• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.1
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• pp.19-28
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• 2017

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.7
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• pp.622-628
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• 2011

The purpose of this study was to analyze the vibro-acoustic characteristics of a stiffened rectangular plate at high frequencies. The stiffeners attached along the plate surface were assumed to have rotational and translational stiffness and inertia. The harmonic response of the stiffened plate were predicted and compared using the Rayleigh-Ritz method with two different trial functions - polynomial and beam functions. The variation of the spatially averaged mean square velocity and the modal characteristics with the number of stiffeners were obtained. The use of the beam function ensured fast convergence which was essential for analyzing the high frequency vibration responses. Using the calculated modal characteristics and the Rayleigh-integral, the radiated sound power was predicted, and the effects of stiffeners were investigated. The proposed model can be applied to study optimal layout of stiffeners for minimal noise generation of the stiffened structures.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.2
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• pp.105-111
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• 2005

Though GF(2) CA can only handle data with bit units GF(2p) CA can handle data with units more than bit units. In this paper we analyze the state-transition of nongroup cellular automata(CA) with a single attractor over GF(2p). And we propose the constructing method the state-transition diagram of a linear SACA over GF(2p) by using the concept of basic path. Also we propose the state-transition diagram of the nonlinear complemented SACA by using the state-transition diagram of a linear SACA.

• Journal of Korean Society for Quality Management
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• v.48 no.2
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• pp.269-282
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• 2020

Purpose: The practical design for experiments with mixtures of q components is consisted in the four types of design points, vertex, center of edge, axial, and center points in a (q-1)-dimensional simplex space. We propose a sequential method for the successful construction of the design space in Quality by Design (QbD) by allowing the different number of replicates at the four types of design points in the practical design when the quadratic canonical polynomial model is assumed. Methods: To compare the mixture designs efficiency, fraction of design space (FDS) plot is used. We search for the practical mixture designs whose the minimal half-width of the tolerance interval per a standard deviation, which is denoted as d₂, is less than 4.5 at 0.8 fraction of the design space. They are found by adding the different number of replicates at the four types of the design points in the practical design. Results: The practical efficient mixture designs for the number of components between three and five are listed. The sequential method to establish a design space is illustrated with the two examples based on the simulated data. Conclusion: The designs with the center of edge points replications are more efficient than those with the vertex points replication. We propose the sample size of at least 23 for three components, 28 for four components, and 33 for the five components based on the list of efficient mixture designs.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.643-702
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• 2021

Fix ℤ/2 is the prime field of two elements and write 𝒜₂ for the mod 2 Steenrod algebra. Denote by GL_d := GL(d, ℤ/2) the general linear group of rank d over ℤ/2 and by ${\mathfrak{P}}_d$ the polynomial algebra ℤ/2[x₁, x₂, …, x_d] as a connected unstable 𝒜₂-module on d generators of degree one. We study the Peterson "hit problem" of finding the minimal set of 𝒜₂-generators for ${\mathfrak{P}}_d$. Equivalently, we need to determine a basis for the ℤ/2-vector space $$Q{\mathfrak{P}}_d:={\mathbb{Z}}/2{\otimes}_{\mathcal{A}_2}\;{\mathfrak{P}}_d{\sim_=}{\mathfrak{P}}_d/{\mathcal{A}}^+_2{\mathfrak{P}}_d$$ in each degree n ≥ 1. Note that this space is a representation of GL_d over ℤ/2. The problem for d = 5 is not yet completely solved, and unknown in general. In this work, we give an explicit solution to the hit problem of five variables in the generic degree n = r(2^t - 1) + 2^ts with r = d = 5, s = 8 and t an arbitrary non-negative integer. An application of this study to the cases t = 0 and t = 1 shows that the Singer algebraic transfer of rank 5 is an isomorphism in the bidegrees (5, 5 + (13.2⁰ - 5)) and (5, 5 + (13.2¹ - 5)). Moreover, the result when t ≥ 2 was also discussed. Here, the Singer transfer of rank d is a ℤ/2-algebra homomorphism from GL_d-coinvariants of certain subspaces of $Q{\mathfrak{P}}_d$ to the cohomology groups of the Steenrod algebra, $Ext^{d,d+*}_{\mathcal{A}_2}$ (ℤ/2, ℤ/2). It is one of the useful tools for studying these mysterious Ext groups.

• Progress in Medical Physics
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• v.11 no.2
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• pp.109-116
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• 2000

One consideration of radiation delivery in cervical cancer is the complication of critical organs, e.g., bladder and rectum. The absorbed dose of bladder and rectum in HDR intracavitary brachytherapy is measured indirectly with TLD dosimetry A method for the complication reduction of bladder and rectum is suggested. For two-hundred cervical cancer patients, follow-up MRI images were reviewed and distances from cervical central axis to bladder and rectum and vaginal wall thickness were measured. The sealed TLDs were placed upon the gauze packing of the ovoids and the distances to the TLDs from the ovoid center were measured in the simulation film and actual doses of bladder and rectum were calculated. From published data, maximal tolerance doses of bladder and rectum were derived and based on the permissible doses per fraction in HDR brachytherapy the packing thicknesses were determined in both directions. The required minimal packing thicknesses for bladder and rectum were 0.43 and 0.92 cm, respectively. The results were compared with computer calculation using the Meisberger polynomial approach. It is our hope this study can be used for a guideline for users in clinic in estimating critical organ dose in bladder and rectum in HDR brachytherapy in vivo dosimetry.