• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2011-2023
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• 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
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• v.28 no.1
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• pp.89-94
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• 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
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• v.33 no.3
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• pp.975-979
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• 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 $N_{in}$ $\tau_{rot}{\sim}N^{1.43}$.

• Journal of the Korean Chemical Society
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• v.10 no.1
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• pp.25-31
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• 1966

It is well known that the coloration and structural changes in thermal treatment of polyacrylonitrile are due to the formation of partly hydrogenated naphthylidine-type ring involving the pendant nitrile groups. Any quantitative study of the reaction, in the sense of kinetics and/or statistics, however, has never been reported. This paper presents that, at first, the disappearance of the nitrile groups follows the first order kinetics, which indicates clearly that nitrile groups do not disappear by a long chain reaction-the kinetic chain length is very short. This observation rules out the long intramolecular and intermolecular propagation chain through which most of the nitrile groups disappear. From the evidence that a similar reaction occurs in propylene carbonate solutions without gel formation, one may conclude that the coloration and structural changes are not necessarily intermolecular reaction. Secondly, a finite amount of nitrile groups remains unreacted at the extrem of reaction-not contributed to the formation of naphthylidine-type ring. The concentration of this unreacted nitrile groups is 19∼22% which is good agreement with the statistically calculated value of 19.2%.

• Korean Journal of Crystallography
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• v.13 no.1
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• pp.21-24
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• 2002

The crystal structure of cholesteryl crotonate was investigated by X-ray diffraction. Crystallo-graphic data for the title compound: P2₁, a = 13.446(4) , b = 11.802(3) , c = 18.782(5) , β = 103.99(2)°, Z = 4. Reflections were collected with an Enraf-Nonius CAD-4 diffractometer equipped with a graphite monochromator. The structure was solved by direct methods and refined by least-squares analyses. The final R value was 0.092 for 1604 reflections. The cholesterol fragment of the title compound were in good agreement with those for related cholesterol derivatives. The molecules were stacked in clearly separated layers. At the center of the layers, there were cholesterol-cholesteryl interactions between the symmetry-related A molecules and the cholesteryl-C(17) side chain of B molecules. There were also interactions between the C(17) side chain of A molecules and the crotonate chains off and B molecules in the interface region between layers. The crystal structure of the title compound turned out to be isostructural with those of cholesteryl ethylcarbonate, cholesteryl propylcarbonate, and cholesterol crotylcarbonate. The crystals show the liquid crystalline state having the cholesteric phase.

• East Asian mathematical journal
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• v.36 no.3
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• pp.337-347
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1067-1079
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• 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 $M_R$.

• Journal of the Korean Chemical Society
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• v.11 no.2
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• pp.70-76
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• 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
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• v.28 no.12
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• pp.2471-2476
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• 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
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• v.14 no.4
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• pp.424-429
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• 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).