• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.559-571
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• 2017

We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.

• Journal of Life Science
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• v.21 no.10
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• pp.1415-1421
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• 2011

The purpose of this study was to identify the effects of an L-arginine supplementation and regular exercise training on NF-${\kappa}B$, TNF-${\alpha}$, iNOS, Cav-1, eNOS and Ang II in the aortas of D-galactose (D-gal) induced aging rats. The male Strague-Dawley rats were treated with a D-galactose aging inducing agent; the D-gal injection (50 mg/kg) was given intraperitoneally for 12 wk. Experimental groups were divided into five groups: (1) Young control group (Y-Con, n=8), (2) Aging control group (A-Con, n=8), (3) Aging exercise group (A-Ex, n=8), (4) Aging exercise group with L-arginine supplementation group (A-Ex+A, n=8), and (5) Aging with L-arginine supplementation group (A-A, n=8). The exercise consisted of running on a treadmill for 60 min/day at 20 m/min for 6 day/wk, at 0% gradient for 12 wk. The L-arginine supplementation was given orally at a dose of 150 mg/kg/day for 12 wk. The findings of this study were as follows: 1. NF-${\kappa}B$, TNF-${\alpha}$, iNOS, Cav-1 and Ang II proteins in the aortas of D-gal induced rats were significantly increased, however, L-arginine supplementation and regular exercise resulted in a significant inhibition in the expression of NF-${\kappa}B$, TNF-${\alpha}$, iNOS, Cav-1 and Ang II proteins. 2. eNOS protein in the aortas of D-gal induced rats was significantly decreased, however, L-arginine supplementation and regular exercise resulted in a significant increase in the expression of eNOS proteins. In conclusion, the findings of the present study reveal that L-arginine supplementation alone or regular exercise alone or in combination with L-arginine supplementation for 12 wk increases anti-inflammatory effects by decreasing NF-${\kappa}B$, TNF-${\alpha}$, and iNOS protein expressions within the aortic tissue. In addition, L-arginine supplementation alone or regular exercise alone or in combination with L-arginine supplementation may prevent endothelial function by up-regulation of eNOS protein in the aortas of D-gal induced aging rats.

• The KIPS Transactions:PartA
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• v.11A no.5
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• pp.341-346
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• 2004

Recently A Hyper-Star Graph HS(m, k) has been introduced as a new interconnection network of new topology for parallel processing. Hyper-Star Graph has properties of hypercube and star graph, further improve the network cost of a hypercube with the same number of nodes. In this paper, we show that Hyper-Star Graph HS(m, k) is subgraph of hypercube. And we also show that regular graph, Hyper-Star Graph HS(2n, n) is node-symmetric by introduced mapping algorithm. In addition, we introduce an efficient one-to-all broadcasting scheme - takes 2n-1 times - in Hyper-Star Graph HS(2n, n) based on a spanning tree with minimum height.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.111-114
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• 1995

A C$\^$$\infty$/ manifold is a pair (M, C) where a) M is a Hausdorff topological space such that every point $\chi$$\in$M has a neighborhood homeomorphic to an open subset of R$^n$. b) C is a collection of these homeomorphisms whose domains cover M. If ø, $\psi$ $\in$ C then ø o $\psi$$\^$-1/ is C$\^$$\infty$/. c) C is maximal with respect to (b).(omitted)

• The KIPS Transactions:PartA
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• v.12A no.6 s.96
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• pp.499-506
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• 2005

Recently, Hyper-Star network HS(m,k) which improves the network cost of hypercube has been proposed. In this paper, we show that the bisection width of regular Hyper-Star network HS(2n,n) is maximum (2n-2,n-1). Using the concept of container, we also show that k-wide diameter of HS(2n,n) is less than dist(u,v)+4, and the fault diameter is less than D(HS(2n,n))+2, where dist(u,v) is the shortest path length between any two nodes u and v in HS(2n,n), and D(HS(2n,n)) is its diameter.

• Journal of Powder Materials
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• v.17 no.3
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• pp.209-215
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• 2010

Mesoporous alumina particles were prepared by spray pyrolysis using cetyltrimethyl-ammonium bromide (CTAB) as a structure directing agent and the effect of Al precursor types on the texture properties was studied using $N_2$ adsorption isotherms, small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The surface area and the microstructure of alumina particles were significantly influenced by the Al precursor type. The largest BET surface area was obtained when Al chloride was used, whereas alumina particles prepared from Al acetate had the largest pore volume. According to small-angle X-ray scattering (SAXS) analysis, the alumina powders prepared using nitrate and acetate precursors had a clear single SAXS peak around $2{\theta}=1.0{\sim}1.5^{\circ}$, indicating that regular mesopores with sponge-like structure were produced. On the basis of TEM, SAXS, and $N_2$ isotherm results, the chloride precursor was most profitable to obtain the largest surface area ($265\;m^2/g$), whereas, the nitrate precursor is useful for the preparation of non-hollow mesoporous alumina with regular pore size, maintaining high surface area (${\sim}233\;m^2/g$).

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• Korean Journal of Materials Research
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• v.14 no.2
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• pp.133-140
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• 2004

We carried out anodic aluminum oxide (AAO) on a Si and a sapphire substrate. For anodic oxidation of Al two types of specimens prepared were Al(0.5 $\mu\textrm{m}$)!Si and Al(0.5 $\mu\textrm{m}$)/Ti(0.1 $\mu\textrm{m}$)$SiO_2$(0.1 $\mu\textrm{m}$)/GaN(2 $\mu\textrm{m}$)/Sapphire. Surface morphology of Al film was analyzed depending on the deposition methods such as sputtering, thermal evaporation, and electron beam evaporation. Without conventional electron lithography, we obtained ordered nano-pattern of porous alumina by in- situ process. Electropolishing of Al layer was carried out to improve the surface morphology and evaluated. Two step anodizing was adopted for ordered regular array of AAO formation. The applied electric voltage was 40 V and oxalic acid was used as an electrolyte. The reference electrode was graphite. Through the optimization of process parameters such as electrolyte concentration, temperature, and process time, a regular array of AAO was formed on Si and sapphire substrate. In case of Si substrate the diameter of pore and distance between pores was 50 and 100 nm, respectively. In case of sapphire substrate, the diameter of pore and distance between pores was 40 and 80 nm, respectively

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.317-326
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• 2002

In this paper, we establish necessary and sufficient conditions for an exchange ring R to satisfy the n-stable range condition. It is shown that an exchange ring R satisfies the n-stable range condition if and only if for any regular a $\in$ R$^n$, there exists a unimodular u $\in$$^n$ R such that au $\in$ R is a group member, and if and only if whenever a$\simeq$$_n$b with a $\in$ R, b $\in$ M$_n$(R), there exist u $\in$ R$^n$, v $\in$$^n$ R such that a = ubv with uv = 1. As an application, we observe that exchange rings satisfying the n-stable range condition can be characterized by Drazin inverses. These also give nontrivial generalizations of [7, Theorem 10], [13, Theorem 10], [15, Theorem] and [16, Theorem. 2A].

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.203-218
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• 2013

Let R be a ring. A right R-module M is called GI-flat if $Tor^R_1(M,G)=0$ for every Gorenstein injective left R-module G. It is shown that GI-flat modules lie strictly between flat modules and copure flat modules. Suppose R is an $n$-FC ring, we prove that a finitely presented right R-module M is GI-flat if and only if M is a cokernel of a Gorenstein flat preenvelope K ${\rightarrow}$ F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various results in [6] are developed, some new characterizations of von Neumann regular rings are given.