• 대한수학회보
• /
• 제59권6호
• /
• pp.1557-1565
• /
• 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.

• 대한수학회지
• /
• 제59권1호
• /
• pp.193-204
• /
• 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.

• 대한수학회보
• /
• 제55권3호
• /
• pp.921-935
• /
• 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 $F_{4^{2k}}[v]/(v^2-v)$.

• 대한수학회보
• /
• 제55권1호
• /
• pp.115-137
• /
• 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.

• 대한수학회보
• /
• 제20권1호
• /
• pp.45-49
• /
• 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.

• 한국진공학회:학술대회논문집
• /
• 한국진공학회 2012년도 제42회 동계 정기 학술대회 초록집
• /
• pp.158-158
• /
• 2012

A new kind of organic-inorganic hybrid polymer, poly(tetraphenyl)silole siloxane (PSS), was invented and synthesized for realization of its unique charge trap properties. The organic portions consisting of (tetraphenyl)silole rings are responsible for electron trapping owing to their low-lying LUMO, while the Si-O-Si inorganic linkages of high HOMO-LUMO gap provide the intrachain energy barrier for controlling electron transport. Such an alternation of the organic and inorganic moieties in a polymer may give an interesting quantum well electronic structure in a molecule. The PSS thin film was fabricated by spin-coating of the PSS solution in THF organic solvent onto Si-wafer substrates and curing. The electron trapping of the PSS thin films was confirmed by the capacitance-voltage (C-V) measurements performed within the metal-insulator-semiconductor (MIS) device structure. And the quantum well electronic structure of the PSS thin film, which was thought to be the origin of the electron trapping, was investigated by a combination of theoretical and experimental methods: density functional theory (DFT) calculations in Gaussian03 package and spectroscopic techniques such as near edge X-ray absorption fine structure spectroscopy (NEXAFS) and photoemission spectroscopy (PES). The electron trapping properties of the PSS thin film of quantum well structure are closely related to intra- and inter-polymer chain electron transports. Among them, the intra-chain electron transport was theoretically studied using the Atomistix Toolkit (ATK) software based on the non-equilibrium Green's function (NEGF) method in conjunction with the DFT.

• Journal of Applied Biological Chemistry
• /
• 제61권4호
• /
• pp.335-340
• /
• 2018

Hemoglobin (Hb) is a member of heme-protein that can perform catalytic non-specific chain reaction in the presence of hydrogen peroxide ($H_2O_2$). Catalytic ability of Hb to degrade pyrene was demonstrated using soil contaminated with $^{14}C$ pyrene and 10 mg pyrene /kg soil. The composition of soil was similar to previously used soil except that it had lower organic carbon content. Bench scale laboratory tests were conducted in the presence of buffer only, $H_2O_2$ only, or Hb with $H_2O_2$ for 24 h. After 24 h reaction, 0.1 and 1.3% of $^{14}C$ pyrene in contaminated soil were mineralized with $H_2O_2$ only or Hb plus $H_2O_2$. No mineralization to $^{14}CO_2$ was detected with buffer only. Approximately 12.2% of pyrene was degraded in the presence of $H_2O_2$ only while 44.0% of pyrene was degraded in the presence of Hb plus $H_2O_2$ during 24 h of catalytic reaction. When degradation intermediate products were examined, two chemicals were observed in the presence of $H_2O_2$ only while 25 chemicals were found in the presence of Hb plus $H_2O_2$. While most degradation products were simple hydrocarbons, four of the 27 chemicals had aromatic rings. However, none of these four chemicals was structurally related to pyrene. These results suggest that Hb catalytic system could be used to treat pyrene-contaminated soil as an efficient and speedy remediation technology. In addition, intermediate products generated by this system are not greatly affected by composition change in soil organic matter content.