• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.9
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• pp.759-764
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• 2013

We present a square root algorithm in $F_q$ which generalizes Atkin's square root algorithm [9] for finite field $F_q$ of q elements where $q{\equiv}5$ (mod 8) and Kong et al.'s algorithm [11] for the case $q{\equiv}9$ (mod 16). Our algorithm precomputes ${\xi}$ a primitive $2^s$-th root of unity where s is the largest positive integer satisfying $2^s|q-1$, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, M$\ddot{u}$ller and Kong et al.

• East Asian mathematical journal
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• v.19 no.1
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• pp.133-150
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• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.

• Childhood Kidney Diseases
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• v.16 no.1
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• pp.46-50
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• 2012

C1q nephropathy is a distinct clinicopathologic entity, characterized by mesangial immunoglobulin and complement deposits, predominantly C1q, with no evidence for systemic lupus erythematosus. Clinically it may present as nephrotic syndrome and non-nephrotic proteinuria per se or associated with microscopic hematuria, gross hematuria, hypertension, or renal insufficiency. So far there is only one report about a familial case of C1q nephropathy (in two sisters). We present two cases of familial C1q nephropathy with nephrotic syndrome which was steroid resistant, but partially remitted with cyclosporine.

• Journal of the Korean Society of Marine Environment & Safety
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• v.28 no.4
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• pp.610-619
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• 2022

Hydrogen is emerging as an alternative fuel for eco-friendly ships because it reacts with oxygen to produce electrical energy and only water as a by-product. However, unlike regular fossil fuels, hydrogen has a material with a high risk of explosion due to its low ignition point and high flammability range. In order to safely use hydrogen in ships, it is an essential task to study the flow characteristics of hydrogen leakage and diffusion need to be studied. In this study, a numerical analysis was performed on the effect of leakage, ventilation, etc. on ventilation performance when hydrogen leaks in an enclosed space such as inside a ship. ANSYS CFX ver 18.1, a commercial CFD software, was used for numerical analysis. The leakage rate was changed to 1 q, 2 q, and 3 q at 1 q = 1 g/s, the ventilation rate was changed to 1 Q, 2 Q and 3 Q at 1 Q = 0.91 m/s, and the ventilation method was changed to type I, type II, type III to analyze the ventilation performance was analyzed. As the amount of leakage increased from 1 q to 3 q, the HMF in the storage room was about 2.4 to 3.0 times higher. Furthermore, the amount of ventilation to reduce the risk of explosion should be at least 2 Q, and it was established that type III was the most suitable method for the formation of negative pressure inside the hydrogen tank storage room.

• Journal of the Korean earth science society
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• v.24 no.8
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• pp.684-690
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• 2003

Recently Choongchung provinces in the central part of South Korea have received increasing attention because of the newly Planned administrative capital construction. In this area, a seismic network of Korea National University of Education has been installed since September 1996, and analyzed Q$_P^{-1}$ and Q$_S^{-1}$ by the extended Coda normalization method based on 60 events recorded by 2 stations of the network. To compensate for insufficient data, we combined the data from 33 events observed at 1 of the stations of the network of Korea Institute of Geology, Mining & Materials. Estimated Q$_P^{-1}$ and Q$_S^{-1}$ showed frequency dependence that decrease from (1.9${\pm}$3.0)${\times}$10$^{-3}$ and (2.4${\pm}$1.4)${\times}$10$^{-3}$ at 3.0 Hz to (5.4${\pm}$1.5)${\times}$10$^{-4}$ and (6.3${\pm}$1.1)${\times}$10$^{-4}$ at 24 Hz, respectively. Using a power law dependent on frequency, the best fit of Q$_P^{-1}$ and Q$_S^{-1}$ are 0.003f$^{-0.62}$ and 0.006f$^{-0.71}$ respectively. These values correspond to those of seismically stable regions, and are slightly less dependent on frequency than those of the southeastern part of Korea due to high Q$^{-1}$ values in high frequencies. Further observations are required in the central part of S. Korea to evaluate the difference of Q$^{-1}$ between central and southeastern parts of S. Korea.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.115-120
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• 2018

In this paper, we discover symmetric properties for generalized Carlitz's q-tangent polynomials.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.235-250
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• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.349-358
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• 2017

The cyclic group $C_n={\langle}(12{\cdots}n){\rangle}$ acts on the set $(^{[n]}_k)$ of all k-subsets of [n]. In this action of $C_n$ the number of orbits of size d, for d | n, is $$O^{n,k}_d={\frac{1}{d}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})(^{n/s}_{k/s})$$. Stanton and White [6] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)={\frac{1}{[d]_{q^{n/d}}}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})[^{n/s}_{k/s}]_{q^s}$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a constructive proof for the positivity of coefficients of the orbit polynomial $O^{n,2}_d(q)$.

• Journal of the Korean Geophysical Society
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• v.9 no.3
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• pp.199-207
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• 2006

Fukuoka earthquake on March 20, 2005 showed the potential hazard of large events out of S. Korea. From the viewpoint of seismic hazard, seismic amplitude decrease Q-1 is very important. Related to the crustal cracks induced by the earthquakes, the value of Q-1- high Q-1 regions are more attenuating than low Q-1 regions - shows a correlation with seismic activity; relatively higher values of Q-1 have been observed in seismically active areas than in stable areas. For the southeastern and central S. Korea, we first simultaneously estimated QP-1 and QS-1 by applying the extended coda-normalization method to KIGAM and KNUE network data. Estimated QP-1 and QS-1 values are 0.009 f-1.05 and 0.004 f-0.70 for southeastern S. Korea and 0.003 f -0.54 and 0.003 f -0.42 for central S. Korea, respectively. These values agree with those of seismically inactive regions such as shield. The low QLg-1 value, 0.0018f -0.54 was also obtained by the coda normalization method. In addition, we studied QLg-1 by applying the source pair/receiver pair (SPRP) method to both domestic and far-regional events. The obtained QLg-1 for all Fc is less than 0.002, which is reasonable value for a seismically inactive region.