1-6
• /
• 1994

In this paper, we introduce the nonlinear combiner structure which improves linear complexity and randomness properties on maximum length sequences generated by LFSR. Choosing the primitive polynomial over GF(2S04T) as feedback tap polynomial, we devise nonlinear combiner structure and analyze the random output sequences generated by LFSR with nonlinear function.

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.377-393
• /
• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.11 no.3
• /
• pp.165-172
• /
• 1999

A probability density function of reliability function is derived in this paper, by which the stability of armor units on the rubble-mound breakwater can be studied on the probabilistic approach. To obtain the distribution, each random variable of the reliability function is assumed to follow Gaussian distribution. The distribution function of reliability function is in agreement with the histogram simulated by the Monte-Carlo method. In addition, the failure probability of armor units on the rubble-mound breakwater evaluated by the derived probability density function is shown to have the same order of magnitude as those calculated by FMA and AFDA of moment method. In particular, it is important to note that random variables of the reliability function may be considered to be statistically independent in the reliability analysis of armor units on the rubble-mound breakwater. Therefore, the present approach may be straightforwardly applicable to all of the cases that any random variables in the reliability function are controlled by other distribution functions as well as normal distribution.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.1
• /
• pp.9-16
• /
• 2005

The random signals defined as sums of the single frequency sinusoidal signals with random amplitudes and random phases or equivalently sums of functions obtained by adding a Sine and a Cosine function with random amplitudes, are used in the double randomization method for the Monte Carlo solution of the turbulent systems. We show that these random signals can be used for studying the properties of the Johnson noise by proving that constant multiples of these signals with uniformly distributed frequencies in a fixed frequency band satisfy the properties of the Gaussian white noise.

• Journal for History of Mathematics
• /
• v.32 no.3
• /
• pp.135-155
• /
• 2019

One of the reasons students have difficulty in studying probability is that they do not understand the meaning of mathematical terms precisely. One such term is a continuous random variable. Students tend not to think of the accurate definition of continuous random variables but to understand the definition of continuity of functions and the meaning of continuity in probability as equal. In this study, we try to explore the degree of pre-service teachers' understanding on the concept of continuation of functions and continuous random variables. To do this, the questionnaire items related to continuous random variables and continuity of functions were developed by experts and examined by pre-service teachers. Based on this, we make suggestions on implications for teaching and learning about continuous random variables.

• Structural Engineering and Mechanics
• /
• v.20 no.3
• /
• pp.293-312
• /
• 2005

In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on "Coefficient of Variation" (C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.12
• /
• pp.4567-4583
• /
• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.3C
• /
• pp.286-292
• /
• 2006

Both composition and XOR are operations widely used to enhance security of cryptographic schemes. The more number of random permutations we compose (resp. XOR), the more secure random permutation (resp. random function) we get. Combining the two methods, we consider a generalized form of random function: $SUM^s - CMP^c = ({\pi}_{sc} ... {\pi}_{(s-1)c+1}){\oplus}...{\oplus}({\pi}_c...{\pi}_1)$ where ${\pi}_1...{\pi}_{sc}$ are random permutations. Given a fixed number of random permutations, there seems to be a trade-off between composition and XOR for security of $SUM^s - CMP^c$. We analyze this trade-off based on some upper bound of insecurity of $SUM^s - CMP^c$, and investigate what the optimal number of each operation is, in order to lower the upper bound.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.17 no.6
• /
• pp.59-68
• /
• 2017

Random process plays a major role in wireless communication system to analytically derive the probability distribution function of the various statistical distribution. In this paper, we derive the decreasing function of the exponential distribution under the given condition which is expressed as wireless channel condition. The probability distribution function of Gaussian, Laplacian, Rayleigh and Nakagami distribution are also derived. Extensive simulation results of these statistical distributions are provided to prove that random process has a significant role in the wireless communications. In addition, the Rayleigh and Rician channels show specific examples of visible distance communication and invisible distance channel environment. This paper is motivated by that we assume a block fading channel model, where the channel is constant during a transmission block and changes independently between consecutive transmission block, can achieve a better performance in high SNR regime with i.i.d channel. This algorithm for realizing these transforms can be applied to the Kronecker MIMO channel.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.11 no.3
• /
• pp.1510-1532
• /
• 2017

In smart grid, privacy implications to individuals and their families are an important issue because of the fine-grained usage data collection. Wireless communications are utilized by many utility companies to obtain information. Network coding is exploited in smart grids, to enhance network performance in terms of throughput, delay, robustness, and energy consumption. However, random linear network coding introduces a new challenge for privacy preserving due to the encoding of data and updating of coefficients in forwarder nodes. We propose a distributed privacy preserving scheme for random linear network coding in smart grid that considers the converged flows character of the smart grid and exploits a homomorphic encryption function to decrease the complexities in the forwarder node. It offers a data confidentiality privacy preserving feature, which can efficiently thwart traffic analysis. The data of the packet is encrypted and the tag of the packet is encrypted by a homomorphic encryption function. The forwarder node random linearly codes the encrypted data and directly processes the cryptotext tags based on the homomorphism feature. Extensive security analysis and performance evaluations demonstrate the validity and efficiency of the proposed scheme.