• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.185-199
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• 2020

In this paper, we introduce the definitions of s_p-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, s_p-convergence, s_∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study s_p-convergence, s_∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define s_p-closed sets, s_∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.135-149
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• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• Journal of the Korean Society of Physical Medicine
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• v.7 no.2
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• pp.173-182
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• 2012

Purpose : This study was investigated the effect of lower extremity muscle activity during open kinetic chain exercise (OKC) and closed kinetic exercise (CKC) in normal young adults. Methods : The participants were consisted of forty-one. All subjects were randomly assigned to two groups of open kinetic chain exercise group (n=21) and closed kinetic chain exercise group(n=20). It was perform 3 sets, 3 times per week for 6 weeks both open kinetic chain exercise group and closed kinetic chain exercise group. Subjects were assessed for each subject took pre-test, post-test in 2 weeks, post-test in 4 weeks, post-test in 6 weeks measurement the surface EMG data for vastus medialis and lateralis, lateral and medial hamstring, lateral and medial gastrocnemius, tibialis anterior. Results : The vastus medialis and lateralis muscle activity was significantly increased within the intervention period both group(p<.05). The lateral and medial part of hamstring muscle activity was significantly increased with in the intervention period(p<.05). The tibialis anterior muscle activity of open kinetic chain exercise group and closed kinetic chain exercise group was significantly increased in the intervention period(p<.05). The lateral and medial part of gastrocnemius muscle activity of open kinetic chain exercise group and closed kinetic chain exercise group was significantly increased with in the intervention period(p<.05). Conclusion : It was found that both open kinetic chain exercise and closed kinetic chain exercise was significantly increased muscle activity. Further studies are needed to analyzed long term effects and subjects resulting from these changed. these exercises can be selectively adapted not only as treatment exercise for patients but also as preventive exercise for normal person to improve balancing ability by conducting proper amount of exercise for each individual's condition and stage.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.27-33
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• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.157-178
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• 2019

The present correspondence is conveyed on to consider the fascinating and novel characteristics of radiative hydromagnetic convective flow of a chemically reacting fluid over an exponentially accelerated inclined porous plate. Exact solutions for the fluid velocity, temperature and species concentration, under Boussinesq approximation, are obtained in closed form by the two term perturbation technique. The interesting parts of thermal dispersing outcomes are accounted in this correspondence. Graphical evaluation is appeared to depict the trademark direct of introduced parameters on non dimensional velocity, temperature and concentration profiles. Also, the numerical assortment for skin friction coefficient, Nusselt number and Sherwood number is examined through tables. The certification of current examination is confirmed by making an examination with past revelations available in composing, which sets a benchmark for utilization of computational approach.

• Journal of Korean Society of Environmental Engineers
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• v.29 no.8
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• pp.895-903
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• 2007

As for the increasing demanding on the development of direct-ecological landfill monitoring methods, it is needed for critically defining the condition of landfills and their influence on the environment, quantifying the amount of enzymes and bacteria mainly concerned with biochemical reaction in the landfills. This study was thus conducted to understand the fates of contaminants in association with groundwater quality parameters. For the study, groundwater was seasonally sampled from four closed unsanitary landfills(i.e. Cheonan(C), Wonju(W), Nonsan(N), Pyeongtaek(P) sites) in which microbial diversity was simultaneously obtained by 16S rDNA methods. Subsequently, a number of primer sets were prepared for quantifying the specific gene of representative bacteria and the gene of encoding enzymes dominantly found in the landfills. The relationship between water quality parameters and gene quantification were compared based on correlation factors. Correlation between DSR(Sulfate reduction bacteria) gene and BOD(Biochemical Oxygen Demand) was greater than 0.8 while NSR(Nitrification bacteria-Nitrospira sp.) gene and nitrate were related more than 0.9. A stabilization indicator(BOD/COD) and MTOT(Methane Oxidation bacteria), MCR(Methyl coenzyme M reductase), Dde(Dechloromonas denitrificans) genes were correlated over 0.8, but ferric iron and Fli(Ferribacterium limineticm) gene were at the lowest of 0.7. For MTOT, it was at the highest related at 100% over BOD/COD. In addition, anaerobic genes(i.e., nirS-Nitrite reductase, MCR. Dde, DSR) and DO were also related more than 0.8, which showing anaerobic reactions generally dependant upon DO. As demonstrated in the study, molecular biological investigation and water quality parameters are highly co-linked, so that quantitative real-time PCR could be cooperatively used for assessing landfill stabilization in association with the conventional monitoring parameters.