• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.13-29
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• 2021

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.

• 한국가축번식학회지
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• 제20권2호
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• pp.215-221
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• 1996

This study was carried out to develop an immunoassay for the diagnosis of the pregnancy and ovarian function of domestic animals. Using 2E92C10 monoclonal antibody(McAb) generated against estrone-3-glucuronide(E1-3-G) and appeared a high cross-reactivity with estrone-3-sulfate(E1-3-S), chemiluminesence immunoassay (CIA) to detect E1-3-S was developed. 2E92C10 McAb cross-reacted with E1-3-S (30%) was purified from ascites fluid using protein G sepharose gel column. The purity of purified antibody fraction was monitored by SDS-PAGE and was better compared to that of crude ascite fluid. The soild and liquid phase CIA for E1-3-S were established utilizing 2E92C10 antibody and E1-3-G-ABEI conjugate used as a tracer. As the results, the titer of 2E92C10 antibody was 5g/ml in soild phase and 1:2000 in liquid phase. The sensitivity on soild and solid phase CIA were about 200 pg/ml. These results indicate that CIA for measurement of E1-3-S was successfully developed by using ant-E1-3-G McAb cross-reacted with E1-3-S and could be usefully used to research this area.

• 대한임상검사과학회지
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• 제52권3호
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• pp.165-171
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• 2020

본 연구의 목적은 대한민국 20세 이상(50.32±16.14세)의 당뇨질환이 없는 성인에서 만성신장질환과 인슐린저항성(homeostasis model assessment of insulin resistance, HOMA-IR) 및 베타세포기능(homeostasis model assessment of beta cell function, HOMA-B)의 관련성에 대하여 조사하였다. 본 연구는 2015년도 국민건강영양조사 자료를 이용하여 당뇨질환이 없는 20세 이상의 대한민국 성인 4,380명을 대상으로 하였다. 본 연구결과에서 중요한 결과는 다음과 같다. 첫째, 만성신장질환과 HOMA-IR와 관련하여, 관련변수를 보정한 후의 결과에서(Model 4), 그룹 1 (G1; estimated glomerular filtrationrate [eGFR], ≥90 mL/min/1.73 ㎡), 그룹 2 (G2; eGFR, 60~89 mL/min/1.73 ㎡), 그룹 3a (G3a; eGFR, 30~59 mL/min/1.73 ㎡), ≥그룹 3b (≥G3b; eGFR, <30 mL/min/1.73 ㎡)의 HOMA-IR 평균값(M±SE, 95% confidence interval [CI])은 각각 1.78±0.03 (1.73~1.83), 1.87±0.03 (1.81~1.93), 2.16±0.13 (1.91~2.42) 및 2.59±0.24 (2.12~3.06)으로 만성신장질환이 진행됨에 따라 HOMA-IR은 증가하였다(P<0.001). 둘째, 만성신장질환과 HOMA-B와 관련하여, 관련변수를 보정한 후의 결과에서(Model 4), G1, G2, G3a 및 ≥G3b의 HOMA-B 평균값(M±SE, 95% CI)은 각각 87.46±1.21 (85.08~89.84), 89.11±1.38(86.40~91.81), 104.82±5.91 (93.23~116.42) 및 123.97±10.87 (102.66~145.29)으로 만성신장질환이 진행됨에 따라 HOMA-B도 증가하였다(P<0.001). 대한민국 당뇨질환이 없는 성인에서 만성신장질환이 진행됨에 따라 인슐린 저항성이 증가하였고, 베타세포기능 또한 증가하였다.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.565-586
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• 2017

In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.

• 대한수학회보
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• 제50권6호
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• pp.2021-2026
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• 2013

Let G = (V,E) be a graph. A function $f:V{\rightarrow}\{-1,+1\}$ defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, ${\gamma}^s_t(G)$, is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total domination number of generalized Petersen graphs P(n, 2) and prove that for any integer $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.

• 대한수학회보
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• 제52권5호
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• pp.1737-1751
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• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• 대한수학회보
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• 제46권1호
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• pp.25-33
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• 2009

Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

• Animal Bioscience
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• 제35권3호
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• pp.399-409
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• 2022

Objective: Follicle-stimulating hormone (FSH) is the central hormone involved in mammalian reproduction, maturation at puberty, and gamete production that mediates its function by control of follicle growth and function. The present study investigated the mutations involved in the regulation of FSH receptor (FSHR) activation. Methods: We analyzed seven naturally-occurring mutations that were previously reported in human FSHR (hFSHR), in the context of equine FSHR (eFSHR); these include one constitutively activation variant, one allelic variant, and five inactivating variants. These mutations were introduced into wild-type eFSHR (eFSHR-wt) sequence to generate mutants that were designated as eFSHR-D566G, -A306T, -A189V, -N191I, -R572C, -A574V, and -R633H. Mutants were transfected into PathHunter EA-parental CHO-K1 cells expressing β-arrestin. The biological function of mutants was analyzed by quantitating cAMP accumulation in cells incubated with increasing concentrations of FSH. Results: Cells expressing eFSHR-D566G exhibited an 8.6-fold increase in basal cAMP response, as compared to that in eFSHR-wt. The allelic variation mutant eFSHR-A306T was not found to affect the basal cAMP response or half maximal effective concentration (EC₅₀) levels. On the other hand, eFSHR-D566G and eFSHR-A306T displayed a 1.5- and 1.4-fold increase in the maximal response, respectively. Signal transduction was found to be completely impaired in case of the inactivating mutants eFSHR-A189V, -R572C, and -A574V. When compared with eFSHR-wt, eFSHR-N191I displayed a 5.4-fold decrease in the EC₅₀ levels (3,910 ng/mL) and a 2.3-fold decrease in the maximal response. In contrast, cells expressing eFSHR-R633H displayed in a similar manner to that of the cells expressing the eFSHR-wt on signal transduction and maximal response. Conclusion: The activating mutant eFSHR-D566G greatly enhanced the signal transduction in response to FSH, in the absence of agonist treatment. We suggest that the state of activation of the eFSHR can modulate its basal cAMP accumulation.

• 약학회지
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• 제41권4호
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• pp.498-511
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• 1997

The effects of UK 14,304, an ${\alpha}_2$-adrenergic agonist, on renal function were investigated in dogs. UK 14,304, when given intravenousely($15.0{\mu}g/kg,\;50{\mu}g/kg$), produced the increase of urine flow accompanied with the marked augmentation of free water clearance ($C_{H_2O}$) and reabsorption rates of sodium in renal tubules ($R_{Na}$), and the remarkable decrease of osmolar clearance ($C_{osm}$) and the amounts of sodium excreted in urine ($E_{Na}$). UK 14,304 given into a renal artery($1.5{\mu}g/kg,\;5.0{\mu}g/kg$) elicited the increase of urine flow with the augmentation of $C_{H_2O}$ in both kidney. UK 14,304, when administered into carotid artery($3.0{\mu}g/kg,\;10.0{\mu}g/kg$). exhibited the same aspect as shown in intravenous UK 14.304 at smaller dose than the intravenous dose. Diuretic action of intravenous UK 14,304 were produced together with increase of $C_{H_2O}$ in situation of water diuresis too, changes of renal function in this state were the increase of $C_{osm},\;E_{Na},\;and\;E_K$ (excreted amounts of potassium in urine), and the decrease of $R_{Na}\;and\;R_K$, these were different appearances from situation of saline diuresis. Diuretic action of intravenous UK 14,304 were blocked completely by post or pretreatment of yohim-bine, ${\alpha}_2$-adrenergic blocking agents, and inhibited by pretreatment of vasopressin, antidiuretic hormone. Above results suggest that UK 14,304 produces the diuretic action by the inhibition of vasopressin secretion and suppression of electrolytes reabsorption of electrolytes in renal tubules mediated with central ${\alpha}_2$-adrenoceptor in dog.