• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.151-157
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• 2003

The aim of this paper is to derive the well-known q-analog of kummer's theorem by using q-integral representation. In addition to this, two results closely related to the q-kummer's theorem have also been obtained by the same method.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1409-1418
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• 2023

The Hurwitz-type Euler zeta function ζ_E(z, q) is defined by the series ${\zeta}_E(z,\,q)\,=\,\sum\limits_{n=0}^{\infty}{\frac{(-1)^n}{(n\,+\,q)^z}},$ for Re(z) > 0 and q ≠ 0, -1, -2, . . . , and it can be analytic continued to the whole complex plane. An asymptotic expansion for ζ^'_E(-m, q) has been proved based on the calculation of Hermite's integral representation for ζ_E(z, q).

• Carbon letters
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• v.1 no.3_4
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• pp.148-153
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• 2001

The initial irreversible capacity, $Q_i$, is one of the parameters to express the material balancing of the cathode to anode. We introduced new terms, which are the initial intercalation Ah efficiency (IIE) and the initial irreversible specific capacity at the surface ($Q_{is}$), to express precisely the irreversibility of an electrode/electrolyte system. Two terms depended on kinds of active-materials and compositions of the electrode, but did not change with charging state. MPCF had the highest value of IIE and the lowest value of $Q_{is}$ in 1M $LiPE_6$/EC + DEC (1 : 1 volume ratio) electrolyte. IIE value of $LiCoO_2$ electrode was 97-98%, although the preparation condition of the material and the electrolyte were different. $Q_{is}$ value of $LiCoO_2$ was 0~1 mAh/g. MPCF-$LiCoO_2$ cell system had the lowest of the latent capacity. $Q_{is}$ value increased slightly by adding conductive material. IIE and $Q_{is}$ value varied with the electrolyte. By introducing PC to EC+DEC mixed solvent, IIE values were retained, but $Q_{is}$ increased. In case of addition of MP, IIE value increased and $Q_{is}$ value also increased a little.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.429-436
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• 2009

We define a projective representation $M_1{^{\rightarrow}_{\rightarrow}}M_2{\rightarrow}M_3$ of a quiver $Q={\bullet}{^{\rightarrow}_{\rightarrow}}{\bullet}{\rightarrow}{\bullet}$ and consider their properties. Then we show that any projective representation $M_1{^{\rightarrow}_{\rightarrow}}M_2{\rightarrow}M_3$ of a quiver $Q={\bullet}{^{\rightarrow}_{\rightarrow}}{\bullet}{\rightarrow}{\bullet}$ is isomorphic to the quotient of a direct sum of projective representations $0{^{\rightarrow}_{\rightarrow}}0{\rightarrow}P,\;0{^{\rightarrow}_{\rightarrow}}P{\rightarrow\limits^{id}}P$ and $P{^{\rightarrow}_{\rightarrow}}^{e1}_{e2}P{\oplus}P{\rightarrow\limits^{id_{P{\oplus}P}}}P{\oplus}P$, where $e_1(a)=(a,0)$ and $e_2(a)=(0,a)$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1563-1567
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• 2021

We show that if M is a Utumi module, in particular if M is quasi-continuous, then M = Q ⊕ K, where Q is quasi-injective that is both a square-full as well as a dual-square-full module, K is a square-free module, and Q & K are orthogonal. Dually, we also show that if M is a dual-Utumi module whose local summands are summands, in particular if M is quasi-discrete, then M = P ⊕ K where P is quasi-projective that is both a square-full as well as a dual-square-full module, K is a dual-square-free module, and P & K are factor-orthogonal.

• Journal of Communications and Networks
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• v.18 no.3
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• pp.273-287
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• 2016

White-box cryptography presented by Chow et al. is an obfuscation technique for protecting secret keys in software implementations even if an adversary has full access to the implementation of the encryption algorithm and full control over its execution platforms. Despite its practical importance, progress has not been substantial. In fact, it is repeated that as a proposal for a white-box implementation is reported, an attack of lower complexity is soon announced. This is mainly because most cryptanalytic methods target specific implementations, and there is no general attack tool for white-box cryptography. In this paper, we present an analytic toolbox on white-box implementations of the Chow et al.'s style using lookup tables. According to our toolbox, for a substitution-linear transformation cipher on n bits with S-boxes on m bits, the complexity for recovering the $$O\((3n/max(m_Q,m))2^{3max(m_Q,m)}+2min\{(n/m)L^{m+3}2^{2m},\;(n/m)L^32^{3m}+n{\log}L{\cdot}2^{L/2}\}\)$$, where $m_Q$ is the input size of nonlinear encodings,$m_A$ is the minimized block size of linear encodings, and $L=lcm(m_A,m_Q)$. As a result, a white-box implementation in the Chow et al.'s framework has complexity at most $O\(min\{(2^{2m}/m)n^{m+4},\;n{\log}n{\cdot}2^{n/2}\}\)$ which is much less than $2^n$. To overcome this, we introduce an idea that obfuscates two advanced encryption standard (AES)-128 ciphers at once with input/output encoding on 256 bits. To reduce storage, we use a sparse unsplit input encoding. As a result, our white-box AES implementation has up to 110-bit security against our toolbox, close to that of the original cipher. More generally, we may consider a white-box implementation of the t parallel encryption of AES to increase security.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.51-60
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• 1995

Let $(M,g_M,F)$ be a (p+q)-dimensional connected Riemannian manifold with a foliation $F$ of codimension q and a complete bundle-like metric $g_M$ with respect to $F$. Let $Ric_D$ be the transverse Ricci field of $F$ with respect to the transverse Riemannian connection D which is a torsion-free and $g_Q$-metrical connection on the normal bundle Q of $F$. We consider transverse confomal (or, projective) fields of $F$. It is clear that a tranverse Killing field s of $F$ preserves the transverse Ricci field of $F$, that is, $\Theta(s)Ric_D = 0$, where $\Theta(s)$ denotes the transverse Lie differentiation with respect to s.

• Journal of Korean Society of Forest Science
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• v.85 no.1
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• pp.76-83
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• 1996

Four natural Quercus stands in Kwangju, Kyonggi-Do, of which ages ranging from 32 to 38 years old, were studied to compare their growth, biomass and net production. Ten $10m{\times}10m$ quadrats were set up and ten sample trees were harvested for dimension analysis in each stand. The largest mean DBH and height were shown by Q. acutissima stand, and followed by Q. variabilis stand, Q. mongolica stand, and Q. dentata stand in descending order. Tree density was the highest at Q. variabilis stand, and followed by Q. dentata stand, Q. mongolica stand, and Q. acutissima stand in descending order. Biomass was the largest at Q. acutissima stand(122.73t/ha), and followed by Q. variabilis stand(87.03t/ha), Q. mongolica stand(72.14t/ha), and Q. dentata stand(38.56t/ha) in descending order. Net production was the greatest at Q. mongolica stand(7.49t/ha/yr.), and followed by Q. variabilis stand(6.47t/ha/yr.), Q. acutissima stand(6.06t/ha/yr.), and Q. dentata stand(3.52t/ha/yr.) in descending order. The highest net assimilation ratio was exhibited by Q. acutissima stand (3.275), and followed by Q. variabilis stand(2.898), Q. mongolica stand(2.888), and Q. dentata stand (1.840) in descending order. The difference in net assimilation ratio and net production among four stands was caused by differences in their leaf biomass. The difference in net production and biomass among four stands was due to that in the distribution of net production among stems, branches and leaves.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.913-926
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• 2011

The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1109-1126
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• 2013

Let $\mathbb{M}^3_q(c)$ denote the 3-dimensional space form of index $q=0,1$, and constant curvature $c{\neq}0$. A curve ${\alpha}$ immersed in $\mathbb{M}^3_q(c)$ is said to be a Bertrand curve if there exists another curve ${\beta}$ and a one-to-one correspondence between ${\alpha}$ and ${\beta}$ such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non-null Bertrand curves in $\mathbb{M}^3_q(c)$ correspond with curves for which there exist two constants ${\lambda}{\neq}0$ and ${\mu}$ such that ${\lambda}{\kappa}+{\mu}{\tau}=1$, where ${\kappa}$ and ${\tau}$ stand for the curvature and torsion of the curve. As a consequence, non-null helices in $\mathbb{M}^3_q(c)$ are the only twisted curves in $\mathbb{M}^3_q(c)$ having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.