• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1557-1565
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• 2022

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is "distance preserving" over the ring R. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy "distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring 𝓡 and the non-chain ring 𝓡_e,s.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.193-204
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• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.1-12
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• 1999

The faithful bi-module \ulcornerM\ulcorner with its endomorphism ring End\ulcorner(M) such that M\ulcorner is flat (in other words, End\ulcorner(M)-flat, or endo-flat)and with a commutative ring R containing an identity has been studied in this paper. The chain conditions of a faithful endo-flat module \ulcornerM relative to those of the endomorphism ring End\ulcorner(M) having the zero annihilator of each non-zero endomorphism are studied.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.45-49
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• 1983

If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.

• Bulletin of the Korean Chemical Society
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• v.17 no.4
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• pp.331-334
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• 1996

New copper(Ⅱ) complex of the pentaaza non-macrocyclic ligand 1-(2-aminoethyl)-3-(N-{2-aminoethyl}aminomethyl)-1,3-diazacyclohexane (2) and a dinuclear copper(Ⅱ) compex of the bis(macrocyclic) ligand 3, in which two 1,5,8,10,12,15-hexaazabicyclo[11.3.11.5]heptadecane subunits are linked together by an ethylene chain through the uncoordinated nitrogen (N10) atoms, have been prepared selectively by the reaction of the metal ion, 1,4,8-triazaoctane, ethylenediamine, and formaldehyde. The dinuclear complex [Cu2(3)]4+ has been also prepared by the reaction of [Cu(2)]2+ with ethylenediamine and formaldehyde. The reaction products largely depend on the molar ratio of the reactants employed. The mononuclear complex or each macrocyclic subunit of the dinuclear complex contains one 1,3-diazacyclohexane ring and has a square-planar geometry with a 5-6-5 or 5-6-5-6 chelate ring sequence. In acidic solution, the copper(Ⅱ) complex of 2 dissociates more slowly than those of other related non-cyclic polyamines.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.115-137
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• 2018

Let $R_{u{^2},v^2,w^2,p}$ be a finite non chain ring ${\mathbb{F}}_p[u,v,w]{\langle}u^2,\;v^2,\;w^2,\;uv-vu,\;vw-wv,\;uw-wu{\rangle}$, where p is a prime number. This ring is a part of family of Frobenius rings. In this paper, we explore the structures of cyclic codes over the ring $R_{u{^2},v^2,w^2,p}$ of arbitrary length. We obtain a unique set of generators for these codes and also characterize free cyclic codes. We show that Gray images of cyclic codes are 8-quasicyclic binary linear codes of length 8n over ${\mathbb{F}}_p$. We also determine the rank and the Hamming distance for these codes. At last, we have given some examples.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.921-935
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• 2018

In this study we determine the structure of m-adic residue codes over the non-chain ring $F_q[v]/(v^2-v)$ and present some promising examples of such codes that have optimal parameters with respect to Griesmer Bound. Further, we show that the generators of m-adic residue codes serve as a natural and suitable application for generating reversible DNA codes via a special automorphism and sets over $F_{4^{2k}}[v]/(v^2-v)$.

• Proceedings of the Membrane Society of Korea Conference
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• 1997.10a
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• pp.39-45
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• 1997

Introduction : Polyimides are one of the most important classes of the high performance polymers due to their excellent electrical, thermal, and high-temperature mechanical properties. But their uses are limited because of their poor solubility. Most polyimide derivatives are processed in the form of polyamic acids, which are subsequently converted into the imide structures.Recently, it has been found that the soluble polyimides with large molecular weight sufficient to application. For enhancing processability, the majority of approaches have involved the following factors. As much as, the separation of the imide ring along the back-bone, that is to say, reducing the density of imide ring in the repeat structure. The introduction of bulky substituents along the back-bone, in order to enhance the free volume of main-chain. The incorporation of flexible or thermally stable linkages in the main-chain, reducing the packing force. The disruption of symmetry or recurrence regularity through copolymerization in order to reduce crystallnity.The objectives of this investigation are the synthesis and characterization of soluble polyimides as membrane materials by the single-step polymerization and the preparation of the asymmetric polyimide membrane by using phase inversion technique. In the present study, three series of polyimide derivatives are synthesized; H series is homopolyimides, A series is prepared from single dianhydride and two diamines, B series is yielded from two dianhydrides and a diamine. The dope solution was directly prepared from the PI solution via one step polymerization from monomers.

• Biomolecules & Therapeutics
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• v.3 no.1
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• pp.34-37
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• 1995

Non-steroidal anti-inflammatory drugs (NSAIDs) have been known as inhibitors of the folate-requiring enzymes. In the present work, we have expanded on these observations and have investigated the inhibitory effects of NSAIDs on Lactobacillus casei thymidylate synthase expressed in E. coli. NSAIDs including sulphasalizine, salicylic acid, indomethacin and mefenamic acid were found to be competitive inhibitors with respect to folate of Lactobacillus casei thymidylate synthase. In contrast, aspirin and the antipyretic-analgesic drugs acetaminophen and antipyrine were weak inhibitors of the enzyme. Structure-activity correlation suggests that an aromatic ring with a side chain containing a carboxylic acid is a requirement for competitive inhibition of the thymidylate synthase. The results are consistent with the hypothesis that the antifolate activity of NSAIDs, and hence cytostatic consequences, are important factors in producing anti-inflammatory activity and aspirin exerts its anti-inflammatory effects after its conversion into salicylic acid, which possesses greater antifolate activity than its parent compound.

• Bulletin of the Korean Chemical Society
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• v.17 no.10
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• pp.919-924
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• 1996

Crystal structure of two inclusion compounds Cd(pn)Ni(CN)4·0.25G (G=toluene and p-xylene, pn=1,2-diaminopropane) have been determined from single-crystal X-ray diffraction data; toluene clathrate: monoclinic P21/n, a=13.838(6), b=26.893(5), c= 7.543(5) Å, γ=90.92(3)°, Z=4, R=0.0616; p-xylene clathrate: monoclinic P21/n, a=13.895(2), b=26.900(3), c=7.613(1) Å, γ=91.06(1)°, Z=4, R=0.0486. The host structures determined for toluene- and pxylene-guest clathrates are substantially identical to the U-type structures observed for the straight chain aliphatic-guest clathrates. However, the alternating arrangement of occupied channels with the guest molecules and vacant channels appears in the host structure. The non-centrosymmetric toluene molecules are distributed about the inversion center to give an image like p-xylene molecule. The guests, toluene and p-xylene, prefer the U-type channel, favoring the interaction between the π-electrons of the aromatic ring and the pn-amino groups to hold the aromatic ring vertical to the cyanometallate meshes.