• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.679-688
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• 1995

Let $(B, \left\$\mid$ \right\$\mid$)$ be a real separable Banach space. Let $(\Omega, F, P)$ denote a probability space. A random elements in B is a function from $\Omega$ into B which is $F$-measurable with respect to the Borel $\sigma$-field $B$(B) in B.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.15-25
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• 2024

In this paper, we obtain common fixed point theorems for three mappings of contractive type in the setting of generalized modular metric spaces. Our results generalize many results available in the literature including common fixed point theorems.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.613-618
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• 1996

In this paper, M will always denote an n- dimensional complete Riemannian manifold and $\omega_n$ is the volume of $S^n$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.8B
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• pp.636-645
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• 2008

Most of routing schemes that protect the source's location from a malicious attacker usually make use of a path of a long length per message for the sake of lengthening the safety period. The biggest problem to such approaches is taking a very long latency in transferring messages to the destination. In this paper we show the problem to find the least-cost single path that is enough to keep the source-location always secure from the attacker, provided that it is used for the delivery of a set of messages given in priori, is NP-complete. Consequently we propose a routing protocol GSLP-w(GPSR-based Source-Location Privacy with crew size co) that is a trade-off between two extreme approaches. The advantage of GSLP-co lies in its enhanced safety period for the source and its lowered delivery latency in messaging. We consider NSP(Normalized Sefety Period) and NDL(Normalized Delivery Latency), measured in terms of the least number of hops to the destination, to achieve tangible interpretation of the results. We ran a simulation to confirm our claim by generating 100 topologies of 50,000 nodes with the average number of neighbors being 8. The results show that GSLP-$\omega$ provides more enhanced NSP compared to other protocols GSLP, an earlier version of GSLP-$\omega$, and PR-SP(Phantom Routing - Single Path), the most notable existing protocol for the source-location privacy, and less NDL than that of GSLP but more than that of PR-SP.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.4
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• pp.253-258
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• 2003

We consider the problem of grouping orders into lots. The problem is modelled by a graph G=(V,E), where each node ${\nu}{\in}V$ denotes order specification and its weight ${\omega}(\nu)$ the orders on hand for the specification. We can construct a lot simply from orders of single specification. For a set of nodes (specifications) ${\theta}{\subseteq}V$, if the distance of any two nodes in $\theta$ is at most d, it is also possible to make a lot using orders on the nodes. The objective is to maximize the number of lots with size exactly $\lambda$. In this paper, we prove that our problem is NP-Complete when $d=2,{\lambda}=3$ and each weight is 0 or 1. Moreover, it is also shown to be NP-Complete when $d=1,{\lambda}=3$ and each weight is 1,2 or 3.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.3
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• pp.325-331
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• 2018

This paper deals with the dynamical analysis of a vessel that leads to capsize in regular beam seas. The complete investigation of nonlinear behaviors includes sub-harmonic motion, bifurcation, and chaos under variations of control parameters. The vessel rolling motions can exhibit various undesirable nonlinear phenomena. We have employed a linear-plus-cubic type damping term (LPCD) in a nonlinear rolling equation. Using the fourth order Runge-Kutta algorithm with the phase portraits, various dynamical behaviors (limit cycles, bifurcations, and chaos) are presented in beam seas. On increasing the value of control parameter ${\Omega}$, chaotic behavior interspersed with intermittent periodic windows are clearly observed in the numerical simulations. The chaotic region is widely spread according to system parameter ${\Omega}$ in the range of 0.1 to 0.9. When the value of the control parameter is increased beyond the chaotic region, periodic solutions are dominant in the range of frequency ratio ${\Omega}=1.01{\sim}1.6$. In addition, one more important feature is that different types of stable harmonic motions such as periodicity of 2T, 3T, 4T and 5T exist in the range of ${\Omega}=0.34{\sim}0.83$.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.20 no.1
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• pp.55-60
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• 2017

Intestinal hypoganglionosis is a rare innervation disorder that provides numerous nutritional, medical and surgical challenges. In this case report, we present a case of a newborn with intestinal hypoganglionosis leading to intestinal failure and intestinal failure-associated liver disease who responded to $Omegaven^{TM}$, a fat emulsion comprised of omega-3 fatty acids. $Omegaven^{TM}$ has been shown to be beneficial in the management of cholestatic liver injury. Clinical success with $Omegaven^{TM}$ was seen in this patient with a clear decrease in aspartate aminotransferase, alanine aminotransferase, alkaline phosphatase and complete resolution of cholestasis with a direct bilirubin of zero within two weeks of initiation of $Omegaven^{TM}$. No current guidelines for the diagnosis and management of hypoganglionosis are available. We recommend a multidisciplinary approach and the use of novel therapies such as fat emulsions composed of omega-3 fatty acids for improved patient outcomes. Appropriate compassionate use protocols should be obtained from the Food and Drug Administration prior to initiation of $Omegaven^{TM}$.

• Economic and Environmental Geology
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• v.28 no.5
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• pp.527-533
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• 1995

A disadvantage of Fourier analysis is that frequency information can only be extracted for the complete duration of a signal f(t). Since the Fourier transform integral extends over all time, from $-{\infty}$ to $+{\infty}$), the information it provides arises from an average over the whole length of the signal. If there is a local oscillation representing a particular feature, this will contribute to the calculated Fourier transform $F({\omega})$, but its location on the time axis will be lost There is no way of knowing whether the value of $F({\omega})$ at a particular ${\omega}$ derives from frequencies present throughout the life of f(t) or during just one or a few selected periods. This disadvantage is overcome in wavelet analysis which provides an alternative way of breaking a signal down into its constituent parts. The main advantage of the wavelet transform over the conventional Fourier transform is that it can not only provide the combined temporal and spectral features of the signal, but can also localize the target information in the time-frequency domain simultaneously. The wavelet transform distinguishes itself from Short Time Fourier Transform for time-frequency analysis in that it has a zoom-in and zoom-out capability.