• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.101-110
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• 2015

A Total Mean Cordial labeling of a graph G = (V, E) is a function $f:V(G){\rightarrow}\{0,1,2\}$ such that $f(xy)={\Large\lceil}\frac{f(x)+f(y)}{2}{\Large\rceil}$ where $x,y{\in}V(G)$, $xy{\in}E(G)$, and the total number of 0, 1 and 2 are balanced. That is ${\mid}ev_f(i)-ev_f(j){\mid}{\leq}1$, $i,j{\in}\{0,1,2\}$ where $ev_f(x)$ denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). If there is a total mean cordial labeling on a graph G, then we will call G is Total Mean Cordial. Here, We investigate the Total Mean Cordial labeling behaviour of prism, gear, helms.

• Parasites, Hosts and Diseases
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• 제30권2호
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• pp.141-146
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• 1992

Kato후층도말변법 (M.C.T.S.)과 Stoll 회석충란계산법(D.E.C.T)으로 회충, 괸충, 간흡 충란 양성자 197명에 대하여 충란 정량검사를 실시하고 그 결과를 비교하여 상관함수식을 도출하였다. M.C.T.S.법에 소요된 검경시간은 표본 1매당 평균 12.6분으로 D.E.C.T.법의 14.6분보다 짧았으며, 층계부하가 낮은 감염자에 있어서도 위음성이 적었다. 각 윤충류 충란에 있어서 M.C.T.S.으로 얻은 결과를 대변 1 g당 충란수(E.P.G.)로 바꾸어 주는 전환함수식은 회충의 경우 E.P.G.=47.86×100.87 logM.C.T.S., 편충은 E.P.G.=41.69×100.83 logM.C.T.S., 간흡충은 E.P.G=63.10×100.55 logM.C.T.S.이었다. 장내 윤충류 감염에 대한 정량적 대변검사법으로 Kato후층도말변법이 Stoll희석충란계산 법보다 더 유용하다고 생각되었다.

• 대한수학회지
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• 제32권4호
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• pp.739-751
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• 1995

Let ${X(t) : 0 \leq t < \infty}$ be an almost surely continuous Gaussian process with X(0) = 0, E{X(t)} = 0 and stationary increments $E{X(t) - X(s)}^2 = \sigma^2($\mid$t - s$\mid$)$, where $\sigma(y)$ is a function of $y \geq 0(e.g., if {X(t);0 \leq t < \infty}$ is a standard Wiener process, then $\sigma(t) = \sqrt{t})$. Assume that $\sigma(t), t > 0$, is a nondecreasing continuous, regularly varying function at infinity with exponent $\gamma$ for some $0 < \gamma < 1$.

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.223-237
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• 2021

Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

• 한국CDE학회논문집
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• 제17권3호
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• pp.216-223
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• 2012

Bill of material (BOM), which structurally represents the relation among parts constructing a product, is usually created when enterprises start to develop a new product. And it is shown as various types of BOM according to business needs and usage such as eBOM (engineering BOM), gBOM (green BOM), mBOM (manufacturing BOM), pBOM (process BOM), etc. eBOM, generally called BOM and created in the design stage of the new product, includes the drawing information of parts in the view of product function. eBOM is extended to gBOM adding the material information of parts to cope with international regulations for environment. eBOM is transformed to mBOM, which includes manufacturing sequence of parts and adds some parts required to fabricate parts and to assemble the product. mBOM is also extended to pBOM adding the process information of each part and additional assembly processes. This study introduces the concept of multi-BOM covering eBOM, gBOM, mBOM and pBOM, and proposes an advanced way to manage product data using multi-BOM system. The multi-BOM system proposed is to manage their relations using transformation function of BOM and master information of all BOMs.

• Journal of Microbiology and Biotechnology
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• 제33권9호
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• pp.1119-1129
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• 2023

Seeds are colonized by diverse microorganisms that can improve the growth and stress resistance of host plants. Although understanding the mechanisms of plant endophyte-host plant interactions is increasing, much of this knowledge does not come from seed endophytes, particularly under environmental stress that the plant host grows to face, including biotic (e.g., pathogens, herbivores and insects) and abiotic factors (e.g., drought, heavy metals and salt). In this article, we first provided a framework for the assembly and function of seed endophytes and discussed the sources and assembly process of seed endophytes. Following that, we reviewed the impact of environmental factors on the assembly of seed endophytes. Lastly, we explored recent advances in the growth promotion and stress resistance enhancement of plants, functioning by seed endophytes under various biotic and abiotic stressors.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권2호
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• pp.189-200
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• 2024

We derive modular equations of degree 3 to find corresponding theta-function identities. We use them to find some new evaluations of $G(e^{-{\pi}{\sqrt{n}}})$ and $G(-e^{-{\pi}{\sqrt{n}}})$ for $n\,=\,\frac{25}{3{\cdot}4^{m-1}}$ and $\frac{4^{1-m}}{3{\cdot}25}$, where m = 0, 1, 2.

• 대한수학회보
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• 제52권2호
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• pp.467-481
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• 2015

Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the $Poincar\acute{e}$ polynomial $P_{M(G)}(z)$, which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a-polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multipartite graphs G.

• 충청수학회지
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• 제22권4호
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).