• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.843-867
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• 2022

Maynard proved that there exists an effectively computable constant q1 such that if q ≥ q1, then $\frac{{\log}\;q}{\sqrt{q}{\phi}(q)}Li(x){\ll}{\pi}(x;\;q,\;m)<\frac{2}{{\phi}(q)}Li(x)$ for x ≥ q8. In this paper, we will show the following. Let 𝛿1 and 𝛿2 be positive constants with 0 < 𝛿1, 𝛿2 < 1 and 𝛿1 + 𝛿2 > 1. Assume that L ≠ ℚ is a number field. Then there exist effectively computable constants c0 and d1 such that for dL ≥ d1 and x ≥ exp (326n𝛿1L(log dL)1+𝛿2), we have $$\|{\pi}_C(x)-\frac{{\mid}C{\mid}}{{\mid}G{\mid}}Li(x)\|\;{\leq}\;\(1-c_0\frac{1og\;d_L}{d^{7.072}_L}\)\;\frac{{\mid}C{\mid}}{{\mid}G{\mid}}Li(x)$$.

• Journal of the Korean GEO-environmental Society
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• v.7 no.5
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• pp.13-20
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• 2006

We have conducted standard penetration tests and static cone penetration tests that are widely used the land base examination on the soft ground subsurface of Yongdong area, and examined the correlation between them. We have also made a comparative analysis of the correlation between the indoor tests on the materials collected on the site and on-the-spot penetration tests. The results are as follows : The relationship between Standard Penetration Test N-value and Dutch Cone Tset show $Q_c=1.93N+0.29$ for organic soil, $Q_c=2.19N+0.20$ for clay, $Q_c=2.34N+1.06$ for silt, $Q_c=3.02N+0.54$ for silty sand, and $Q_c=3.47N+0.46$ for sand. In this case of sand $Q_c/N$ increases when the soil particles are larger. The relationship between standard penetration test N-value and Unconfined Compression Strength $q_u$ show $q_u=0.11N+0.03$ for organic soil, $q_u=0.11N+0.25$ for clay, and $q_u=0.18N-0.03$ for silt.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.507-552
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• 2016

For a complex number q and a divisor function ${\sigma}_1(n)$ we define $$C(q):=q{\prod_{n=1}^{\infty}}(1-q^n)^{16}(1-q^{2n})^4,\\D(q):=q^2{\prod_{n=1}^{\infty}}(1-q^n)^8(1-q^{2n})^4(1-q^{4n})^8,\\L(q):=1-24{\sum_{n=1}^{\infty}}{\sigma}_1(n)q^n$$ moreover we obtain the number of representations of $n{\in}{\mathbb{N}}$ as sum of 24 squares, which are possible for us to deduce $L(q^4)C(q)$ and $L(q^4)D(q)$.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.69-77
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• 2017

If q(z) is a polynomial of degree n with all zeros in the unit circle, then the self-reciprocal polynomial $q(z)+x^nq(1/z)$ has all its zeros on the unit circle. One might naturally ask: where are the zeros of $q(z)+x^nq(1/z)$ located if q(z) has different zero distribution from the unit circle? In this paper, we study this question when $q(z)=(z-1)^{n-k}(z-1-c_1){\cdots}(z-1-c_k)+(z+1)^{n-k}(z+1+c_1){\cdots}(z+1+c_k)$, where $c_j$ > 0 for each j, and q(z) is a 'zeros dragged' polynomial from $(z-1)^n+(z+1)^n$ whose all zeros lie on the imaginary axis.

• Journal of Korean Society of Forest Science
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• v.78 no.2
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• pp.151-159
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• 1989

The present study has been designed to define the effects of photosynthetically active radiation, leaf temperature, and water stress on photosynthesis and respiration of leaves of four oak species (Quercus mongolica, Quercus aliens, Quercus variabilis, and Quercus serrate). The results obtained are as follows : 1. The estimated light compensation points at which Pn approached zero were 38, 24, 20, and $18{\mu}Em^{-2}s^{-1}$ for Q. aliens, Q. variabilis, Q, mongolica, and Q. serrate, respectively. The light saturation points occurred at $500{\mu}Em^{-2}s^{-1}$ in three oak species except Q, aliens. 2. The maximum rates of Pn were 19.7, 15.2, 11.2, and 11.0 mg $CO_2$ $dm^{-2}h^{-1}$ for Q. variabilis, Q. serrate, Q. monglica, and Q. aliens leaves, respectively. 3. The transpiration rates of Q. variabilis and Q. serrate leaves were slightly higher than those of Q. mongolica and Q. aliens leaves at various photosynthetically active radiations(PAR), but cuticular transpiration rates at dark were similar in four oak species. 4. The optimum photosynthesis occurred at $25^{\circ}C$ in Q. aliens, Q. variabilis, and Q. serrate leaves, but $20^{\circ}C$ in Q. mongolica leaves. In four oak species, the net photosynthesis approached zero at about $40^{\circ}C$. 5. The dark respiration rates of leaves exhibited the following ranking of species : Q, variabilis > Q. mongolica > Q. aliens > Q. serrate. 6. The maximum productive efficiency (Pg/Rd) of leaves occurred highest in Q, serrate at $20^{\circ}C$, then in Q. mongolica at $20^{\circ}C$, then in Q, aliens at $25^{\circ}C$, and finally in Q. variabilis at $15^{\circ}C$. 7. The decrease of net photosynthesis in Q. serrate began at about -1.2 MPa, and then approached zero at -2.9 MPa of leaf water potential. The decrease of net photosynthesis began at 3% of water loss, and then approached zero at 17.5% of water loss. 8. As indicated by tissue-water relations parameters, it may be suggested that Q. aliens and Q. variabilis are more tolerant and favored on xeric forest soils than Q. mongolica and Q. serrate.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.131-138
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• 2000

Let D be the open unit disk in the complex plane $\mathbb{C}$. For any q > 0, the operator $Q_q$ defined by $$Q_qf(z)=q\int_{D}\frac{f(\omega)}{(1-z{\bar{\omega}})^{1+q}}d{\omega},\;z{\in}D$$. maps $L^{\infty}(D)$ boundedly onto $B_q$ for each q > 0. In this paper, weighted Bloch spaces $\mathcal{B}_q$ (q > 0) are considered on the open unit ball in $\mathbb{C}^n$. In particular, we will investigate the possibility of extension of this operator to the Weighted Bloch spaces $\mathcal{B}_q$ in $\mathbb{C}^n$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.105-116
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• 2013

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, then every positive solution blows up in finite time, but for $q$ > $q_c$, there exist both global and non-global solutions to the problem.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.319-339
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• 2010

In this paper, we prove that if $f^nf'\;-\;P$ and $g^ng'\;-\;P$ share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.

• The Korean Journal of Ecology
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• v.22 no.5
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• pp.305-309
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• 1999

The occurrence of tetQ and aacC2 genes encoding tetracycline and gentamicin resistance determinant, respectively, was assessed in total bacterial community DNA isolated from Dongchon stream of Sunchon area. To examine the resistance potential of bacteria that were not cultured, total DNA from 1 liter of stream water was extracted by freeze-thaw method. The PCR technique was employed to determine the abundance of the target genes. The highest frequency of tetQ gene was obtained from site 1, located near the animal farms area, whereas the incidence of aacC2 was highest in site 5, the downstream area. These results showed that the occurrence of antibiotic resistance gene may be used as a convenient marker of water quality related to source.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.665-677
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• 2021

The main object of this study is to introduce the spaces $c_0({\hat{F}^q)$ and $c({\hat{F}^q)$ derived by the matrix ${\hat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the 𝛼-, 𝛽-, 𝛾- duals of these spaces and give the characterization of matrix classes (${\Lambda}({\hat{F}^q)$, Ω) and (Ω, ${\Lambda}({\hat{F}^q)$) for 𝚲 ∈ {c₀, c} and Ω ∈ {ℓ₁, c₀, c, ℓ_∞}.