• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.6
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• pp.1401-1411
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• 2016

The Multi-Prime RSA and the Prime Power RSA are the variants of the RSA cryptosystem, where the Multi-Prime RSA uses the modulus $N=p_1p_2{\cdots}p_r$ for distinct primes $p_1,p_2,{\cdots},p_r$ (r>2) and the Prime Power RSA uses the modulus $N=p^rq$ for two distinct primes p, q and a positive integer r(>1). This paper analyzes the security of these systems by using the technique given by Heninger and Shacham. More specifically, this paper shows that if the $2-2^{1/r}$ random portion of bits of $p_1,p_2,{\cdots},p_r$ is given, then $N=p_1p_2{\cdots}p_r$ can be factorized in the expected polynomial time and if the $2-{\sqrt{2}}$ random fraction of bits of p, q is given, then $N=p^rq$ can be factorized in the expected polynomial time. The analysis is then validated with experimental results for $N=p_1p_2p_3$, $N=p^2q$ and $N=p^3q$.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.145-157
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• 2020

In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-15
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• 2017

Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.745-756
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• 2019

In this paper, we establish the log convexity and Turán type inequalities of extended (p, q)-beta functions. Likewise, we present the log-convexity, the monotonicity and Turán type inequalities for extended (p, q)-confluent hypergeometric function by utilizing the inequalities of extended (p, q)-beta functions.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.601-609
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• 2020

In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.297-305
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• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.789-797
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• 2017

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and its associated alternating version whose terms contain a (p, q)-extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.561-582
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• 2018

In this paper the growth properties of the composition of integer translated entire and meromorphic functions in terms of their (p, q)-th order are discussed and based upon that some new results are developed.

• 한국해양학회지
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• v.26 no.1
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• pp.59-66
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• 1991

Laboratory studies were carried out to measure the sound velocity (V/SUB p/) and quality factor (Q/SUB p/, inverse attenuation) in the horizontal (H) and vertical (V) direction on the core sampled sediment of deep-sea basin (1,850 meter water depth), East Sea of Korea (Sea of Japan). Sampled core was about 250 cm long and 500 kHz ultrasonic p-wave transducer was used for a sound soured. V/SUB p/ varies from 1,480 m/sec to 1,500 m/sec, it is not clear which direction is faster, V/SUB PH/ or V/SUB pv/, within${\pm}$ 1.0% anisotropy (A/SUB p/). It is thought because the core sediment facies is highly (or slightly) bioturbated homogeneous mud with very high porosity (more than 80%). The general trend of Q/SUB p/ is decreasing 10 to 5 with the buried depth, it is strongly affected by the variation of sediment texture (increasing silt, decreasing clay) with increasing of CaCO$_3$ and organic matter content, But Q/SUB PH/ is jumping up to 14.9 near the bottom of core sediment as including volcanic ash richly. The relationship between V/SUB PH/ and Q/SUB PH/ shows the mirror image nearly, it is interpreted that not only the geotechnical properties and texture but also sea-water characteristics (high Q/SUB p/, low V/SUB p/) according to rich water content affect strongly in the upper part of the unconsolidated deep-sea basin sediment.