• 대한수학회보
• /
• 제52권6호
• /
• pp.2011-2023
• /
• 2015

This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].

• Bulletin of the Korean Chemical Society
• /
• 제28권1호
• /
• pp.89-94
• /
• 2007

The new pinane derivative containing unique multifused ring system was synthesized. The crystal, molecular and electronic structure of the title compound has been determined. Both pinane ring systems have the same conformation. The five-membered oxazolidine ring exists in twisted chair conformation. The structure is expanded through O-H…O hydrogen bond to semiinfinite hydrogen-bonded chain. The bond lengths and angles in the optimised structure are similar to the experimental ones. The CH3 and CH2 groups (except this of oxazolidine ring) are negatively charged whereas the CH groups are positively charged. The largest negative potential is on the oxygen atoms. The C-N natural bond orbitals are polarised towards the nitrogen atom (ca. 61% at N) whereas the C-O bond orbitals are polarised towards the oxygen atom (ca. 67% at O). It is consistent with the charges on the nitrogen and oxygen atom of oxazolidine ring and the direction of the dipole moment vector (3.08 Debye).

• Bulletin of the Korean Chemical Society
• /
• 제33권3호
• /
• pp.975-979
• /
• 2012

Structure and Dynamics of dilute two-dimensional (2D) ring polymer solutions are investigated by using discontinuous molecular dynamics simulations. A ring polymer and solvent molecules are modeled as a tangent-hard disc chain and hard discs, respectively. Some of solvent molecules are confined inside the 2D ring polymer unlike in 2D linear polymer solutions or three-dimensional polymer solutions. The structure and the dynamics of the 2D ring polymers change significantly with the number ($N_{in}$) of such solvent molecules inside the 2D ring polymers. The mean-squared radius of gyration ($R^2$) increases with $N_{in}$ and scales as $R{\sim}N^{\nu}$ with the scaling exponent $\nu$ that depends on $N_{in}$. When $N_{in}$ is large enough, ${\nu}{\approx}1$, which is consistent with experiments. Meanwhile, for a small $N_{in}{\approx}0.66$ and the 2D ring polymers show unexpected structure. The diffusion coefficient (D) and the rotational relaxation time ($\tau_{rot}$) are also sensitive to $N_{in}$: D decreases and $\tau$ increases sharply with $N_{in}$. D of 2D ring polymers shows a strong size-dependency, i.e., D ~ ln(L), where L is the simulation cell dimension. But the rotational diffusion and its relaxation time ($\tau_{rot}$) are not-size dependent. More interestingly, the scaling behavior of $\tau_{rot}$ also changes with $N_{in}$; for a large $N_{in}$ $\tau_{rot}{\sim}N^{2.46}$ but for a small $N_{in}$ $\tau_{rot}{\sim}N^{1.43}$.

• 대한화학회지
• /
• 제10권1호
• /
• pp.25-31
• /
• 1966

폴리아크릴로니트릴을 加熱할 때 着色과 同時에 構造變化가 있다는 것은 잘 알려진 事實이며 이것은 部分水素化나프틸리딘型環을 形成함에 基因하는 것으로 알려지고 있다. 本硏究는 이와 같은 構造變化의 反應을 動力學的 및 統計學的으로 取扱하여 지금까지 알려지지 않았던 새로운 事實들을 發見하였다. 첫째로 폴리아크릴로니트릴을 加熱할 때의 니트릴基의 減少는 一次反應이라는 것이며 이는 環形成反應이 긴連鎖反應으로 이루어지지 않는다는 것을 말해 주는 것이다. 다시 말하면 環形成時의 kinetic chain length는 極히 짧다는 것이다. 또 本 構造變化는 반드시 分子間反應(架橋結合)이 아니드라도, 일어날 수 있다는 것을 證明했다. 둘째로 環形成으로 니트릴基가 減少할 때 19~22%의 니트릴基가 殘存한다는 것이며 이를 統計學的으로 解析해본 結果 19.2%라는 計算値를 얻었으며 이는 實驗値와 잘 맞는 數値이다.

• 한국결정학회지
• /
• 제13권1호
• /
• pp.21-24
• /
• 2002

Cholesterol crotonate(CH₃CH = CHCOOC/sub 27/H/sub 45/)의 분자 및 결정 구조를 X-선 회절법으로 연구하였다. 결정은 P2₁, a = 13.446(4) , b = 11.802(3) , c = 18.782(5) , β = 103.99(2)°, Z = 4이다. 회절 반점들의 세기는 흑연 단색화 장치가 있는 Enraf-Nonius CAD-4 diffractometei로 얻었으며 (2θ/sub max/ = 25°, Mo-Kα X선(λ= 0.7107 )을 사용하였다. 분자 구조는 직접법으로 풀었으며, 최소자승법으로 정밀화하였고, 최종신뢰도 R값은 1604개의 회절 반점에 대하여 0.092이었다. 화합물의 결정 구조는 cholesterol ethylcarbonate, propylcarbonate, crotylcarbonate등의 결정 구조와 isostructure로, 분자들은 monolayer를 이루면서 쌓여 있으며, monolayer 중심부에서는 A 분자의 cholesteryl ring system들끼리, B 분자의 cholesterol ring system과 분자 B의 C(17)-side chain들이 서로 촘촘히 쌓여있다. 층(layer)들 사이에는 crotonate tail들과 분자 A의 C(17)-side chain들이 느슨하게 모여있다. 결정은 cholesteric phase를 갖는 liquid crystalline state을 보여주고 있다.

• East Asian mathematical journal
• /
• 제36권3호
• /
• pp.337-347
• /
• 2020

Let R be a ring with unity, and let I be an ideal of R. Then R is called I-semiregular if for every a ∈ R there exists b ∈ R such that ab is an idempotent of R and a - aba ∈ I. In this paper, basic properties of I-semiregularity are investigated, and some equivalent conditions to the primitivity of e are observed for an idempotent e of an I-semiregular ring R such that I∩eR = (0). For an abelian regular ring R with the ascending chain condition on annihilators of idempotents of R, it is shown that R is isomorphic to a direct product of a finite number of division rings, as a consequence of the observations.

• 대한수학회보
• /
• 제49권5호
• /
• pp.1067-1079
• /
• 2012

Let M be a right R-module, (S, ${\leq}$) a strictly totally ordered monoid which is also artinian and ${\omega}:S{\rightarrow}Aut(R)$ a monoid homomorphism, and let $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ denote the generalized inverse polynomial module over the skew generalized power series ring [[$R^{S,{\leq}},{\omega}$]]. In this paper, we prove that $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same uniform dimension as its coefficient module $M_R$, and that if, in addition, R is a right perfect ring and S is a chain monoid, then $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same couniform dimension as its coefficient module $M_R$.

• 대한화학회지
• /
• 제11권2호
• /
• pp.70-76
• /
• 1967

Structural changes attending polyacrylonitrile(PAN) upon heating and treating with nucleophilic reagents have been studied for some time and a few authors have studied on the thermal degradation, particularly on the characterization of degradation products in PAN. It is the purpose of this paper to report the kinetic study on the thermal degradation above $250^{\circ}C$ and make some suggestions as to the degradation process and mechanism in PAN. The degradation process in PAN is considered that three reactions are combined in two steps. Random chain scission accompanying the naphthylidine-type ring formation is the first step and the degradation of naphthylidine-type ring occurred as the next step. The reactions in the first step are competitive so that the maximum weight loss on pyrolysis of PAN, under such a condition that the degradation of naphthylidine-type ring is negligible, is depended on the relative reaction rate of these two competitive reactions.

• Bulletin of the Korean Chemical Society
• /
• 제28권12호
• /
• pp.2471-2476
• /
• 2007

A series of titanium complexes containing terdentate β-ketoiminate ligands were found to be efficient for the ring-opening polymerization of ε-caprolactone (ε-CL), producing poly(ε-caprolactone) (PCL) with bimodal distribution. Steric factors imposed by methyl substituents on the back bone of the alkoxy group affected significantly the polymerization rate and physical properties of the resulting PCL. Intra- and intermolecular transesterifications rather than disproportional rearrangements were responsible for the bimodal behavior and for the change in the molecular weight (Mw). Dilution with toluene reduced yield, and lowered polydispersity (PDI) and Mw of PCL, while the catalytic activities of the dimeric complex, [Ti(Oi-Pr)2(N-alkoxy-β- ketoiminate)]2 and Ti(Oi-Pr)4 were not sensitive to the added solvent. The dimeric complex showed living character, while other catalysts suffered from chain termination reactions.

• Macromolecular Research
• /
• 제14권4호
• /
• pp.424-429
• /
• 2006

The synthesis of a series of poly(POSS-NBE-b-MTD) copolymers was successfully accomplished, taking advantage of sequential, ring-opening, metathesis block copolymerization using $RuCl_2(=CHPh)(PCy_3)_2$ catalyst. By using cyclopentyl-POSS-norbornene (POSS-NBE) monomer as the first block in the block copolymer, living poly(POSS-NBE) with controlled molecular weight and narrow molecular weight distribution was produced. Then, poly(POSS-NBE-b-MTD) copolymers were successfully prepared, in which sequential monomer addition of methyltetracyclododecene (MTD) to the living poly(POSS-NBE) chain ends was utilized to achieve quantitative crossover efficiency. Characterization by $^1H$ NMR spectroscopy and GPC confirmed the high definition and structural integrity of the poly(PO$S-NBE-b-MTD) copolymers. Thermal properties-and morphologies of the POSS-containing block copolymer nanocomposites were also investigated by using thermogravimetric analysis (TGA), transmission electron microscopy (TEM), and wide-angle X-ray scattering (WAXS).