• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.59-74
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• 2017

A radio labeling of a graph G is a function $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ with the property that ${\mid}f(u)-f(v){\mid}{\geq}1+diam(G)-d(u,v)$ for every pair of vertices $u,v{\in}V(G)$, where diam(G) and d(u, v) are diameter and distance between u and v in the graph G respectively. The radio number of a graph G, denoted by rn(G), is the smallest integer k such that G admits a radio labeling. In this paper, we completely determine radio number of all transformation graphs of a path.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.305-313
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• 2016

In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following ${\gamma}$-Laplacian systems in the whole space ${\mathbb{R}}^n$ has the components symmetry property $u{\equiv}v$ $$\{\array{-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u,v)\text{ in }{\mathbb{R}}^n,\\-div({\mid}{\nabla}v{\mid}^{{\gamma}-2}{\nabla}v)=g(u,v)\text{ in }{\mathbb{R}}^n.}$$ Here n > ${\gamma}$, ${\gamma}$ > 1. Thus, the systems will be reduced to a single ${\gamma}$-Laplacian equation: $$-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u)\text{ in }{\mathbb{R}}^n$$. Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.115-137
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• 2018

Let $R_{u{^2},v^2,w^2,p}$ be a finite non chain ring ${\mathbb{F}}_p[u,v,w]{\langle}u^2,\;v^2,\;w^2,\;uv-vu,\;vw-wv,\;uw-wu{\rangle}$, where p is a prime number. This ring is a part of family of Frobenius rings. In this paper, we explore the structures of cyclic codes over the ring $R_{u{^2},v^2,w^2,p}$ of arbitrary length. We obtain a unique set of generators for these codes and also characterize free cyclic codes. We show that Gray images of cyclic codes are 8-quasicyclic binary linear codes of length 8n over ${\mathbb{F}}_p$. We also determine the rank and the Hamming distance for these codes. At last, we have given some examples.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1137-1144
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• 2024

We are concerned with the T-Graphs, denoted by G_T, which are graphs defined based on the Topological structure of the given set. Precisely, for a given topology T on a set X, a T-Graph G = (V,E) is an undirected graph. In this graph, the vertex set V is P(X) and the edge set E consists of all unordered pairs of nodes u and v in V, denoted by (u, v). The pair of nodes satisfies the condition that u ∈ T and u^c ∩ v ∈ T, where u^c is the complement of the subset u of X. The primary objective of this paper is threefold: (i) Find that the number of triangles (ii) we intend to establish that the number of rectangles and (iii) the number of Hamiltonian cycles and Eulerian closed trials in a graph G_T.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.2
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• pp.33-42
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• 1980

This paper compared the seakeeping quality of U, V type ships in infinite depth by using the finite element method. From the calculated results, it is found that heaving and pitching motions of V type are comparatively better than those of U type ship in the water of infinite depth and the reversed phenomenon occures in the water of finite depth. And the seakeeping quality of U type is better than V type ship in larger ranges than the nondimensional wave number 2.0.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1753-1769
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• 2016

This paper is concerned with the quasilinear $Schr{\ddot{o}}dinger$ system $$(0.1)\;\{-{\Delta}u+a(x)u-{\Delta}(u^2)u=Fu(u,v)+h(x)\;x{\in}{\mathbb{R}}^N,\\-{\Delta}v+b(x)v-{\Delta}(v^2)v=Fv(u,v)+g(x)\;x{\in}{\mathbb{R}}^N,$$ where $N{\geq}3$. The potential functions $a(x),b(x){\in}L^{\infty}({\mathbb{R}}^N)$ are bounded in ${\mathbb{R}}^N$. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (0.1).

• East Asian mathematical journal
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• v.33 no.1
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• pp.103-113
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• 2017

We provide quantitative two weight estimates for the commutator of the Hilbert transform under certain conditions on a pair of weights (u, v) and b in $Carl_{u,v}$. In [10] and [11], Bloom's inequality is shown in a modern setting, and the boundedness of the commutators is provided by assuming both weights u, v are $A_2$ and $b{\in}BMO_{\rho}$. In the present paper we show that the condition on b can be replaced by $Carl_{u,v}$ by using the joint $A^d_2$ condition.

• Korean Journal of Microbiology
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• v.6 no.4
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• pp.122-130
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• 1968

Action of various wavelengths of visible light on ultraviolet-radiation damage to haploid yeast cells, Saccharomyces cerevisiae 23971, was studied. The results were obtained on the basis of the survival and respiration rates by pre- and post-illuminations of various wavelengths before and after U.V.-irradiations on the yeast cells. Among the wavelengths tested, 635 $m{\mu}$, 429 $m{\mu}$ and white light which caused increase of respiration in pre-treatment alone, induced less resistance to the U. V.-damage than in the control, in both pre- and U.V.-treatment. On the contrary, such wavelengths as 574 $m{\mu}$and 530 $m{\mu}$, showing a weak effect on respiration in pre-treatment increased the susceptability to U.V.-radiation. Photoinactivation was generally obtained by both pre- and post- illuminations along with U.V.-treatment. At 635 $m{\mu}$ the PI rate was the lowest and also a low PI rate was shown at 429 $m{\mu}$. But 429 $m{\mu}$, in the post-treatment of the yeast cells pre-treated by the white light and the darkness respectively, showed the highest PI rate. In both pre- and post- treatment of 574, 530 and 473 $m{\mu}$,the PI rates were high to the same degree. Post-treatments of the wavelengths on U.V.-treated yeasts incubated rather under the white light than the darkness induced lower PI rate. It is assumed that there are great differences in action even of the same wavelength, depending upon the various combination of pre- and post-treatments, and that, moreover, the action of various wavelengths of visible light on U.V.-damage on the cells are concerned with the doses and dose rates of U.V. and visible lights. These observations led to an interpretation that each wavelength of visible light might exert distinctively different effects oil U. V.-damage, mainly causing the inhibition or stimulation of enzymes in the yeast cells.

• East Asian mathematical journal
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• v.14 no.1
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• pp.15-20
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• 1998

Obtained the conditions for the product UV of two fuzzy subgroups U and V to be a fuzzy subgroup. Moreover, given an example of two fuzzy subgroups U and V which their product UV does not intersect neither U nor V.