• Journal of applied mathematics & informatics
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• v.33 no.1_2
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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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• v.30 no.2
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• pp.141-146
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• 1992

A total of 197 fecal specimens was prepared for quantitative examination of helminth eggs by modified Kato's cellophane thick smear (M.C.T.S.) and Stoll's dilution egg counting technique (D.E,C.T.). The comparative effectiveness of two techniques was evaluated and conversion function was deduced. The average time required for the microscopic examination on one slide by M.C.T.S. was 12.6 minutes and that of D.E.C.T. was 14.6 minutes. M.C.T.S. showed lower false negative rate than D.E.C.T in light worm burden cases. Functions to convert the counts obtained by M.C.T.S. to E.P.G. by Stoll's dilution egg counting technique were $47.86{\times}10^{0.87{\;}logM.C.T.S.},{\;}$ in A. lumbricoides, $41.69{\times}10^{0.82{\;}logM.C.T.S.}$ in T. trichiura and $63.10{\times}10^{0.85{\;}logM.C.T.S.}$ in C. sinensis. It was suggested M.C.T.S. be better than D.E.C.T. for the quantitative examination of intestinal helminthiases such as A. lumbricoides, T. trichiura, and C. sinensis infections even in the cases with low worm burden.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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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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• v.49 no.3
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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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• v.39 no.1_2
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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.

• Korean Journal of Computational Design and Engineering
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• v.17 no.3
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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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• v.33 no.9
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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.

• The Pure and Applied Mathematics
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• v.31 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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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).