• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.985-995
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• 2024

We see fundamental properties of the log-determinant α-divergence including the convexity of weighted geometric mean and the reversed sub-additivity under tensor product. We introduce a symmetrized divergence and show its properties including the boundedness and monotonicity on parameters. Finally, we discuss the barycenter minimizing the weighted sum of symmetrized divergences.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.83-98
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• 2014

During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.27 no.1
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• pp.103-108
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• 2023

We study the problem of selecting a subset of sensor nodes in sensor networks in order to maximize the performance of parameter estimation. To achieve a low-complexity sensor selection algorithm, we propose a greedy iterative algorithm that allows us to select one sensor node at a time so as to maximize the log-determinant of the inverse of the estimation error covariance matrix without resort to direct minimization of the estimation error. We apply QR factorization to the observation matrix in the log-determinant to derive an analytic selection rule which enables a fast selection of the next node at each iteration. We conduct the extensive experiments to show that the proposed algorithm offers a competitive performance in terms of estimation performance and complexity as compared with previous sensor selection techniques and provides a practical solution to the selection problem for various network applications.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.5
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• pp.649-655
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• 2022

In this paper, a determinant-based two-channel noise reduction method which utilizes speech presence probability (SPP) is proposed. The proposed method improves noise reduction performance from the conventional determinant-based two-channel noise reduction method in [7] by applying SPP to the Wiener filter gain. Consequently, the proposed method adaptively controls the amount of noise reduction depending on the SPP. For performance evaluation, the segmental signal-to-noise ratio (SNR), the perceptual evaluation of speech quality, the short time objective intelligibility, and the log spectral distance were measured in the simulated noisy environments considered various types of noise, reverberation, SNR, and the direction and number of noise sources. The experimental results presented that determinant-based methods outperform phase difference-based methods in most cases. In particular, the proposed method achieved the best noise reduction performance maintaining minimum speech distortion.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.159-166
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• 1999

For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.

• Journal of Integrative Natural Science
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• v.13 no.2
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• pp.69-75
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• 2020

Multiple Input Multiple Output (MIMO) is one of the important wireless communication technologies. This paper proposes MIMO system capacity enhancement by using convolution of periodic circulating vector signals. This signal represents statistical dependencies between transmission signal with discrete noise and receiver signal with the linear shifting of MIMO channel capacity by positive extents. We examine the channel capacity, outage probability and SNR of MIMO receiver by adding log determinant signal with validated in terms of numerical simulation.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.21-44
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• 2017

Accelerated life tests (ALTs) are frequently used in manufacturing industries to evaluate the reliability of products within a reasonable amount of time and cost. Test units are subjected to elevated stresses which yield quick failures. Most of the previous works on designing ALT plans are focused on tests that involve a single stress. Many times more than one stress factor influence the product's functioning. This paper deals with the design of optimum modified ramp-stress ALT plan for Burr type XII distribution with Type-I censoring under two stress factors, viz., voltage and switching rate each at two levels- low and high. It is assumed that usage time to failure is power law function of switching rate, and voltage increases linearly with time according to modified ramp-stress scheme. The cumulative exposure model is used to incorporate the effect of changing stresses. The optimum plan is devised using D-optimality criterion wherein the ${\log}_{10}$ of the determinant of Fisher information matrix is maximized. The method developed has been explained using a numerical example and sensitivity carried out.

• Nutrition Research and Practice
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• v.5 no.2
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• pp.150-156
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• 2011

Few studies have shown the correlation between metabolic syndrome and bone mineral density (BMD). The main pathogenic mechanisms of metabolic syndrome rely on chronic low-level inflammatory status and oxidative stress. There are few studies that examine the gender-specific effects of inflammation and antioxidants on BMD. In this study, we evaluated the relative contribution of these factors in patients with metabolic syndrome. We conducted a cross-sectional study of 67 men and 46 postmenopausal women with metabolic syndrome; metabolic syndrome was defined as having three or more metabolic syndrome risk factors. BMD, body fat mass, and lean body mass were evaluated. We also examined the levels of high sensitive C-reactive protein (hs-CRP), interleukin-6 (IL-6), adiponectin, vitamin E, and C in serum. Log-transformed hs-CRP levels were significantly higher in lumbar spine osteoporotic subjects than in normal subjects for women but not for men. There was no significant difference between the normal group and the osteoporotic group in other inflammatory markers. Stepwise regression analyses for BMD of the lumbar spine showed that lean body mass and vitamin E were significant determinants in men. Lean body mass and log-transformed hs-CRP were significant determinants in women Analysis for BMD of the femoral neck showed that lean body mass was a significant determinant for both men and women. There was no significant factor among the inflammatory markers or antioxidant vitamins affecting the femoral neck BMD for either gender. In conclusion, while hs-CRP is an independent predictor of the BMD of the lumbar spine in women, vitamin E showed profound effects on BMD in men but not women with metabolic syndrome.

• KIEAE Journal
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• v.15 no.6
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• pp.63-68
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• 2015

Purpose: Most if buildings need various repair works for preventing or delaying the deterioration which gives rise to affect the living condition or function after constructed. Therefore, a long-term repair schedule should be planned and a repair cost is required. In this paper, it aimed at providing the statistical forecast model for a repair cost in roof water-proofing work and elevator work using statistical approach with three variables such as number of household, management area and a elapsed year. Data are collected in apartment housings which are located in Seoul area and conducted with interview and questionnaire sheet. Each analyzed work is divided into a partly work and fully work. Results of this study are shown that, first, the regression model takes a multiplying type like a Cobb-Douglas function and is changed into the log-linear type to include the three variable simultaneously. Second, the goodness-of-fit of the repair cost forecasting model has a good statistics in determinant's coefficient and Dubin-Watson value. Third, the management area is stronger factor than other the number of household and an elapsed year in roof water-proofing work and elevator work.