• 대한수학회지
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• 제52권4호
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• pp.685-697
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• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.17-33
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• 2007

Suppose F is an arbitrary field. Let ${\mid}F{\mid}$ be the number of the elements of F. Let $T_{n}(F)$ be the space of all $n{\times}n$ upper-triangular matrices over F. A map ${\Psi}\;:\;T_{n}(F)\;{\rightarrow}\;T_{n}(F)$ is said to preserve idempotence if $A-{\lambda}B$ is idempotent if and only if ${\Psi}(A)-{\lambda}{\Psi}(B)$ is idempotent for any $A,\;B\;{\in}\;T_{n}(F)$ and ${\lambda}\;{\in}\;F$. It is shown that: when the characteristic of F is not 2, ${\mid}F{\mid}\;>\;3$ and $n\;{\geq}\;3,\;{\Psi}\;:\;T_{n}(F)\;{\rightarrow}\;T_{n}(F)$ is a map preserving idempotence if and only if there exists an invertible matrix $P\;{\in}\;T_{n}(F)$ such that either ${\Phi}(A)\;=\;PAP^{-1}$ for every $A\;{\in}\;T_{n}(F)\;or\;{\Psi}(A)=PJA^{t}JP^{-1}$ for every $P\;{\in}\;T_{n}(F)$, where $J\;=\;{\sum}^{n}_{i-1}\;E_{i,n+1-i}\;and\;E_{ij}$ is the matrix with 1 in the (i,j)th entry and 0 elsewhere.

• 대한화학회지
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• 제23권6호
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• pp.368-373
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• 1979

염화 N,N-이메틸 및 N,N-이에틸카르바모일의 가용매분해반응과 할라이드 교환$(Cl^-,\;Br^-,\;I^-)$반응, 및 염화 N,N-이페닐카르바모일의 가용매분해반응을 속도론적으로 연구하였다. 속도자료와 MO결과로부터 (1) 이 알킬화합물들은$S_N2$ 메카니즘으로, 이페닐화합물은 $S_N1$ 메카니즘으로 반응함을 알았고, (2) 염화이온교환에서는 결합절단이 중요한 반면, $Br^-$ 및 $I^-$ 교환반응에서는 결합 형성이 중요함을 알 수 있었다.

• 대한화학회지
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• 제11권3호
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• pp.100-104
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• 1967

사염화탄소 용액에 대하여 分光光度法으로 연구한 결과 아닐린, N,N-디메틸아닐린 및 N,N-디에틸아닐린과 요오드 또는 일염화요오드 사이에 1:1 錯物이 형성됨을 알았다. 이들 錯物형성에 대한 실온에서의 평형상수는 다음과 같다. $C_6H_5NH_2{\cdot}I_2\;2.05$, $C_6H_5N(CH_3)_2{\cdot}I_2\;15.2$, $C_6H_5N(C_2H_5)_2{\cdot}I_2\;35.5$, $C_6H_5NH_2{\cdot}ICl\;18.5$, $C_6H_5N(CH_3)_2{\cdot}ICl\;25.6$, 및 $C_6H_5N(C_2H_5)_2\;42.0$ l $mole^{-1}$.

• 대한수의학회지
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• 제33권2호
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• pp.199-209
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• 1993

The effects of ${\alpha}_1$-adrenergic stimulation on membrane potential, intracellular sodium activity $(a_N{^i{_a}})$, and contractility were investigated in the isolated papillary muscle of euthyroid, hyperthyroid, and hypothyroid guinea pigs. Cardiac alterations in the thyroid state have been shown to induce marked changes in action potential characteristics, the most pronounced shortening of action potential duration by hyperthyroidism and an increase in duration by hypothyroidism. $10^{-5}M$ Phenylephrine produced a decrease in $(a_N{^i{_a}})$ in euthyroid and hypothyroid preparations, but an increase in $(a_N{^i{_a}})$ in hyperthyroid ones. The major findings were that phenylephrine produced a stronger positive inotropic effect(PIE) without initial negative inotropic effect(NIE) in hyperthyroid preparations, while phenylephrine produced markedly NIE in hypothyroid ones. The alterations in membrane potential, $(a_N{^i{_a}})$, and contractility were abolished by $3{\times}10^{-5}M$ prazosin in hypothyroidism. In hypothyroid ventricular muscle, the decrease in $(a_N{^i{_a}})$ caused by phenylephrine were not abolished or reduced by $10^{-5}M$ strophanthidin, $10^{-5}M$ TTX, $3{\times}10^{-4}M$ lidocaine, or $100^{-5}M$ verapamil. These results indicate that the ${\alpha}_1$-adrenoceptor-mediated decrease in $(a_N{^i{_a}})$ is not associated with a stimulation of the $Na^+$-$K^+$ pump, inhibition of the $Na^+$ or $Ca^+$ channel in hypothyroid ventricular muscle. $10^{-5}M$ Phenylephrine decreased $(a_N{^i{_a}})$ but increased $(a_N{^i{_a}})$ in the presence of a PKC activator phorbol dibutyrate$(PDB_u)$. In conclusion, it is suggested that the following sequence of events in response to phenyleplhane occur in guinea pig ventricular muscle. First, changes in thyroid state may contribute to the ventacular electrophysiological propeties or ion transport system. Second, the adrenoceptor-mediated initial transient NIE may be associated with the decrease in $(a_N{^i{_a}})$ by PKC activation.

• 대한수학회보
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• 제35권3호
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• pp.491-501
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• 1998

If N is any cartesian product of a closed simply connected n-manifold $N_1$ and a closed aspherical m-manifold $N_2$, then N is a codimension 2 fibrator. Moreover, if N is any closed hopfian PL n-manifold with $\pi_iN=0$ for $2 {\leq} i < m$, which is a codimension 2 fibrator, and $\pi_i N$ is normally cohopfian and has no proper normal subroup isomorphic to $\pi_1 N/A$ where A is an abelian normal subgroup of $\pi_1 N$, then N is a codimension m PL fibrator.

• 대한수학회보
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• 제32권1호
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• pp.45-56
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• 1995

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$ \cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial $$ $$ \cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A) $$ where $i_*, j_*$ and \partial$ are restrictions of the usual homomorphisms of the homotopy sequence $$ \cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X) $$.

• 대한수학회지
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• 제45권2호
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• pp.355-365
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• 2008

Let ${Y_i;-\infty<i<\infty}$ be a doubly infinite sequence of identically distributed and $\phi$-mixing random variables with zero means and finite variances and ${a_i;-\infty<i<\infty}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of ${{\sum}_{k=1}^{n}\;{\sum}_{i=-\infty}^{\infty}\;a_{i+k}Y_i/n^{1/p};n\geq1}$ under some suitable conditions.

• 응용통계연구
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• 제13권2호
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• pp.343-352
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• 2000

K-평균 군집화(K-means clustering)는 비계층적 군집화 방법이 하나로서 큰 자료에서 개체 군집화에 효율적인 것으로 알려져 있다. 그러나 종종 비교적 균일한 대군집의 일부를 소군집에 떼어주는 오류를 범하기도 한다. 이 연구에서는 그러한 현상을 정확히 인지하고 이에 대한 대책으로서 ‘이중 K-평균 군집화(double K-means clustering)’방법을 제시한다. 또한 실증적 사례에 새 방법론을 적용해보고 토의한다.

• 대한수학회논문집
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• 제9권3호
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• pp.539-545
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• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.