• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let 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 < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• 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 $\mathcal{A}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1513-1521
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• 2013

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_q[u]/(u^i)$, $\mathbb{F}_q[u_1,{\ldots},u_i]/(u^2_1,u^2_2,{\ldots},u^2_i,u_1u_2-u_2u_1,{\ldots},u_ku_j-u_ju_k,{\ldots})$, and $\mathbb{F}_q[u,v]/(u^i,v^j,uv-vu)$, where $\mathbb{F}_q$ is a field with $q$ elements $q=p^r$ for some prime number $p$ and $r{\in}\mathbb{N}-\{0\}$.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.467-485
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• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• East Asian mathematical journal
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• v.31 no.1
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• pp.1-18
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• 2015

In this paper we characterize different classes of hemirings by the properties of their (${\in},{\in}{\vee}q$)-fuzzy ideals, (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and (${\in},{\in}{\vee}q$)-fuzzy bi-ideals.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.121-130
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• 2017

This study is concerned with the existence of positive solution for the following nonlinear elliptic system $$\{-M_1(\int_{\Omega}{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^pdx)div({\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)\\{\hfill{120}}={\mid}x{\mid}^{-(a+1)p+c_1}\({\alpha}_1A_1(x)f(v)+{\beta}_1B_1(x)h(u)\),\;x{\in}{\Omega},\\-M_2(\int_{\Omega}{\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^qdx)div({\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^{q-2}{\nabla}v)\\{\hfill{120}}={\mid}x{\mid}^{-(b+1)q+c_2}\({\alpha}_2A_2(x)g(u)+{\beta}_2B_2(x)k(v)\),\;x{\in}{\Omega},\\{u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}$ is a bounded smooth domain of ${\mathbb{R}}^N$ with $0{\in}{\Omega}$, 1 < p, q < N, $0{\leq}a$ < $\frac{N-p}{p}$, $0{\leq}b$ < $\frac{N-q}{q}$ and ${\alpha}_i,{\beta}_i,c_i$ are positive parameters. Here $M_i,A_i,B_i,f,g,h,k$ are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.2
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• pp.18-26
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• 2015

In this paper, we studied the method for analyzing and estimating the parameters that induce I/Q imbalance in the repeater using direct conversion RF. In repeater, amplitude, phase, and filter mismatch are generated in the receiving-end which converts RF signal to baseband signal. And amplitude and phase mismatch are generated in the transmitting-end which converts baseband signal to RF signal. Accordingly, we modeled the parameters that cause I/Q imbalance in the structure of the repeater in order, and proposed a feedback test structure from the transmitting-end to the receiving-end for estimating the corresponding parameters. By comparing the test transmitting signal and received signal, it is possible to estimate the I/Q imbalance parameters which occurred from mixed components of real and imaginary part. And it was confirmed that I/Q imbalance phenomenon has been properly compensated with estimated parameters at the direct conversion RF repeater.