• Kyungpook Mathematical Journal
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• v.58 no.4
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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.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.36 no.4
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• pp.310-318
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• 1991

This experiment was carried out to obtain the information on the variation of chromosome number in pollen mother cell (PMC) and somatic cell of the progeny from the cross between hexaploid triticale cv. Sinkihomil and five hexaploid wheat varieties. The results were summarized as follows: Number of uni-, bi- and tri-valent in PMC was 11.9, 14.4 and 0.44, respectively, in the F$_1$ between triticale and wheat. Significant positive correlation between the pollen fertility and seed set rate, pollen fertility and bivalent number of PMC, and seed set rate and bivalent number of PMC, and negative correlation between pollen fertility and uni-or tri-valent of PMC in the cross between triticale and wheat were detected. F$_1$ (crossed seed) had 42 chromosomes, F$_2$ and F$_1$/P$_1$ showed high frequency of hyperploid (42-49) and F$_1$/P$_2$ showed high frequency of hypoploid (36- 42), which suggest non-random segregation for somatic chromosome number. in the cross between the triticale and wheat.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.109-127
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• 2017

In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• Research in Plant Disease
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• v.18 no.4
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• pp.310-316
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• 2012

Gibberellea fujikuroi species (Gf) complex comprises at least 15 species, most of which not only causes serious plant diseases, but also produces mycotoxins including fumonisins. Here, we focused on the abilities of the field isolates belonging to the Gf complex associated with rice and corn, respectively in Korea to produce fumonisin, all of which were confirmed to carry FUM1, the polyketide synthase gene essential for fumonisin biosynthesis. A total of 88 Gf complex isolates (55 F. fujikuroi, 10 F. verticillioides, 20 F. proliferatum, 2 F. subglutinans, and 1 F. concentricum), and 4 isolates of F. commune, which is a non-member of Gf complex, were grown on rice substrate and determined for their production levels of fumonisins by a HPLC method. Most isolates of F. verticillioides and F. proliferatum, regardless of host origins, produced fumonisin $B_1$ and $B_2$ at diverse ranges of levels ($0.5-2,686.4{\mu}g/g$, and $0.7-1,497.6{\mu}g/g$, respectively). In contrast, all the isolates of F. fujikuroi and other Fusarium species examined produced no fumonisins or only trace amounts ($<10{\mu}g/g$) of fumonisins. Interestingly, the frequencies of relatively high fumonisin-producers among the F. proliferatum and F. fujikuroi isolates derived from corn were higher than those among the fungal isolates from rice. In addition, it is a first report demonstrating the ability of the FUM1-carrying F. commune isolates from rice to produce fumonisins.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.75-80
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• 1999

First, we shall improve the superstability result of the exponential equation f(x+y)=f(x) f(y) which was obtained in [4]. Furthermore, the superstability problems of the functional equation f(x\ulcorner+…+x\ulcorner)=f(x\ulcorner)…f(x\ulcorner) shall be investigated in the special settings (2) and (9).

• Journal of Acupuncture Research
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• v.30 no.2
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• pp.9-15
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• 2013

Objectives : This study was done for reporting the effect of moxibustion therapy on Ryodoraku score of the patients with degenerative arthritis of knee joint. Methods : We investigated 65 cases of patients with degenerative arthritis of knee joint, and devided patients into two groups : One group treated by moxibustion therapy, which was not applied to the other group we analyzed of each group the Ryodoraku score(F1, F6) of each group before and after moxibustion therapy and compared it. Results : 1. In moxibustion therapy group compared with baseline, at final, Ryodoraku score(F1, F6) was significantly increased. 2. At final, moxibustion therapy group showed significant increase on Ryodoraku score(F1, F6) score compared with non moxibustion therapy group. Conclusions : It is suggested that Ryodoraku score(F1, F6) should be available for diagnosing degenerative arthritis of knee joint.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.701-706
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• 2013

Summation theorems for hypergeometric series $_2F_1$ and generalized hypergeometric series $_pF_q$ play important roles in themselves and their diverse applications. Some summation theorems for $_2F_1$ and $_pF_q$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $_3F_2$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.1-21
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• 2013

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{\bot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.43-65
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• 2023

In this paper, by using the difference analogue of Nevanlinna's theory, the authors study the shared-value problem concerning two higher order difference operators of a transcendental entire function with finite order. The following conclusion is proved: Let f(z) be a finite order transcendental entire function such that λ(f - a(z)) < ρ(f), where a(z)(∈ S(f)) is an entire function and satisfies ρ(a(z)) < 1, and let 𝜂(∈ ℂ) be a constant such that ∆_𝜂ⁿ⁺¹ f(z) ≢ 0. If ∆_𝜂ⁿ⁺¹ f(z) and ∆_𝜂ⁿ f(z) share ∆_𝜂ⁿ a(z) CM, where ∆_𝜂ⁿ a(z) ∈ S ∆_𝜂ⁿ⁺¹ f(z), then f(z) has a specific expression f(z) = a(z) + Be^Az, where A and B are two non-zero constants and a(z) reduces to a constant.

• Korean Journal of Microbiology
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• v.27 no.4
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• pp.342-347
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• 1989

by use of HCl-Giemsa technique and light microscope, dividing vegetative nuclei in hyphae of Fusarium species were observed and the results are summerized. The chromosome number of these fungi was ranged 4 to 8. Of the 20 strains, the highest haploid chromosome number is 8 in F. solani S Hongchun K4, F. moniliforme (from banana) and F. raphani (from radish). The lowest is 4 in F. sporotrichioides NRRL 3510 and F. equiseti KFCC 11843 IFO 30198. F. solani 7468 (from Sydney), F. solani 7475 (from Sydney), F. oxysporum(from tomato). F. roseum (from rice), F. sporotrichioides C Jngsun 1, F. equiseti C Kosung 1 and F. avenaceum 46039 are n=7. F. moniliforme (from rice) F. graminearum, F. proliferatum 6787 (from Syndey), F. proliferatum 7459 (from Synder) and F. anguioides ATCC 20351 are n=6. F. moniliforme NRRL 2284, F. poae NRRL 3287 and F. trincinctum NRRL 3299 are n=5. From these results, it may be concluded that the basic haploid chromosome number of the genus Fusarium is 4 and mat have been evolutionary variation of chromosome number through aneuploidy and polyploidy.