• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.451-465
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• 2016

A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ⁺ such that |g(u) - g(v)| ≥ diam(G) + 1 - d_G(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V(G)} = k. We investigate radio number for some families of generalized caterpillar graphs.

• The Mathematical Education
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• v.25 no.3
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• pp.77-100
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• 1987

Let G : R$^n$${\times}$R\longrightarrowR$^n$ be defined by a Homotopy solving a system F($\chi$)=0 of nonlinear equations. For the vector v$\^$k/ with G'(u$\sub$k/)v$\^$k/=0, ∥v$\^$k/∥=1 where uk is one point in Zero Curve let u$\sub$0/$\^$k/=v$\^$k/＋$\tau$v$\^$k/ be the first prediction for the next point u$\^$k+1/, $\tau$$\in$(0, 1). When u$\sub$0/$\^$k/ approaching too losely to some unwanted point. to follow the Zero Curve may occur the returning or cycling. One lion for it is discussed and tile parametrizied Homotopy algorithm for solving F($\chi$)=0 with it been established. Also some theorems by means of the regular value have been discussed for Zero Curves of G(u)=0 and some theorems for algorithm have been obtained.

• Nuclear Engineering and Technology
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• v.45 no.7
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• pp.859-870
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• 2013

The paper summarizes the irradiation test and post-irradiation examination (PIE) data for the U-Mo low-enriched fuel that was irradiated in the MIR reactor under the RERTR Program. The PIE data were analyzed for both full-size fuel rods and mini-rods with atomized powder dispersed in Al matrix as well as with additions of 2%, 5% and 13% of silicon in the matrix and ZrN protective coating on the fuel particles. The full-size fuel rods were irradiated up to an average burnup of ${\sim}60%^{235}U$; the mini-rods were irradiated to an average burnup of ${\sim}85%^{235}U$. The presented data show a significant increase of the void fraction in the U-Mo alloy as the U-235 burnup rises from ~ 40% up to ~ 85%. The effect of irradiation test conditions and U-235 burnup were analyzed with regard to the formation of an interaction layer between the matrix and fuel particles as well as generation of porosity in the U-Mo alloy. Shown here are changes in distribution of U fission products as the U-235 burnup increases from ~ 40% up to ~ 85%.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.259-269
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• 2008

The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals $${\Delta}u+u(a-bu+g(v))=0\;in\;{\Omega}\\{\Delta}v+v(d+h(u)-cv)=0\;in\;{\Omega}\\u=v=0\;on\;{\partial}{\Omega}$$ are investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.139-146
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• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.

• Korean Journal of Heritage: History & Science
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• v.55 no.4
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• pp.278-294
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• 2022

To date, cultural property education has seen rapid quantitative growth due to national and personal needs. However, qualitative growth is lacking. The objectives of cultural property education have not been established, and therefore, even its identity is not clear. The most pressing issue at present in cultural property education is to first set objectives. This study aimed to analyze the objectives of current cultural property education, identify the problems, and set new objectives to meet significant national and personal needs in terms of education. The problems with the objectives of current cultural property education are that the persons interested in the education do not understand the concept of the education objectives clearly and that the objectives do not contain much actual content of the education. Also, the objectives of the education do not take into account the dynamic competencies and interests of the learners and do not satisfy the changes of the times. To solve these problems, new cultural property education, called 'U.V.E.C.,' was offerred. U.V.E.C. education is aimed at understanding cultural properties, recognizing their value, and enjoying them, and at creating culture. The objectives of U.V.E.C. cultural property education were set such that they can be modified flexibly in a learner-centric way with clear and practical format and contents. Based on this direction, stepwise objectives were set including overall objectives, detailed objectives, and practice objectives, and objective cases of each step were proposed. Considering the generality of the education and the distinct characteristics of the cultural properties, the U.V.E.C. education objectives took into account the diversity of behavioral objectives, clearness in statements, the objectives of problem solving, the initiative of learners and openness for expression outcomes. The U.V.E.C. objectives are clear and specific so that teachers can enhance their pedagogical efficiency and learners are able to develop interesting and diversified competencies. In addition, it is expected that the U.V.E.C. objectives will significantly affect objective setting for education on cultural properties which have not been studied widely. Further systemic and specific studies on the contents and methods of the U.V.E.C. education would help to change the overall education on cultural properties and position the field as a new academic area.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.147-161
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• 2021

In this paper, we introduced and studied sa-supplement submodules. A submodule U of a module V is called an sa-supplement submodule in V if there exists a submodule T of V such that V = T + U and U ∩ T is semiartinian. The class of sa-supplement sequences ������ is a proper class which is generated by socle-free modules injectively. We studied modules that have an sa-supplement in every extension, modules whose all submodules are sa-supplement and modules whose all sa-supplement submodules are direct summand. We provided new characterizations of right semiartinian rings and right SSI rings.

• 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.