• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.39-57
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• 1978

It is given in the Lecture Note [1] of Berger, Gauduchon and Mazet that, if ${\pi}$n: (${\tilde{M}}$, ${\tilde{g}}$)${\rightarrow}$(${\tilde{M}}$, ${\tilde{g}}$) is a Riemannian submersion with totally geodesic fibers, ${\Delta}$ and ${\tilde{\Delta}}$ are Laplace operators on (${\tilde{M}}$, ${\tilde{g}}$) and (M, g) respectively and f is an eigenfunction of ${\Delta}$, then its lift $f^L$ is also an eigenfunction of ${\tilde{\Delta}}$ with the common eigenvalue. But such a simple relation does not hold for an eigenform of the Laplace-Beltrami operator ${\Delta}=d{\delta}+{\delta}d$. If ${\omega}$ is an eigenform of ${\Delta}$ and ${\omega}^L$ is the horizontal lift of ${\omega}$, ${\omega}^L$ is not in genera an eigenform of the Laplace-Beltrami operator ${\tilde{\Delta}}$ of (${\tilde{M}}$, ${\tilde{g}}$). The present author has obtained a set of formulas which gives the relation between ${\tilde{\Delta}}{\omega}^L$ and ${\Delta}{\omega}$ in another paper [7]. In the present paper a Sasakian submersion is treated. A Sasakian manifold (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$) considered in this paper is such a one which admits a Riemannian submersion where the base manifold is a Kaehler manifold (M, g, J) and the fibers are geodesics generated by the unit Killing vector field ${\tilde{\xi}}$. Then the submersion is called a Sasakian submersion. If ${\omega}$ is a eigenform of ${\Delta}$ on (M, g, J) and its lift ${\omega}^L$ is an eigenform of ${\tilde{\Delta}}$ on (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$), then ${\omega}$ is called an eigenform of the first kind. We define a relative eigenform of ${\tilde{\Delta}}$. If the lift ${\omega}^L$ of an eigenform ${\omega}$ of ${\Delta}$ is a relative eigenform of ${\tilde{\Delta}}$ we call ${\omega}$ an eigenform of the second kind. Such objects are studied.

• Ocean and Polar Research
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• v.31 no.1
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• pp.51-61
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• 2009

In this study we define the two different types of El $Ni{\tilde{n}}o$, i.e., the eastern Pacific El $Ni{\tilde{n}}o$ (i.e., EP-El $Ni{\tilde{n}}o$) versus the central Pacific El $Ni{\tilde{n}}o$ (i.e., CP-El $Ni{\tilde{n}}o$), during the boreal summer (June-July-August, JJA) and winter (December-January-February, DJF) using the two NINO indices in the tropical Pacific. The two different types of El $Ni{\tilde{n}}o$ significantly differ in terms of the location of the maximum anomalous sea surface temperature (SST) in the tropical Pacific. The CP-El $Ni{\tilde{n}}o$ has been observed more frequently during recent decades compared to the EP-El $Ni{\tilde{n}}o$. In addition, our analysis indicates that the statistics of CP-El $Ni{\tilde{n}}o$ during JJA is closely associated with the warming trend in the central equatorial Pacific. We also examine the different responses of the East Asian marginal SST to the two types of El $Ni{\tilde{n}}o$ during JJA and DJF. The CP-El $Ni{\tilde{n}}o$ during both JJA and DJF is concurrent with warm SST anomalies around the Korean Peninsula including the East China Sea, which is in contrast to the EP-El $Ni{\tilde{n}}o$. Such different responses are associated with the difference in tropics/mid-latitude teleconnections via atmosphere between the two types of El $Ni{\tilde{n}}o$. Furthermore, our results indicate that atmospheric diabatic forcing in relation to the precipitation variability is different in the tropical Pacific between the EP-El $Ni{\tilde{n}}o$ and the CP-El $Ni{\tilde{n}}o$.

• Atmosphere
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• v.23 no.1
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• pp.63-71
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• 2013

KMA is operationally monitoring El Ni$\tilde{n}$o and La Ni$\tilde{n}$a events, which have tremendous impacts on global climate. Many scientific studies have used to define onset of El Ni$\tilde{n}$o and La Ni$\tilde{n}$a events based on the moving average and persistency of SST indices, and KMA has adopted such definition. Though the definition has been widely accepted, in the operational aspect there is a critical problem to use moving average and condition for the persistence. Because the future values for the SST indices cannot be used in the operational monitoring, the onset timing in El Ni$\tilde{n}$o and La Ni$\tilde{n}$a can be significantly delayed. We suggest here an appropriate definition of El Ni$\tilde{n}$o and La Ni$\tilde{n}$a events in the operational aspect. Instead of using the moving average and the condition for the persistence, the onset is defined based on NINO3.4 SST during last 3 months. In order to compare the new definition with the current KMA definition, we applied them to recent 60-years SST data. It is clear that the new definition can declare the onset timing of El Ni$\tilde{n}$o and La Ni$\tilde{n}$a several months earlier than that of the KMA definition. It suggest that the new definition is more appropriate to the operational monitoring on El Ni$\tilde{n}$o and La Ni$\tilde{n}$a.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.197-197
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• 2012

본 연구에서는 대기 순환패턴 및 수문 환경변화에 영향을 미치는 주요인자인 El Ni$\tilde{n}$o-Southern Oscillation (ENSO)의 서로 다른 형태인 Warm-pool (WP) El Ni$\tilde{n}$o, Cold-tongue (CT) El Ni$\tilde{n}$o에 따른 한강유역의 봄철 (March~May)과 여름철 (June~August) 강수 및 유출의 특성을 분석하였다. 봄철 강수량의 경우, WP El Ni$\tilde{n}$o 시기에 증가추세를 보이며, 강수의 변동특성 또한 크게 나타났다. 여름철 강수량의 경우, CT El Ni$\tilde{n}$o 시기에는 평년보다 대체로 건조한 경향을 보이나, WP El Ni$\tilde{n}$o 시기에는 유역 전체에서 습한 경향을 보였으며 강수의 변동성은 매우 작은 것으로 분석되었다. 봄철 유출량의 경우, CT El Ni$\tilde{n}$o 시기와 WP El Ni$\tilde{n}$o 시기에 모두 평년치보다 크게 나타났으며, WP El Ni$\tilde{n}$o 시기에 한강 남부 대부분 유역에서 유출량이 통계적으로 유의한 증가 경향을 보였다. 여름철 유출량의 경우, CT El Ni$\tilde{n}$o 시기에는 대부분 유역에서 평년치보다 감소하나 수문 변량의 변동성은 큰 것으로 분석되었다. WP El Ni$\tilde{n}$o 시기에는 거의 모든 유역에서 유출이 증가하는 것으로 나타났으며, 특히 13개 중권역에서는 유출의 변동성이 작고 통계적으로 유의한 증가패턴이 분석되었다. 따라서 본 연구는 서로 다른 두가지 형태의 El Ni$\tilde{n}$o패턴에 대하여 한강유역의 봄철과 여름철 수자원 변동성에 민감하게 영향을 미치고 있음을 확인하였으며 수자원의 효율적인 예측 및 관리와 안정적인 용수공급을 위한 수문기상인자와 수문자료간의 관계 규명에 유용하게 활용될 것으로 기대한다.

• Atmosphere
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• v.22 no.4
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• pp.465-472
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• 2012

Using various observed data, we examined the evolution of tropical Pacific sea surface temperature (SST) during 2011-2012, with focusing on the development of 2012 El Ni$\tilde{n}$o. It is observed that a La Ni$\tilde{n}$a event during 2011 was followed by a moderate El Ni$\tilde{n}$o during 2012 summer. The 2012 summer El Ni$\tilde{n}$o initiated near the west coast of South America on February 2012, and continued to expand westward till August. Given this evolutionary pattern, the 2012 summer El Ni$\tilde{n}$o can be categorized as 'Eastern Pacific (EP) El Ni$\tilde{n}$o' because Ni$\tilde{n}$o-3 index is greater than Ni$\tilde{n}$o-4 index, and it may be the first well-defined EP El Ni$\tilde{n}$o since 2001. On February 2012, this event was initiated mainly by the local air-sea interaction, and at the same time the ocean heat content was accumulated over the tropical western Pacific due to the easterly wind anomaly over the tropical western Pacific. Then, the accumulated heat content slowly propagates to the tropical eastern Pacific, which attributes to maintain El Ni$\tilde{n}$o state during 2012 summer. After August, the positive SST anomaly over the equatorial eastern Pacific decays possibly due to the exhausted heat content and the weakening of air-sea interaction, but the weak positive SST anomaly over the central Pacific remains till now (2012 November).

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.121-136
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• 1996

Met $\tilde{M} = (\tilde{M}, \tilde{J}, <>)$ be an almost Hermitian manifold and M a submanifold of $\tilde{M}$. According to the behavior of the tangent bundle TM with respect to the action of $\tilde{J}$, we have two typical classes of submanifolds. One of them is the class of almost complex submanifolds and another is the class of totally real submanifolds. In 1990, B. Y. Chen [4], [5] introduced the concept of the class of slant submanifolds which involve the above two classes. He used the Wirtinger angle to measure the behavior of TM with respect to the action of $\tilde{J}$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.1-9
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• 2011

The notion of ${\tilde{g}}{\alpha}$-closed sets in a topological space introduced by R. Devi and A. selvakumar [2]. In this paper, we introduce the concept of ${\tilde{g}}{\alpha}$-US spaces by utilizing ${\tilde{g}}{\alpha}$-open sets and study the basic properties of this space.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.331-360
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• 2013

Let ${\sigma}_s(N)$ denote the sum of the sth powers of the positive divisors of a positive integer N and let $\tilde{\sigma}_s(N)={\sum}_{d|N}(-1)^{d-1}d^s$ with $d$, N, and s positive integers. Hahn [12] proved that $$16\sum_{k. In this paper, we give a generalization of Hahn's result. Furthermore, we find the formula ${\sum}_{k=1}^{N-1}\tilde{\sigma}_1(2^{n-m}k)\tilde{\sigma}_3(2^nN-2^nk)$ for $m(0{\leq}m{\leq}n)$.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.982-982
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• 2012

본 연구에서는 우리나라의 중 소규모 유역의 수문학적 위험도 분석을 위하여 한강유역을 대상으로 통합위험지수(IRI: Integrated Risk Index)를 산정하였으며, El Ni$\tilde{n}$o-Southern Oscillation (ENSO)에 의한 대규모 대기순환 패턴의 변화가 한강 유역의 통합위험지수 변화에 미치는 영향을 평가하였다. ENSO자료는 전통적인 El Ni$\tilde{n}$o에 해당하는 Cold-tongue (CT) El Ni$\tilde{n}$o와 중앙태평양 부근의 이상적인 해수면 온도 상승에 의한 Warm-pool (WP) El Ni$\tilde{n}$o, 그리고 해수면 온도가 이상적으로 낮게 관측되는 La Ni$\tilde{n}$a 기간으로 구분하였으며, 각 기간 중 가장 강한 ENSO가 발생한 해(CT El Ni$\tilde{n}$o, 1998; WP El Ni$\tilde{n}$o, 2005; La Ni$\tilde{n}$a, 2000)를 대상으로 통합위험지수를 산정하였다. 통합위험지수는 수문학적 요인(Hydrologic Components), 사회 경제적 요인(Socio-Economic Components)과 생태적 요인(Ecological Components)으로 구분하였고, 엔트로피(entropy) 기법을 통하여 각 인자와 요인별 가중치를 적용하였다. 중권역별 통합위험지수의 평가는 5개의 계급구간(Very High, High, Medium, Low, Very Low)으로 구분하였다. 분석결과, CT El Ni$\tilde{n}$o해의 유역평균 IRI 값은 0.58, WP El Ni$\tilde{n}$o해의 IRI 값은 0.57로 비슷한 결과를 보였으나, La Ni$\tilde{n}$a해에는 IRI 값이 0.41로 낮게 나타났다. CT와 WP El Ni$\tilde{n}$o해에는 한강 서쪽일부 중권역에서 통합위험지수가 높게 나타났으며, La Ni$\tilde{n}$a해에는 한강 중 동부 대부분 유역에서 낮게 분석되었다. 향후 유역별 통합위험지수 산정과 더불어 서로 다른 형태의 ENSO에 따른 수자원 변동 예측이 이루어진다면, 수자원의 효율적인 관리와 안정적인 용수공급에 도움을 줄 것으로 사료되며, 이는 유역별 수자원의 취약성 평가 및 위험도 분석을 위한 기초자료로 활용이 가능하리라 사료된다.

• Journal of Astronomy and Space Sciences
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• v.34 no.4
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• pp.257-270
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• 2017

Solar activity is known to be linked to changes in the Earth's weather and climate. Nonetheless, for other types of extreme weather, such as tropical cyclones (TCs), the available evidence is less conclusive. In this study the modulation of TC genesis over the western North Pacific by the solar activity is investigated, in comparison with a large-scale environmental parameter, i.e., El-$Ni{\tilde{n}}o$-Southern Oscillation (ENSO). For this purpose, we have obtained the best track data for TCs in the western North Pacific from 1977 to 2016, spanning from the solar cycle 21 to the solar cycle 24. We have confirmed that in the El-$Ni{\tilde{n}}o$ periods TCs tend to form in the southeast, reach its maximum strength in the southeast, and end its life as TSs in the northeast, compared with the La-$Ni{\tilde{n}}o$ periods. TCs occurring in the El-$Ni{\tilde{n}}o$ periods are found to last longer compared with the La-$Ni{\tilde{n}}o$ periods. Furthermore, TCs occurring in the El-$Ni{\tilde{n}}o$ periods have a lower central pressure at their maximum strength than those occurring in the La-$Ni{\tilde{n}}o$ periods. We have found that TCs occurring in the solar maximum periods resemble those in the El-$Ni{\tilde{n}}o$ periods in their properties. We have also found that TCs occurring in the solar descending periods somehow resemble those in the El-$Ni{\tilde{n}}o$ periods in their properties. To make sure that it is not due to the ENSO effect, we have excluded TCs both in the El-$Ni{\tilde{n}}o$ periods and in the La-$Ni{\tilde{n}}o$ periods from the data set and repeated the analysis. In addition to this test, we have also reiterated our analysis twice with TCs whose maximum sustained winds speed exceeds 17 m/s, instead of 33 m/s, as well as TCs designated as a typhoon, which ends up with the same conclusions.