• 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 Nutrition and Health
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• v.24 no.4
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• pp.299-307
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• 1991

The present study was designed to evaluate the effects of dietary coenzyme $Q_{10}$ on mitochondrial coenzyme $Q_{10}$ and fatty acid composition in adriamycin (ADR)-treated rats. Two experiments were conducted in rats. Experiment 1 was undertaken under the condition of simultaneous administration of ADR and coenzyme $Q_{10}$ for 4 weeks. Experiment 2 was undertaken under the same condition as experiment 1 after feeding the experimental diets alone without administration of ADR for 4 weeks. Heart mitochondrial coenzyme $Q_{10}$ level of rats was greatly decreased by ADR treatment. but higher level of dietary coenzyme $Q_{10}$ elevated this decrease to control ranges. Pretreatment with dietary supplementation of coenzyme $Q_{10}$ showed a significant increase in myocardial coenzyme $Q_{10}$ level. With ADR treatment. polyunsaturated fatty acids such as arachidonic acid (20 : 4) and docosahexaenoic acid (22 : 6) were decreased. However, dietary supplementation of coenzyme $Q_{10}$ modified this decrement to some extent. In both experiment 1 and 2. the polyunsaturated fatty acids/saturated and polyunsaturated fatty acids (P/S+ M) ratio of ADR-treated rats tended to be lower than that of control rats.

• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.1-10
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• 2007

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.29-38
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• 2016

For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

• Korean Journal of Breeding Science
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• v.41 no.3
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• pp.236-243
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• 2009

This study was conducted to develop a japonica-type rice cultivar with brown planthopper (BPH) resistance using DNA markers. A doubled haploid (DH) population consisting of 120 pure-lines was established by anther culture of $F_1$ hybrids between 'Samgang', a Tongil type BPH resistance cultivar, and 'Nagdong', a japonica cultivar. To determine the map position of genes responsible for BPH resistance in rice, a genetic map was constructed based on 120 DH lines. A total of 162 molecular markers were classified into 12 linkage groups, covering 1,884 Kosami centimorgan (cM) with an average of 11.6 cM. Five QTLs (qBPR3, qBPR6, qBPR7, qBPR8, and qBPR12) associated with BPH resistance were identified and mapped on chromosomes 3, 6, 7, 8, and 12, respectively, using the genetic map constructed in this study. To analyze the relationship between BPH resistance and agronomic traits, a total of eight QTLs related to the agronomic traits were detected on 12 rice chromosomes. In an analysis of relationships, three QTLs (qBPR3, qBPR7, and qBPR8) showed a linkage with tested agronomic traits. A QTL (qBPR3) located on chromosome 3 (RM282-3023) was closely linked to culm length (qCL3). The QTL (qBPR8) for BPH resistance on the short arm of chromosome 8 also overlapped the region detected in culm length (qCL8).

• 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).

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.6
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• pp.2519-2522
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• 2012

Objective: Data from a recent genome-wide association studiesy of gastric cancer (GC) and oesophageal squamous cell carcinoma in Chinese living in the Taihang Mountains of north-central China suggest that 1q22 and 10q23 are susceptibility-associated regions for GC. However, this has not been confirmed in southern Chinese populations. The aim of this study was to investigate whether these polymorphisms at 1q22 and 10q23 are associated with the risk of GC in a southern Chinese population. Methods: We selected seven top significant associated single nucleotide polymorphisms (SNPs) at 1q22 and 10q23 and conducted a population-based case-control study in a southern Chinese population. Genotypes were determined using MassARRAYTM system (Sequenome, San Diego, CA). Results: Two SNPs at 1q22, rs4072037 and rs4460629, were significantly associated with a reduced risk of GC, best fitting the dominant genetic model. Logistic regression models adjusted for age and sex showed that rs4072037 AG and GG (OR=0.64, P=0.017, compared with AA) and rs4460629 CT and TT (OR=0.54, P=0.0016, compared with TT) significantly reduced the risk of GC. However, no significant results for the five SNPs at 10q23 were obtained in this study. Conclusion: These outcomes indicate that 1q22 is associated with GC susceptibility in this southern Chinese population, while an association for the locus at 10q23 was not confirmed.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.18
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• pp.8247-8252
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• 2016

Background: The ubiquitin-proteasome system (UPS) degrades a variety of proteins which attach to specific signals. The ubiquitination pathway facilitates degradation of damaged proteins and regulates growth and stress responses. This pathway is altered in various cancers, including acute lymphoblastic leukemia, head and neck squamous cell carcinoma and breast cancer. Recently it has been reported that expression of newly characterized human genes, UBE2Q1 and UBE2Q2, putative members of ubiquitin-conjugating enzyme family (E2), has been also changed in colorectal cancer. Epigenetics is one of the fastest-growing areas of science and nowadays has become a central issue in biological studies of diseases. According to the lack of information about the role of epigenetic changes on gene expression profiling of UBE2Q1 and UBE2Q2, and the presence of CpG islands in the promoter of these two human genes, we decided to evaluate the promoter methylation status of these genes as a first step. Materials and Methods: The promoter methylation status of UBE2Q1 and UBE2Q2 was studied by methylation-specific PCR (MSP) in tumor samples of 60 colorectal cancer patients compared to adjacent normal tissues and 20 non-malignant controls. The frequency of the methylation for each gene was analyzed by chi-square method. Results: MSP results revealed that UBE2Q2 gene promoter were more unmethylated, while a higher level of methylated allele was observed for UBE2Q1 in tumor tissues compared to the adjacent normal tissues and the non malignant controls. Conclusions: UBE2Q1 and UBE2Q2 genes show different methylation profiles in CRC cases.

• 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.