• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.26 no.3
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• pp.245-253
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• 2000

The development and progression of oral cancer is associated with an accumulation of multiple genetic alterations through the multistep processes. Comparative genomic hybridization(CGH), newly developed cytogenetic and molecular biologic technique, has been widely accepted as a useful method to allow the detection of genetic imbalance in solid tumors and the screening for chromosome sites frequently affected by gains or losses in DNA copy number. The authors examined 19 primary oral squamous cell carcinomas using CGH to identify altered chromosome regions that might contain novel oncogenes and tumor suppressor genes. Interrelationship between these genetic aberrations detected and major oncogenes and tumor suppressor genes previously recognized in carcinogenesis of oral cancers was studied. 1. Changes in DNA copy number were detected in 14 of 19 oral cancers (78.9%, mean: 5.58, range: $3{\sim}13$). High level amplification was present in 4 cases at 9p23, $12p21.1{\sim}q13.1$, 3q and $8q24{\sim}24.3$. Fourteen cases(78.9%, mean: 3.00, range: $1{\sim}8$) showed gains of DNA copy number and 12 cases(70.5%, mean: 2.58, range: $1{\sim}9$) revealed losses of DNA copy number. 2. The most common gains were detected on 3q(52.6%), 5p(21.0%), 8q(21.0%), 9p(21.0%), and 11q(21.0%). The losses of DNA copy number were frequently occurred at 9p(36.8%), 17q(36.8%), 13q(26.3%), 4p(21.0%) and 9p(21.0%). 3. The minimal common regions of gains were repeatedly observed at $3q24{\sim}26.7$, $3q27{\sim}29$, $1q22{\sim}31$, $5p12{\sim}13.3$, $8q23{\sim}24$, and 11q13.1-13.3. The minimal common regions of losses were detected at $9q11{\sim}21.3$, 17p31, $13q22{\sim}34$, and 14p16. 4. In comparison of CGH results with tumor stages, the lower stage group showed more frequent gain at 3q, 5q, 9p, and 14q, whereas gains at 1q($1q22{\sim}31$) and 11q($11q13.1{\sim}13.3$) were mainly detected in higher stage group. The loss at $13q22{\sim}34$ was exclusively detected in higher stage. The results indicate that the most frequent genetic alterations in the development of oral cancers were gains at $3q24{\sim}26.3$, $1q22{\sim}31$, and $5p12{\sim}13.3$ and losses at $9q11{\sim}21.3$, 17p31, and 13q. It is suggested that genetic alterations manifested as gains at $3q24{\sim}26.3$, $3q27{\sim}29$, $5p12{\sim}13.3$ and 5p are associated with the early progression of oral cancer. Gains at $1q22{\sim}31$ and $11q13.1{\sim}13.3$ and loss at 13q22-34 could be involved in the late progression of oral cancers.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.97-103
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• 2019

In this paper, we give some interesting symmetric identities of the (p, q)-Hurwitz zeta function. We also give some new interesting properties, explicit formulas, a connection with (p, q)-Bernoulli numbers and polynomials.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.107-118
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• 1995

We study the asymptotic behavior of nonnegative singular solutions of semilinear parabolic equations of the type $$u_t={\Delta}u-(u^q)_y-u^p$$ defined in the whole space $x=(x,y){\in}R^{N-1}{\times}R$ for t>0, with initial data a Dirac mass, ${\delta}(x)$. The exponents q, p satisfy $$1 where $q^*=max\{q,(N+1)/N\}$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.1
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• pp.58-63
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• 2022

The daily number of confirmed cases of Coronavirus disease 2019(COVID-19) ranges between 1,000 and 2,000. Despite higher vaccination rates, the number of confirmed cases continues to increase. The Mu variant of COVID-19 reported in some countries by WHO has been identified in Korea. In this study, we predicted the number of confirmed COVID-19 cases in Korea using the SARIMA for the Covid-19 prevention strategy. Trends and seasonality were observed in the data, and the ADF Test and KPSS Test was used accordingly. Order determination of the SARIMA(p,d,q)(P, D, Q, S) model helped in extracting the values of p, d, q, P, D, and Q parameters. After deducing the p and q parameters using ACF and PACF, the data were transformed and schematized into stationary forms through difference, log transformation, and seasonality removal. If seasonality appears, first determine S, then SARIMA P, D, Q, and finally determine ARIMA p, d, q using ACF and PACF for the order excluding seasonality.

• Fisheries and Aquatic Sciences
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• v.11 no.4
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• pp.219-223
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• 2008

To increase the level of $CoQ_{10}$ production in mass culture, the effects of pH and light irradiation on $CoQ_{10}$ production by Rhodobacter sphaeroides were investigated in a 1-L bioreactor. $CoQ_{10}$ production was growth-associated, and the highest production of $CoQ_{10}$ (1.69 mg/g dry cell) was obtained under uncontrolled pH: this production was 1.7 times higher than that obtained at controlled pH 7. Therefore, pH was a key factor affecting $CoQ_{10}$ production. The effect of light irradiation on $CoQ_{10}$ production was negligible. This result offers an advantage for mass production of $CoQ_{10}$.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.35-41
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• 1995

We consider the linear differential equations y〃'＋ P($\chi$)y'＋Q($\chi$)y=0 (1)(y"＋P($\chi$)y)'-Q($\chi$)y =0 (2) Where (2) in the adjoint of (1) and P($\chi$), Q($\chi$) are continuous functions satisfying P($\chi$)$\geq$0, Q($\chi$)$\leq$0, P($\chi$)-Q($\chi$)$\geq$0 on [a, ${\alpha}$). (3) In this, we show that a condition a oscillatory of(1).(omitted)

• Honam Mathematical Journal
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• v.39 no.1
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• 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.