• Korean Journal of Mathematics
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• v.23 no.2
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• pp.313-321
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• 2015

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 3-dimensional $^*g-ESX_3$ and to display a surveyable tnesorial representation of 3-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.751-766
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• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

• The KIPS Transactions:PartC
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• v.12C no.6 s.102
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• pp.793-798
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• 2005

We focus on the RP (Rendezvous Point) system model in the multicast network based on BcN (Broadband Convergence Network) integrating broadcasting, telecommunication and Internet with one. Based on the condition multiple queues with different service and single server, when the arrivals tome in group with the site of the group geometrically distributed, we define the relationship between incoming arrival rate and corresponding buffer size. We also investigate the Profit according to both Service Provider and Network Operator Then we make a decision whether a new service request is accepted or not based on given interning rate range.

• Journal of Korean Society on Water Environment
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• v.34 no.6
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• pp.642-649
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• 2018

The effect of gas sparging on sonochemical oxidation was investigated in a 300 kHz sonoreactor under various liquid height/volume conditions ($5{\sim}30{\lambda}$, 3.4 ~ 9.0 L), determined by the wavelength of the applied frequency. The electrical input power was maintained constant for all cases . Sonochemical activity drastically decreased from $15{\lambda}$ and the liquid height of $10{\lambda}$ was suggested as the optimal height for 300 kHz without gas sparging. In our previous research, the sonochemical activity observed was five-times higher when air sparging was applied for 36 kHz. On the other hand, no enhancement was obtained at 10, 15, 25 and $30{\lambda}$ using air sparging (1, 3, and 6 L/min) for 300 kHz in this study $20{\lambda}$ and optimization of gas sparging was conducted at $20{\lambda}$ using various gases including air, Ar, $O_2$, $N_2$, and mixtures of Ar and $O_2$. It was found that gas sparging using pure Ar or pure $O_2$ resulted in lower sonochemical activity compared to that of air sparging due to the imbalance between the intensity of cavitation phenomena and the generation of oxidizing radical species. Consequently, the gas mixture of $Ar:O_2$ = 80 % : 20 % (DO saturation ${\approx}100%$) was suggested as an optimal gas sparging condition.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.43.3-43.3
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• 2017

NGC 6822 is a dwarf irregular galaxy in the Local Group and it is located in 500 kpc, further than the Large Magellanic Cloud and the Small Magellanic Cloud. Therefore, we can study star-forming processes by local condition in NGC 6822 instead of tidal force of the Galactic gravitational field. Hubble V is the brightest of several H II complexes in this galaxy. We observed Hubble V by using IGRINS attached on the 2.7 m telescope at the McDonald Observatory in Texas, US in May 2016. We performed a spectral mapping of $15^{{\prime}{\prime}}{\times} 7^{{\prime}{\prime}}$area on H and K bands, and detected emission lines of bright $Br{\gamma}\;{\lambda}2.1661{\mu}m$ and weak He I ${\lambda}2.0587{\mu}m$. Molecular hydrogen lines of 1-0S(1) ${\lambda}2.1218{\mu}m$, 2-1 S(1) ${\lambda}2.2477{\mu}m$, and 1-0 S(0) ${\lambda}2.2227{\mu}m$ was also detected. These emission lines show the structure of an ionized core and excited surface of clouds by far-ultraviolet photons, photodissociation region (PDR). We present three-dimensional maps of emission line distributions through multi slit scanning data and compare these results with the previous study. This presentation shows the physical structure of the star-forming regions and we discuss a PDR model and an evolution of Hubble V complex.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.603-616
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• 2008

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1451-1470
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• 2020

We are concerned with the following elliptic equations: $$\{(-{\Delta})^s_pu={\lambda}f(x,u)\;{\text{in {\Omega}}},\\u=0\;{\text{on {\mathbb{R}}^N{\backslash}{\Omega}},$$ where λ are real parameters, (-∆)^s_p is the fractional p-Laplacian operator, 0 < s < 1 < p < + ∞, sp < N, and f : Ω × ℝ → ℝ satisfies a Carathéodory condition. By applying abstract critical point results, we establish an estimate of the positive interval of the parameters λ for which our problem admits at least one or two nontrivial weak solutions when the nonlinearity f has the subcritical growth condition. In addition, under adequate conditions, we establish an apriori estimate in L^∞(Ω) of any possible weak solution by applying the bootstrap argument.

• Tribology and Lubricants
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• v.16 no.6
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• pp.477-483
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• 2000

Rolling contact fatigue (RCF) tests were performed for two kinds of commercial silicon nitride balls using 4-Ball rolling contact fatigue life tester under EHL condition (Λ=8.9) and boundary lubrication condition (Λ=0.2). All the test balls were finished up to the dimensional accuracy of Grade 5 defined in KS B 2001 (Steel Balls for Ball Bearings) with a size of 8.731 mm. RCF tests were then conducted under the initial theoretical maximum contact stress 6.63 GPa and the spindle speed 10,000 rpm. All the test balls were not failed until 3.75 $\times$ 107 contact cycles and wear tracks of test balls were not conspicuous under EHL condition (Λ= 8.9). In the operations of low lambda regime (Λ= 0.2), all the test balls were surface damaged and high rolling wear resistance was achievable in fully densified using MgO 1 wt% and HIPed balls. Rolling wear of silicon nitride balls under boundary lubrication condition depend mainly on grain size and intergranular phase content of silicon nitride balls.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.51-54
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• 1983

Let M be a n-dimensional compact Riemannian manifold with sectional curvature bounded below by one. Then Li and Zhong[3], and Li and Treibergs [4] proved that if the first eigenvalue of the Laplacian .lambda.$_{1}$ is less than some universal constant and if n.leq.4, then M is diffeomorphic to the n-sphere S$^{n}$ . The purpose of this paper is to prove this pinching theorem for all n with some extra condition.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.11-17
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• 2002

In this paper we give several necessary and sufficient conditions for an operator on the Hilbert space to obey Browder's theorem. And it is shown that if S has totally finite ascent and $T{\prec}S$ then $f(T)$ obeys Browder's theorem for every $f{\in}H({\sigma}(T))$, where $H({\sigma}(T))$ denotes the set of all analytic functions on an open neighborhood of ${\sigma}(T)$.