• 대한수학회보
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• 제57권2호
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• pp.407-417
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• 2020

Let (R, m) be a d-dimensional Cohen-Macaulay local ring with infinite residue field. Let I be an ideal of R that has analytic spread ℓ(I) = d, satisfies the G_d condition, the weak Artin-Nagata property AN^-_d-2 and m is not an associated prime of R/I. In this paper, we show that if j₁(I) = λ(I/J) + λ[R/(J_d-1 :_RI+(J_d-2 :_RI+I):_R m^∞)] + 1, then I has almost minimal j-multiplicity, G(I) is Cohen-Macaulay and r_J(I) is at most 2, where J = (x₁, _…, x_d) is a general minimal reduction of I and J_i = (x₁, _…, x_i). In addition, the last theorem is in the spirit of a result of Sally who has studied the depth of associated graded rings and minimal reductions for m-primary ideals.

• Bulletin of the Korean Chemical Society
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• 제34권4호
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• pp.1232-1236
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• 2013

The Cu cation binding sites of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex have been investigated to explain the $[Cu{\cdot}DNA]$ biological activity caused by the Cu association to DNA. The structure of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex was investigated by electrospray ionization mass spectrometry (ESI-MS). The fragmentation patterns of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex were analyzed by MS/MS spectra. In the MS/MS spectra of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex, three fragment ions were observed with the loss of d(CpG), {d(CpG) + Cyt}, and {d(CpG) + Cyt + dR}. The Cu cation binds to d(CpG) mainly by substituting the $H^+$ of phosphate group. Simultaneously, the Cu cation prefers to bind to a guanine base rather than a cytosine base. Five possible geometries were considered in the attempt to optimize the $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex structure. The ab initio calculations were performed at B3LYP/6-31G(d) level.

• 대한전자공학회논문지TC
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• 제45권3호
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• pp.1-6
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• 2008

본 논문에서는 2.4GHz 및 5GHz의 이중대역에서 동작하는 I/Q 모듈레이터를 설계하였다. 광대역 믹서에 $90^{\circ}$ 위상천이기를 이용하여 quadrature 신호를 입력하여 베이스밴드 신호를 변조된 RF 신호로 출력한다. 제안한 I/Q 모듈레이터의 변환 손실은 2.4GHz에서 약 15dB이고 5.8GHz 대역에서 약 16dB이다. 사이드밴드 억압특성은 2.4GHz/5GHz에서 각각 15dBc, 16dBc이며, carrier suppression은 두 대역에서 약 40dBc이다. 또한 11Mbps 의 QPSK 신호입력시의 EVM 특성은 2.4GHz에서 약 8.5%, 5GHz에서 10% 이며, 반송파 억압은 두 대역에서 40dB 이상으로, 무선 랜 신호를 인가시 출력 스펙트럼 규격을 만족하였다.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.395-407
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• Archives of Pharmacal Research
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• 제20권3호
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• pp.259-263
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• 1997

In the preparation of acyclic thymidine nucleoside analogues, $K_2CO_3$(or NaH) treated thymine in DMSO was alkylated with .omega.-chloroalkyl nitrite (Cl-(CH_2)n-CN; n=1, 2, 3, 4) to provide an isomeric mixture of 1-(${\omega}$-cyanoalkyl)thymine (2a-d) and 1,3-bis(${\omega}$-cyanoalkyl)thymine in approximately 5:1 ratios. Reduction of the cyano function 2a-d with $NaBH_{4}/CoCl_{2}$ center dot$ 6H_{2}O$gave the corresponding 1-(${\omega}$aminoalkyl)thymine (3a-d). The newly formed primary amino function in 3a-d was directly reacted with 2-chloroethylisocyanate to afford the 1-[.omega.($N^{I}$-2-chloroethylureido) alkyl]thymine (4a-d) in good yields. Nitrosation of 1-[5-($ N^{I}-2$-chloroethylureido)pentyl] thymine (4d) with glacial acetic acid and dry $NaNO_{2}$-powder in anhydrous $CH_{2}Cl_{2}$gave two types of regioisomeric nitrosoureas, 1-[5-($N^{I}$--chloroethyl-$N^{I}$--nitrosoureido)pentylithymine (5d) and 1-[5-($N^{I}-2$-chloroethyl-N-nitrosoureido)pentyllthymine in approximately 5 :1 ratios. The in vitro cytotoxicity of the synthesized compounds (2a-d, 3a-d, 4a-d and 5a-d) against three cell lines (K-562, P-388 and FM-3A) are measured as $IC^{50}$ values. Compounds 3b and 4c showed moderate activities against all three cell lines, and all other compounds were found to be not active.

• 대한수학회지
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• 제33권4호
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• pp.801-811
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• 1996

Let $Z^d$ denote the set of all d-tuples of integers$(d \geq 1, a positive integer)$. The points in $Z^d$ will be denoted by $\underline{m},\underline{n}$, etc., or sometime, when necessary, more explicitly by $(m_1, m_2, \cdots, m_d)$, $(n_1, n_2, \cdots, n_d)$ etc. $Z^d$ is partially ordered by stipulating $\underline{m} \underline{<}\underline{n} iff m_i \leq n_i$ for each i, $1 \leq i \leq d$.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.605-614
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• 2005

We show that an Artinian O-sequence $h_0,h_1,{\cdots},h_{d-1},h_d\;=\;h_{d-1},h_{d+l}\;>\;h_d$ of codimension 3 is not level when $h_{d-1}\;=\;h_d\;=\;d + i\;and\;h{d+1}\;=\;d+(i+1)\;for\;i\;=\;1,\;2,\;and\;3$, which is a partial answer to the question in [9]. We also introduce an algorithm for finding noncancelable Betti numbers of minimal free resolutions of all possible Artinian O-sequences based on the theorem of Froberg and Laksov in [2].

• 대한수학회논문집
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• 제10권2호
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• pp.293-300
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• 1995

Let $R = k[y_1,\cdots,y_n] \otimes E[x_1, \cdots, x_n]$ with characteristic $k = p > 2$ (odd prime), where $$\mid$y_i$\mid$ = 2, $\mid$x_i$\mid$ = 1$ and $y_i = \betax_i, \beta$ is the Bockstein homomorphism. Topologically, $R = H^*(B(Z/p)^n,k)$. For a symmetric group $\sum_n, R^{\sum_n} = k[\sigma_1,\cdots,\sigma_n] \otimes E[d\sigma_1, \cdots, d\sigma_n]$ where d is the derivation satisfying $d(y_i) = x_i$ and $d(x_iy_i) = x_iy_i + x_jy_i, 1 \leq i, j \leq n$. We give a direct proof of this theorem by using induction.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.189-200
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• 2020

Let G be a simple connected graph with n vertices and m edges. Denote by d₁ ≥ d₂ ≥ ⋯ ≥ d_n > 0 and d(e₁) ≥ d(e₂) ≥ ⋯ ≥ d(e_m) sequences of vertex and edge degrees, respectively. If vertices v_i and v_j are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳_α(G) = ∑_i~j(d_i + d_j)^α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳_α(G) and 𝒳_α-1(G). Then we use it to obtain some new bounds for 𝒳_α(G).

• 생약학회지
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• 제31권1호
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• pp.34-38
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• 2000

Three compounds were isolated from the roots of Astragalus membranaceus (Leguminosae). On the basis of spectroscopic evidences, the structures were characterized as $3-0-{\beta}-D-xylopyranosyl-(2',3'-O-diacetyl)-6-0-{\beta}-D-glucopyranosyl-3{\beta},6{\alpha},16{\beta},25-tetrahydroxy-20(R)$,24(S)-epoxy-cycloartane(Astragaloside I), $3-0-{\beta}-D-xylopyranosyl-(2'-O-acetyl)-6-0-{\beta}-D-glucopyranosyl-3{\beta},6{\alpha},16{\beta},25-tetrahydroxy-20(R)$,24(S)-epoxy-cycloartane(Astragaloside II), $3-0-{\beta}-D-xylopyranosyl-(2',4'-O-diacetyl)-6-0-{\beta}-D-glucopyranosyl-3{\beta},6{\alpha},16{\beta},25-tetrahydroxy-20(R)$,24(S)-epoxycycloartane(Isoastragaloside I). Full data of NMR including HMBC and 1D-TOCSY experiment of these compounds were reported for the first time.