• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• 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 $\mathcal{A}$.

• Korean Journal of Head & Neck Oncology
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• v.24 no.1
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• pp.33-42
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• 2008

Head and neck squamous cell carcinoma(HNSCC) is notorious for its poor outcome and increasing incidence. But, the studies of cytogenetic analysis in HNSCC are relatively rare, because of difficulties in culturing solid tumor cells and complexity in chromosomal DNA abberations associated with the lesions. The purpose of this study is to evaluate the location of chromosomal aberrations in Korean HNSCC cell lines (SNU-1041, 1066, and 1076) with comparative genomic hybridization(CGH) and array based CGH(array-CGH). Chromosomal gains of 3q23-q27, 5p13-p15.3, 7p21-pter, 8q11.2-q12, 8q21.1-qter, 9q22-q34, 16q22-q24, and 20q11.2-qter, as well as chromosomal losses on 3p10-p14 were found in all 3 SNU cell lines. Losses on 3p15- p23, 4q22-q27, 4q31.3-qter, 6q14-q15, 7q31-q34, 8p12-pter, 18q21-q23, and 21q11.2-q12 were observed in 2 of 3 cell lines. In array-CGH, many genes were altered including gains of PIK3CA, MYC, EVI1, MAD1L1 genes and losses of SERPIN genes. These aberrations of gene and chromosome coincide with other results of study, generally. These data about the patterns of chromosomal aberrations could be a basic step for understanding more detailed genetic events in the carcinogenesis and also provide information for diagosis and treatment in HNSCC.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.27-32
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• 1988

In this paper, we study the multipliers of $A^p_q$ into $L^{p^{\prime}}$ when 0 < p' < p. For this purpose, we study the condition on the measure ${\mu}$ satisfying $A^p_q{\subset}A^{p^{\prime}}(d{\mu})$. It turns out that the quotient $k_q={\mu}/v_q$ over hyperbolic ball of radius less than 1 belongs to $L^s_q$, where $\frac{1}{s}+\frac{p^{\prime}}{p}=1$. For the proof, we replace the norm of $k_q$ by the Riemann sum, and then use a result of interpolation theory.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.519-527
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• 2011

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

• The Korean Journal of Ecology
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• v.21 no.3
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• pp.283-290
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• 1998

The vegetation pattern of Mt. Odae based on the soil humidity gradient showed 3 types: (1) the forest of Pinus densiflora under the mesic or xeric conditions of the low altitudinal area, (2) the forest of Acer including A. mono, A. pseudo-sieboldianum and Tilia amurensis under the submesic or subxeric conditions and (3) the forest of Quercus including Q. mongolica of the higher elevational area and Q. variabilis of the lower elevational area under the xeric condition. Water content, organic matter and total nitrogen of soil were relatively low in Pinus densiflora and Quercus variabilis communities while they were relatively high in Betula platyphylla var. japonica and Quercus mongolica communities. According to the result of cluster analysis based on similarity indices of the communities, the proposed successional sere in the forest vegetation of Mt. Odae was as follows. P. densiflora community $\longrightarrow$ P. densiflore + Q. mongolica community $\longrightarrow$ Q. mongolica + A. pseudo-sieboldianum community. P. densiflora community $\longrightarrow$ P. densiflora + Q. variabilis community $\longrightarrow$ Q. variabilis community $\longrightarrow$ Q. mongolica + Q. variabilis community $\longrightarrow$ Q. mongolica + A. pseudo-sieboldianum community.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.11C
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• pp.874-879
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• 2008

In this paper, a new extending method of q-ary low correlation zone(LCZ) sequence sets is proposed, which is a generalization of binary LCZ sequence set by Kim, Jang, No, and Chung. Using this method, q-ary LCZ sequence set with parameters (N,M,L,${\epsilon}$) is extended as a q-ary LCZ sequence set with parameters (pN,pM,p[(L+1)/p]-1,p${\epsilon}$), where p is prime and p|q.

• 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 $T/Q_1$.