• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.915-923
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• 2015

Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with $q{\equiv}1$ (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with $q=p^r{\equiv}3$ (mod 4) with an odd prime p satisfying $p{\equiv}3$ (mod 4) with r odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual [16, 8, 7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24, 12, 9].

• 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.

• 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.

• Proceedings of the KIPE Conference
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• 1998.10a
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• pp.888-893
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• 1998

In practice, not only the load current but also the load voltage may contain asymmetric and harmonic components. Instantaneous power using p-q theory is analyzed to have compensation of reactive power, harmonics and asymmetry at the same time. In this paper, the limitation of p-q theory by using only shunt or series active filter is analyzed. A new scheme is proposed to solve the above issues.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.493-507
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• 2013

We construct a new family of simply connected minimal complex surfaces of general type with $p_g$ = 1, $q$ = 0, and $K^2$ = 3, 4, 5, 6, 8 using a $\mathbb{Q}$-Gorenstein smoothing theory.

• Proceedings of the KIEE Conference
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• 1998.11a
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• pp.131-133
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• 1998

This paper, proposed the p-q-r coordinate system where the instantaneous active power p, and the two instantaneous reactive powers $q_{q}$, $q_{r}$ were defined. The three power components are linearly independent, so the compensation for the two instantaneous reactive powers leads to control the two components of the current space vector. With the theory, the neutral current of the three-phase four-wire system can be eliminated by only compensating the instantaneous reactive power using no energy storage element.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.221-229
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• 1998

Let $k$ be a real abelian field and $k_{\infty}$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension. By using the main conjecture of Iwasawa theory, we have the following: If $p$ does not divide $\prod_{{{\chi}{\in}\hat{\Delta}_k},{\chi}{\neq}1}B_{1,{\chi}{\omega}^{-1}$, then $A_n$ = {0} for all $n{\geq}0$, where ${\Delta}_k=Gal(k/\mathbb{Q})$ and ${\omega}$ is the Teichm$\ddot{u}$ller character for $p$. The converse of this statement does not hold in general. However, we have the following when $k$ is of prime conductor $q$: Let $q$ be an odd prime different from $p$. and let $k$ be a real subfield of $\mathbb{Q}({\zeta}_q)$. If $p{\mid}{\prod}_{{\chi}{\in}\hat{\Delta}_{k,p},{\chi}{\neq}1}B_{1,{\chi}{\omega}}-1$, then $A_n{\neq}\{0\}$ for all $n{\geq}1$, where ${\Delta}_{k,p}$ is the $Gal(k_{(p)}/\mathbb{Q})$ and $k_{(p)}$ is the decomposition field of $k$ for $p$.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Journal of the Korean Chemical Society
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• v.53 no.6
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• pp.671-676
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• 2009

Described here for the first time is an investigation on geometrical and electronic molecular structure of metol (N-methyl-p-aminophenol sulphate) as corrosion inhibitor of steel using density functional theory (DFT) calculations. Quantum chemical parameters such as highest occupied molecular orbital energy (EHOMO), lowest unoccupied molecular orbital energy (ELUMO), energy gap ((${\Delta}E$), Mulliken charges (($q_M$) and natural atomic (($q_n$) charge have been calculated both for gas and aqueous phases by using B3LYP/6-31G+(d,p) basis set. The relation between the inhibition efficiency and quantum chemical parameters have been discussed in order to elucidate the inhibition mechanism of the title compound.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.331-340
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• 2009

We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.