• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• Bulletin of the Korean Chemical Society
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• v.28 no.11
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• pp.2003-2008
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• 2007

The aminolysis of diphenyl thiophosphinic chloride (2) with substituted anilines in acetonitrile at 55.0 oC is investigated kinetically. Kinetic results yield large Hammett ρX (ρnuc = ?3.97) and Bronsted βX (βnuc = 1.40) values. A concerted mechanism involving a partial frontside nucleophilic attack through a hydrogen-bonded, four-center type transition state is proposed on the basis of the primary normal kinetic isotope effects (kH/kD = 1.0-1.1) with deuterated aniline (XC6H4ND2) nucleophiles. The natural bond order charges on P and the degrees of distortion of 42 compounds: chlorophosphates [(R1O)(R2O)P(=O)Cl], chlorothiophosphates [(R1O)(R2O)P(=S)Cl], phosphonochloridates [(R1O)R2P(=O)Cl], phosphonochlorothioates [(R1O)R2P(=S)Cl], chlorophosphinates [R1R2P(=O)Cl], and chlorothiophosphinates [R1R2P(=S)Cl] are calculated at the B3LYP/ 6-311+G(d,p) level in the gas phase.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1647-1659
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• 2008

Let R be a ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. First, we investigate some connected conditions of the zero-divisor graph $\Gamma(R)$ of a noncommutative ring R as follows: (1) if $\Gamma(R)$ has no sources and no sinks, then $\Gamma(R)$ is connected and diameter of $\Gamma(R)$, denoted by diam($\Gamma(R)$) (resp. girth of $\Gamma(R)$, denoted by g($\Gamma(R)$)) is equal to or less than 3; (2) if X is a union of finite number of orbits under the left (resp. right) regular action on X by G, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3, in addition, if R is local, then there is a vertex of $\Gamma(R)$ which is adjacent to every other vertices in $\Gamma(R)$; (3) if R is unit-regular, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3. Next, we investigate the graph automorphisms group of $\Gamma(Mat_2(\mathbb{Z}_p))$ where $Mat_2(\mathbb{Z}_p)$ is the ring of 2 by 2 matrices over the galois field $\mathbb{Z}_p$ (p is any prime).

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.457-466
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• 2008

Let R be a right near-ring. An R-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An R-group of type-5/2 is an R-group of type-2 and an R-group of type-3 is an R-group of type-5/2. Using it $J_{5/2}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that $J_2(R){\subseteq}J_{5/2}(R){\subseteq}J_3(R)$. It is shown that $J_{5/2}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But $J_{5/2}$ is not a KA-radical in the class of all near-rings. By introducing an R-group of type-(5/2)(0) it is shown that $J_{(5/2)(0)}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical $J_{5/2}$ of zero-symmetric near-rings to the class of all near-rings.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.541-547
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• 2008

Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.21
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• pp.9385-9390
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• 2014

Introduction: Human adiponectin (ApN) is a 30 kDa glycoprotein of 244-amino acids which is extensively produced by adipocytes. ApN acts via two receptors, namely adiponectin receptor-1 (Adipo-R1) and adiponectin receptor-2 (Adipo-R2). Studies have shown the presence of Adipo-R1 and Adipo-R2 expression immunohistochemically in human colorectal cancers (CRCs). However, only a few studies exist which investigated effects of adiponectin receptor expression on CRC characteristics. Objectives: In the present study, we aimed to explore Adipo-R1/-R2 expression in human colorectal cancers and any association with clinicopathological characteristics and survival. Materials and Methods: The study enrolled 58 colorectal cancer patients with tumor resection and a control group of 30 subjects with normal colon mucosa. Results: Positivity for Adipo-R1/-R2 expression was significantly more common in the control group in comparison to the patient group (both p<0.001). There was no significant association between Adipo-R1/-R2 expression and clinicopathological characteristics including age, sex tumor location, pTNM stage, Duke's stage, metastasis, histological differentiation, perineural invasion, venous invasion sex, lymphatic invasion, cancer-related mortality, tumor size and recurrence. Adipo- R1/-R2 positivity was also not significantly linked to progression-free or overall survival [p values (0.871, 0.758) and (0.274, 0.232), respectively]. Conclusions: Although significantly reduced Adipo-R1/-R2 expression was found in colorectal cancer patients, it had no influence on survival.

• KIPS Transactions on Computer and Communication Systems
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• v.11 no.12
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• pp.419-428
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• 2022

Since in-place updates for pages are not allowed in flash memory, all new page writes should be written in an out-of-place manner. The old overwritten pages are invalidated. Such invalidated pages eventually trigger the costly garbage collection process. Since the garbage collection causes numerous read and write operations, it is one of the flash memory's major performance issues. In 2R, it modified the garbage collection algorithm, which applies the I/O characteristics of the On-Line Transaction Process workload to improve the Write Amplification Factor. However, this algorithm has a region pollution problem. Therefore, in this paper, we developed 2R++ that additionally separates pages with long access intervals to solve the region pollution problem. 2R++ introduces an extra bit per block to separate warm pages based on a second chance mechanism. Prevents warm pages from being misidentified as cold pages to solve region pollution problem. We conducted the experiments on TPC-C and Linkbench to make the performance comparison. The experiment showed that 2R++ achieved a Write Amplification Factor improvement of 57.8% and 13.8% compared to 2R, respectively.

• Bulletin of the Korean Chemical Society
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• v.18 no.12
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• pp.1301-1304
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• 1997

Elimination reactions of (E)-2,4-dinitrobenzaldehyde O-pivaloyloxime promoted by R2NH/R2NH2+ buffer in 70% MeCN(aq) have been studied kinetically. The reaction exhibited second order kinetics and general base catalysis with Bronsted β=0.45. The Hammett ρ value decreased from 2.3 to 1.6 as the base-solvent system was changed from DBU in MeCN to R2NH/R2NH2+ buffer in 70% MeCN(aq). From these results an E2 mechanism is proposed.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.647-673
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• 2002

There are many models to study topological $R^2$-planes. Unlike topological $R^2$-planes, it is difficult to find models to study topological R$^3$)-spaces. If an 4-dimensional affine plane intersects with R$^3$, we are able to get a geometrical structure on R$^3$ which is similar to R$^3$-space, and called $R^2$-divisible R$^3$-space. Such spatial geometric models is useful to study topological R$^3$-spaces. Hence, we introduce some classes of topological $R^2$-divisible R$^3$-spaces which are induced from 4-dimensional anne planes.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.607-617
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• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.