• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.421-426
• /
• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• Journal of Photoscience
• /
• v.4 no.3
• /
• pp.97-103
• /
• 1997

The effect of temperature on the fluorescence quenching of 2-(4-Methoxyphenyl)-5-(1-naphthyl)-1,3,4-oxadiazole (MPNO1), 2-(4-Methoxyphenyl)-5-(2-naphthyl)-1,3,4-oxadiazote(MPNO2), by aniline, and 2-Phenylindole (2-PI) by CCk, in toluene by steady state method and in benzene by time-resolved method have been carried out in the temperature range 30 - 70$\circ$C. The Stem-Volmer (S-V) plots, I$_0$/I against quencher concentration [Q] at different temperanares show positive deviations. The fluorescence lifetimes determined at different temperatures show no systematic variations and the variations being within the experimental error, the average values of lifetimes $ $\tau$ (t) are taken for further calculations. Rate constants such as Stem-Volmer quenching constants K$_sv}$, quenching rate parameters k$_q$ and k'$_q$, static quenching constant V and kinetic distance r are determined using the modified Stem-Volmer equation and sphere of action static quenching model. In order to see whether the reactions are diffusion limited, equations k$_q$ = e$^{-Eq/RT}$ and k'$_q$ = e$^{-Eq/RT}$ are used to determine the values of E$_q$ and E'$_q$, the activation energies for collisional quenching and the values of E$_q$ are 14.53. 17.28 and 16.20 kJ mole$^{-1}$ for MPNO1, MPNO2 and 2-PI respectively and the values of E'$_q$ are 14.62 and 17.73 for MPNO1 and MPNO2 respectively. From the magnitudes of various quantities it has been concluded that the reactions are diffusion limited and the observed positive deviations in the S-V plot are due to static and dynamic quenching.

• Journal of Environmental Health Sciences
• /
• v.43 no.1
• /
• pp.1-22
• /
• 2017

'The worstest environment disaster', 'World's first biocide massacre', 'Home-based Sewol ferry disaster' are all phrases attached to the recent humidifier disinfectant disaster. In the spring of 2011, four of 8 pregnant women including 1 adult man passed away at a university hospital in Seoul due to breathing failure. Epidemiologic investigation conducted by the Korean CDC soon revealed the inhalation of humidifier disinfectant, which had been widely used in Korea during the winter, to be responsible for the disease. As well as lung fibrosis hardening of the lungs, other diseases including asthma, rhinitis, skin disease, liver disease, fetal disease or cancers have been researched for their relation with exposure to the products. By February 9, 2017, 5,342 cases had registered for health problems and 1,131 of them were already dead (20.8% mortality rate). Based on studies by government agencies and a telephone survey of the general population by Seoul National University and civic groups, around 20% of the general public of Korea has used these products. Since the market release of the first product by SK Chemical in 1994, over 7.1 million items from around 20 brands were sold up to 2011. Most of the products were manufactured by well-known large conglomerates such as SK, Lotte, Samsung, Shinsegye, LG, and GS, as well as some European companies including UK-based Reckitt Benckiser and TESCO, the German firm Henkel, the Danish firm KeTox, and an Irish company. Even though this disaster was unveiled in 2011 by the Korean government, the issue of the victims was neglected for over five years. In 2016, an unexpected but intensive investigation by prosecutors found that Reckitt Benckiser manipulated and concealed animal tests for its own brand and brought several university experts and company employees to court. The matter was an intense social issue in Korea from May to June with a surge in media coverage. The prosecutor's investigation and a nationwide boycott campaign organized by victims and environmental groups against Reckitt Benckiser, whose product had been used by more than 70% of victims, led to the producer's official apology and a compensation scheme. A legislative investigation organized after the April 2016 national election revealed the producers' faults and the government's responsibility, but failed to meet expectations. A special law for the victims passed the National Assembly in January 2017 and a punitive system together with a massive environmental epidemiology investigation are expected to be the only solutions for this tragedy. Sciences of medicine, toxicology and environmental health have provided decisive evidence so far, but for the remaining problems the perspectives of social sciences such as sociology and jurisprudence are highly necessary, similar to with the Minamata disease and Wonjin Rayon events. It may not be easy to follow this issue using unfamiliar terminology from medical and chemical science and the long, complicated history of the event. For these reasons the author has attempted to write this article in a question and answer format to render it easier to follow. The 17 questions are: Q1 What is humidifier disinfectant? Q2 What kind of health problems are caused by humidifier disinfectant? Q3 How many victims are there? Q4 What is the analysis of the 1,112 cases of death? Q5 What is the problem with the government's diagnostic criteria and the solution? Q6 Who made what brands? Q7 Has there been a recall? What is still on sale? Q8 Was safety not checked by any producers? Q9 What are the government's responsibilities? Q10 Is it true that these products were sold only in Korea? Q11 Why and how was it unveiled only in 2011 after 17 years of sales? Q12 What delayed the resolution of the victim issue? Q13 What is the background of the prosecutor's investigation in early 2016? Q14 Is it possible to report new victim cases without evidence of product purchase? Q15 What is happening with the victim issue? Q16 How does it compare with the cases of Minamata disease and Wonjin Rayon? Q17 Are there prevention measures and lessons?

• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.219-224
• /
• 2015

In this paper it is investigated as to when a nonempty invariant closed subset A of a $S^1$-space X containing the set of stationary points (S) can be the fixed point set of an equivariant continuous selfmap on X and such space X is said to possess the S-equivariant complete invariance property (S-ECIP). It is also shown that if X is a metric space and $S^1$ acts on $X{\times}S^1$ by the action $(x,p){\cdot}q=(x,p{\cdot}q)$, where p, $q{\in}S^1$ and $x{\in}X$, then the hyperspace $2^{X{\times}S^1}$ of all nonempty compact subsets of $X{\times}S^1$ has the S-ECIP.

• Tuberculosis and Respiratory Diseases
• /
• v.49 no.1
• /
• pp.49-59
• /
• 2000

Backgrounds : Recent cytogenetic studies indicated that long of the long arm of chromosome 5 is a frequent event in small cell lung canær (SCLC), suggesting the presence of a tumor suppressor gene in its place. To map the precise tumor-suppressor loci on the chromosome arm for further positional cloning efforts, we tested 15 primary SCLCs. Methods : The DNAs extracted from paraffin-embedded tissue blocks with primary tumor and corresponding control tissue were investigated. Nineteen polymorphic microsatellite markers located in the long arm of chromosome 5 were used in the microsatellite analysis. Results : We found that ten (66.7%) of 15 tumors exhibited LOH in at least one of tested microsatellite markers. Two (13%) of 10 tumors exhibiting LOH lost a larger area in chromosome 5q. LOH was observed in five common deleted regions at 5q. Among those areas, LOH between 5q34-qter and 5q35.2-35.3 was most frequent (75%). LOH was also observed in more than 50% of the tumors at four other regions, between 5q14-15 and 5q23-31, 5q31.1, 5q31.3-33.3, and 5q34-35. Three of 15 tumors exhibited shifted bands in at least one of the tested microsatellite markers. Shifted bands occurred in 2.5% (7 of 285) of the loci tested. Conclusion : Our data demonstrated that at least five tumor-suppressor loci exist in the long arm of chromosome 5 and that they may play an important role in small cell lung cancer tumorigenesis.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.1-16
• /
• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".

• Proceedings of the Korean Magnestics Society Conference
• /
• 2008.12a
• /
• pp.244.1-244.1
• /
• 2008

• Journal of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.861-877
• /
• 2010

The works of Erd$\ddot{o}$s et al. about expansions of 1 with respect to a non-integer base q, referred to as q-expansions, are investigated to determine how far they continue to hold when the number 1 is replaced by a positive number x. It is found that most results about q-expansions for real numbers greater than or equal to 1 are in somewhat opposite direction to those for real numbers less than or equal to 1. The situation when a real number has a unique q-expansion, and when it has exactly two q-expansions are studied. The smallest base number q yielding a unique q-expansion is determined and a particular sequence is shown, in certain sense, to be the smallest sequence whose corresponding base number q yields exactly two q-expansions.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.169-177
• /
• 2005

A Hilbert Space operator T is of class Q if $T^2{\ast}T^2-2T{\ast}T + I$ is nonnegative. Every paranormal operator is of class Q, but class-Q operators are not necessarily normaloid. It is shown that if a class-Q contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = $T^2{\ast}T^2-2T{\ast}T + I$ also is a proper contraction.

• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.1-11
• /
• 2021

In this paper, we define degenerate Carlitz-type twisted q-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz's type degenerate q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, symmetric properties, a connection with degenerate Carlitz-type twisted q-Euler numbers and polynomials.