• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.589-596
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• 2013

This paper is an attempt to study and introduce the notion of ${\omega}$-dense set in weak structures and the notion of m-dense set in minimal structures. We have also investigate the relationships between ${\omega}$-dense sets, $m$-dense sets, ${\sigma}({\omega})$ sets, ${\pi}({\omega})$ sets, $r({\omega})$ sets, ${\beta}({\omega})$ sets, m-semiopen sets and $m$-preopen sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1341-1356
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• 2018

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.53-67
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• 2019

The notions of closed elements and dense elements are introduced in BE-algebras. Characterization theorems of closed elements and closed filters are obtained. The notion of dense elements is introduced in BE-algebras. Dense BE-algebras are characterized with the help of maximal filters and congruences. The concept of D-filters is introduced in BE-algebras. A set of equivalent conditions is derived for every D-filter to become a closed filter.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.477-484
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• 2007

Let h : M ${\rightarrow}$ M be an almost periodic homeomorphism of a compact metric space M onto itself. We prove that h is topologically transitive iff every element of M has a dense orbit. It follows as a corollary that an almost periodic homeomorphism of a compact metric space onto itself can not be chaotic. Some additional related observations on a Cantor set are made.

• Journal of The Korean Astronomical Society
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• v.26 no.2
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• pp.99-101
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• 1993

We have searched for the 2 mm transitions of $H_2COH^+(2_{02}-1_{01})$ and $H_2\;^{13}CO(2_{02} - 1_{01},\; 2_{12}-1_{11},\;and\;2_{11}-1_{10})$ toward the dense interstellar molecular clouds Orion A, TMC-1 and L134N using the FCRAO 14 m telescope. None of the transitions have been detected except the $H_2\;^{13}CO$ transitions toward Orion-KL. We set upper limits for the abundances of the protonated formaldehyde ion $(H_2COH^+)$, which are close to the abundances expected from ion-molecule chemistry.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.1
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• pp.45.1-45.1
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• 2018

Formation of filaments and subsequent dense cores in ISM is one of the essential questions to address in star formation. To investigate this scenario in detail, we recently started a molecular line survey namely 'Filaments, the Universal Nursery of Stars (FUNS)' toward nearby filamentary clouds in Gould Belt using TRAO 14m single dish telescope equipped with a 16 multi-beam array. In the present work, we report the first look results of kinematics of a low mass star forming region L1478 of California molecular cloud. This region is found to be consisting of long filaments with a hub-filament structure. We performed On-The-Fly mapping observations covering ~1.1 square degree area of this region using C18O(1-0) as a low density tracer and 0.13 square degree area using N2H+(1-0) as a high density tracer, respectively. CS (2-1) and SO (32-21) were also used simultaneously to map ~290 square arcminute area of this region. We identified 10 filaments applying Dendrogram technique to C18O data-cube and 13 dense cores using FellWalker and N2H+ data set. Basic physical properties of filaments such as mass, length, width, velocity field, and velocity dispersion are derived. It is found that filaments in L~1478 are velocity coherent and supercritical. Especially the filaments which are highly supercritical are found to have dense cores detected in N2H+. Non-thermal velocity dispersions derived from C18O and N2H+ suggest that most of the dense cores are subsonic or transonic while the surrounding filaments are transonic or supersonic. We concluded that filaments in L~1478 are gravitationally unstable which might collapse to form dense cores and stars. We also suggest that formation mechanism can be different in individual filament depending on its morphology and environment.

• Korean Journal of Digital Imaging in Medicine
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• v.12 no.1
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• pp.33-41
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• 2010

National Cancer Screening Project and Korean Society of Breast Imaging recommend that breast cancer screening should be performed on those aged 40 and above. Nevertheless, this recommendation is usually ignored by a number of medical institutions. The purpose of this study is to emphasize the necessity of an age limitation in screening mammography. Ten institutions were randomly selected and telephone inquiries about patients' age limitation and internal guidelines were set up. The 3,214 women, who underwent screening mammography through 'GE Senography 2000D' in each hospital, were classified into five groups according to age(from 20s to 40s, at intervals of 5). And then, collected data was analyzed by a radiologist in accordance with ACR-BIRADS(American College of Radiology Breast Imaging Reporting and Data System), through which breast parenchymal density and the results of analysis were categorized in order to predict the sensitivity of mammography. Information about craniocaudal-view mammograms was automatically produced by use of GE Senography 2000D, and the average glandular dose was retrospectively analyzed through the program 'Excel 2007.' Two institutions did not set the age limitation. Other seven institutions internally allowed those who wanted to receive mammography regardless of age. Approximately 99% of those aged 20 to 29 were judged as having the dense breast. In those aged 35 to 39, breast parenchymal density tended to be lower, but the fatty breast to increase. In the case of 'category-zero' that does not need additional tests, the rate of 'heterogeneously dense' and 'extremely dense' reached to 83.1% and 15.1% respectively. Regarding dense breasts, there was no sufficient information for image reading. The glandular dose, applied to 3,214, was 1.47mGy on the average. In those aged 20 to 24 who are sensitive to radiation, the average glandular dose indicated 1.59mGy. Those aged 35 and above showed the lowest value, 1.43mGy. In those aged 35 to 39, the breast tended to change from denseness to fattiness. The average glandular dose was lowest in those aged 35 and above, which suggests that screening mammography should be periodically performed on those aged 35 and above in order that breast cancer may be early detected. On the other hand, in those aged less than 35, it is difficult to analyze mammograms due to the high density of breast parenchyma, and also retakes become frequent. In particular, subjects may be exposed to excessive doses. Accordingly, it should be substituted by breast self-examination or clinical breast examination. In case of need, it is advisable to perform ultrasonography.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• East Asian mathematical journal
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• v.23 no.1
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• pp.83-101
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• 2007

In this paper the concept of somewhat pairwise fuzzy continuous functions and somewhat pairwise fuzzy open functions are introduced. Some interesting properties of these functions are investigated besides giving some characterizations of these functions.