• 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).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.2
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• pp.730-740
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• 1996

Boiling heat transfer coefficients of pure refrigerants (R22, R32, R134a, R125, R290, and R600a) and refrigerant mixtures (R32/Rl34a, R290/ R600a, and R32/R125) are measured experimentally and compared with Chen's correlation. The test section is a seamless stainless steel tube with inner diameter of 7.7mm and uniformly heated by applying electric current directly to the tube. Heat fluxes range from 10 to 30kW$^2$. Mass fluxes are set to 424 ~ 742kg/m$^{2}$s for R22, R32, R134a, R32/R134a, and R32/Rl25 ; 265 ~ 583kg/m$^{2}$s for R290, R600a, and R290/R600a. Heat transfer coefficients depend strongly on heat flux at a low quality region and become independent as quality increases. Convective boiling term in the Chen's correlation predicts experimental data of the pure refrigerants fairly well (relative error of 12.1% for the data of quality over 0.2). The correlation for pure substances overpredicts the heat transfer coefficients for nonazeotropic refrigerant mixtures.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.818-822
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• 2003

We propose a software-reliability growth model incoporating the amount of uniform and Weibull testing efforts during the software testing phase in this paper. The time-dependent behavior of testing effort is described by uniform and Weibull curves. Assuming that the error detection rate to the amount of testing effort spent during the testing phase is proportional to the current error content, the model is formulated by a nonhomogeneous Poisson process. Using this model the method of data analysis for software reliability measurement is developed. The optimum release time is determined by considering how the initial reliability R(x|0) would be. The conditions are $R(x|0)>R_o$, $R_o>R(x|0)>R_o^d$ and $R(x|0)<R_o^d$ for uniform testing efforts. Ideal case is $R_o>R(x|0)>R_o^d$. Likewise, it is $R(x|0){\geq}R_o$, $R_o>R(x|0)>R_o^{\frac{1}{g}$ and $R(x\mid0)<R_o^{\frac{1}{g}}$ for Weibull testing efforts. Ideal case is $R_o>R(x|0)>R_o^{\frac{1}{g}}$.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

• Journal of Information Technology Services
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• v.10 no.4
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• pp.295-307
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• 2011

The purpose of this research is to find a better knowledge service R&D management process. There are four basic characteristics in service : intangibility, inseparability, inconsistency, and no inventory. These intrinsic characteristics require us to change the traditional manufacturing sector based R&D management process. It is necessary to develop an effective knowledge service R&D management model to improve the competitiveness of the service industry and Korean economy. A model case knowledge service R&D has been performed to find a better R&D management model. The whole cycle of R&D process, such as planning, selection, performing, and evaluation has been reviewed by real experience. Several important aspects of R&D process are compared between manufacturing R&D and service R&D. A knowledge service R&D management framework has been suggested. The results of this research can be used for building a better service R&D management process.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.619-626
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• 2006

Let m be any positive integer, R be a ring with identity, $M_m(R)$ be the matrix ring of all m by m matrices eve. R and $G_m(R)$ be the multiplicative group of all n by n nonsingular matrices in $M_m(R)$. In this pape., the following are investigated: (1) for any pairwise coprime ideals ${I_1,\;I_2,\;...,\;I_n}$ in a ring R, $M_m(R/(I_1{\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $M_m(R/I_1){\times}M_m(R/I_2){\times}...{\times}M_m(R/I_n);$ and $G_m(R/I_1){\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $G_m(R/I_1){\times}G_m(R/I_2){\times}...{\times}G_m(R/I_n);$ (2) In particular, if R is a finite ring with identity, then the order of $G_m(R)$ can be computed.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.23-34
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• 2005

Let R be a ring with left identity. Let G : $R{\times}R{\to}R$ be a symmetric biadditive mapping and g the trace of G. Let ${\alpha}\;:\;R{\to}R$ be an endomorphism and ${\beta}\;:\;R{\to}R$ an epimorphism. In this paper we show the following: (i) Let R be 2-torsion-free. If g is (${\alpha},{\beta}$)-skew-commuting on R, then we have G = 0. (ii) If g is (${\beta},{\beta}$)-skew-centralizing on R, then g is (${\beta},{\beta}$)-commuting on R. (iii) Let $n{\ge}2$. Let R be (n+1)!-torsion-free. If g is n-(${\alpha},{\beta}$)-skew-commuting on R, then we have G = 0. (iv) Let R be 6-torsion-free. If g is 2-(${\alpha},{\beta}$)-commuting on R, then g is (${\alpha},{\beta}$)-commuting on R.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.

• Journal of Technology Innovation
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• v.11 no.2
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• pp.175-193
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• 2003

The purpose of this study is to examine relationship between public R&D investment and private R&D investment in Korea, and to obtain policy implications of the results. To this end, the author attempts to provide more careful consideration of the causality issues by applying rigorous techniques of Granger causality. Tests for unit roots, co-integration, and Granger causality based on an error-correction model are presented. The existence of bi-directional causality between public R&D investment and private R&D investment is detected. This finding has various implications for policy analysts and forecasters. Increasing private R&D investment requires enormous public R&D investment, though there are many other factors contributing to private R&D investment, and public R&D investment is but one part of it. Thus, this study generates confidence in decisions to invest in public R&D. Moreover, this study lends support to the argument that increase in private R&D investment, ceteris paribus, gives rise to public R&D investment. Increase in private R&D investment results in greater national income to be spent on R&D investment and stimulates further public R&D investment.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.709-737
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• 2020

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x₁, …, x_n) be a non central multilinear polynomial over C. If F(f(r₁, …, r_n))G(f(r₁, …, r_n)) - f(r₁, …, r_n)T(f(r₁, …, r_n)) = H(f(r₁, …, r_n)²) for all r₁, …, r_n ∈ R, then we describe all possible forms of F, G, H and T.