• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.959-970
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• 2017

In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.255-263
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• 2009

For an endomorphism ${\alpha}$ of R, in [1], a module $M_R$ is called ${\alpha}$-compatible if, for any $m{\in}M$ and $a{\in}R$, ma = 0 iff $m{\alpha}(a)$ = 0, which are a generalization of ${\alpha}$-reduced modules. We study on the relationship between the quasi-Baerness and p.q.-Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [2] and some results in [9]. In particular, we show: for an ${\alpha}$-compatible module $M_R$ (1) $M_R$ is p.q.-Baer module iff $M[x;{\alpha}]_{R[x;{\alpha}]}$ is p.q.-Baer module. (2) for an automorphism ${\alpha}$ of R, $M_R$ is p.q.-Baer module iff $M[x,x^{-1};{\alpha}]_{R[x,x^{-1};{\alpha}]}$ is p.q.-Baer module.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.505-514
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• 2019

In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.365-372
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• 2013

The essential aim of this paper is to define weighted $q$-Hardylittlewood-type maximal operator by means of $p$-adic $q$-invariant distribution on $\mathbb{Z}_p$. Moreover, we give some interesting properties concerning this type maximal operator.

• East Asian mathematical journal
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• v.24 no.3
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• pp.263-274
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• 2008

Let $r\;{\geq}\;q$. We get the stability of the estimates of the $\bar{\partial}$-Neumann problem for (p, r)-forms on a weakly q-convex complex submanifold. As a by-product of the stability of the $\bar{\partial}$-estimates, we get the Mergelyan approximation property for (p, r)-forms on a weakly q-convex complex submanifold which satisfies property (P).

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Journal of the Korean earth science society
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• v.28 no.6
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• pp.720-732
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• 2007

For the Seoul metropolitan area and the eastern Kyeongsang Basin, we simultaneously calculated $Q_P^{-1}$ and $Q_S^{-1}$ by applying the extended coda-normalization method for 98 seismograms of local Earthquakes. As frequency increases from 1.5 Hz to 24 Hz, the result decreased from $(4.0{\pm}9.2){\times}10^{-3}$ to $(4.1{\pm}4.2){\times}10^{-4}$ for $Q_P^{-1}$ and $(5.5{\pm}5.6){\times}10^{-3}$ to $(3.4{\pm}1.3){\times}10^{-4}$ for $Q_S^{-1}$ in Seoul Metropolitan Area. The result of eastern Kyeongsang basin also decreased from $(5.4{\pm}8.8){\times}10^{-3}$ to $(3.7{\pm}3.4){\times}10^{-4}$ for $Q_P^{-1}$ and $(5.7{\pm}4.2){\times}10^{-3}$ to $(3.5{\pm}1.6){\times}10^{-4}$ for $Q_S^{-1}$. If we fit a frequency-dependent power law to the data, the best fits of $Q_P^{-1}$ and $Q_S^{-1}$ are $0.005f^{-0.89}$ and $0.004f^{-0.88}$ in Seoul metropolitan Area, respectively. The value of $Q_P^{-1}$ and $Q_S^{-1}$ in the eastern Kyeongsang basin are $0.007f^{-1.02}$ and $0.006f^{-0.99}$, respectively. The $Q_S^{-1}$ value of the eastern Kyeongsang basin is almost similar to Seoul metropolitan area. But the $Q_P^{-1}$ value of the eastern Kyeongsang basin is a little higher than that of Seoul metropolitan area. This may be that the crustal characteristics of the eastern Kyeongsang basin is seismologically more heterogeneous. However, these $Q_P^{-1}$ values in Korea belong to the range of seismically stable regions all over the world.

• Journal of the Korean earth science society
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• v.22 no.2
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• pp.112-119
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• 2001

The Yangsan fault in the southeastern Korea has been receiving increasing attention in its seismic activity. In this fault region, by using the extended coda-normalization method for 707 seismograms of local earthquakes, were obtained 0.009f$^{-1.05}$ and 0.004f$^{-0.70}$ for fitting values of Q$_p^{-1}$ and Q$_s^{-1}$, respectively. These results indicate that Q$_p^{-1}$ and Q$_s^{-1}$ in the southeastern Korea is the lowest level in the world although the exponent values agree well with those in the other areas. The low Q-1 is not related to the movement of the Yangsan fault but to the tectonically inactive status like a shield area.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.46 no.12
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• pp.1021-1027
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• 2018

Experimental studies have been conducted to verify that the positive coupling between pressure oscillation (p') and combustion oscillation (q') of high frequency range is a prerequisite for the initiation of low frequency instability in hybrid rocket combustion. The post-chamber length and combustion equivalence ratio were selected as critical parameters to control the phase difference between p' and q', and p' amplitude in relation to the suppression of LFI. In the results, even if the post-chamber length increases, the phase difference between p' and q' maintains below pi/2, which is a necessary condition for the LFI development, but the amplification of RI (Rayleigh index) was substantially decreased leading to a stable combustion. In addition, results confirmed that combustion stability is achieved by changing the momentary equivalence ratio and/or by suppressing the positive coupling status of p' and q'. Thus, the periodic amplification of RI was identified as the middle path of the mechanism of occurrence of LFI.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.977-991
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• 2008

We characterize the boundedness and compactness of the weighted composition operator $uC_{\psi}$ from the general function space F(p, q, s) into the logarithmic Bloch space ${\beta}_L$ on the unit disk. Some necessary and sufficient conditions are given for which $uC_{\psi}$ is a bounded or a compact operator from F(p,q,s), $F_0$(p,q,s) into ${\beta}_L$, ${\beta}_L^0$ respectively.