• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1595-1603
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• 2022

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.94.1-94.1
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• 2011

Recurrent substorms occur when high-speed solar wind streamers pass by Earth's magnetosphere. Most of the previous researches have been done using the observations obtained at the geosynchronous orbit focusing on the relationship between the solar wind disturbances and the occurrence of substorms. However, it is important to investigate the dynamics of the magnetotail because the magnetotail is the place where substorms develop. In this study we investigated the observations of recurrent dipolarizations in the near-Earth magnetotail that occurred during high-speed solar wind streamers. The dipolarizations and subsequent stretchings have occurred for more than three days with the average period of ~2 - 3 hours. The average period of ~2 - 3 hours is consistent with the average occurrence period of recurrent substorms. Also, the observed signatures on the geosynchronous orbit and the ground show recurrent substorms have occurred during the event. These suggest that the recurrent dipolarizations in the near-Earth magnetotail should be closely related to the recurrent substorms. On the other hand, there was no clear flow activities directly associated with the dipolarizations, except for some intermittent bursty flow activities. We will discuss the detailed characteristics of the dipolarizations and the relationship with recurrent substorms.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.293-304
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• 2018

In this paper, we study ${\varphi}$-recurrent almost cosymplectic (${\kappa},{\mu}$)-space and prove that it is an ${\eta}$-Einstein manifold with constant coefficients. Next, we show that a three-dimensional locally ${\varphi}$-recurrent almost cosymplectic (${\kappa},{\mu}$)-space is the space of constant curvature.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.243-252
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• 2001

The purpose of this paper is to study some properties of n-dimensional recurrent space-like complex hypersurfaces in an (n+1)-dimensional semi-definite complex space form M(sub)0+t(sup)n+1 (c), t = 0 or 1, c$\neq$0.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.97-104
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• 2010

The article is devoted to exhibit some general properties of strong chain recurrent set and strong chain transitive components for a continuous map f on a compact metric space X. We investigate the relation between the weak shadowing property and strong chain transitivity. It is shown that a continuous map f from a compact metric space X onto itself with the average shadowing property is strong chain transitive.

• Journal of Astronomy and Space Sciences
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• v.20 no.2
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• pp.101-108
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• 2003

This study reports one approach for the classification of magnetic storms into recurrent patterns. A storm event is defined as a local minimum of Dst index. The analysis of Dst index for the period of year 1957 through year 2000 has demonstrated that a large portion of the storm events can be classified into a set of recurrent patterns. In our approach, the classification is performed by seeking a categorization that minimizes thermodynamic free energy which is defined as the sum of classification errors and entropy. The error is calculated as the squared sum of the value differences between events. The classification depends on the noise parameter T that represents the strength of the intrinsic error in the observation and classification process. The classification results would be applicable in space weather forecasting.

• East Asian mathematical journal
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• v.15 no.2
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• pp.337-344
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• 1999

If any geodesic on $F^n$ is also a geodesic on $\={F}^n$ and the inverse is true, the change $\sigma:L{\rightarrow}\={L}$ of the metric is called projective. In this paper, we will find the condition that a recurrent Finsler space remains to be a recurrent one under the projective change.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2089-2101
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• 2013

The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.37-45
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• 1980

The Riemannian space of recurrent curvature was defined and studied by Ruse [8] and Walker [10]. In 1963, $M{\acute{o}}or$ [4] generalised this idea for Finsler spaces and defined and studied Finsler spaces of recurrent curvature. These spaces for various curvature tensors have subsequently been studied by Mishra and Pande [1], Sen [9] and Misra [3] etc. The purpose of the present paper is to study Finsler space based on the recurrency of the curvature tensors derived from non-linear connections.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.331-338
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• 2000

In the present paper, we investigate a problem in a sym-metric Finsler space, which is a special space. First we prove that if a symmetric space remains to be a symmetric one under the Z-projective change, then the space is of zero curvature. Further we will study W-recurrent space and D-recurrent space under the pro-jective change.