• 충청수학회지
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• 제17권2호
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• pp.111-124
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• 2004

In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weak-compatibility in D-metric space which improves and generalizes the above mentioned result.

• Journal of Astronomy and Space Sciences
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• 제22권1호
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• pp.21-34
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• 2005

본 연구에서는 타원궤도상에서 위성의 편대비행을 유지하기 위하여 필요한 포기조건을 결정하고자 한다. 타원궤도일 경우 Hill 방정식으로는 위성간의 상대운동을 기술할 수 없기 때문에, Hill 방정식의 초기조건에 비선형성과 이심률에 대한 보정을 하여 얻은 새로운 운동방정식을 사용했다. 편대비행에서 상대적 거리를 유지하기 위하여 주위성과 부위성의 평균각속도를 일치시키는 구속조건을 이용했다. 이 구속조건은 J2 섭동항을 고려한 것이므로, 이 구속조건을 만족하는 편대비행의 초기조건은 타원궤도에서의 위성편대비행을 유지하는데 잘 적용될 수 있다. 타원궤도에서의 상대운동방정식 초기조건에 J2 섭동을 고려한 구속조건을 적용할 때, 이심률이 0.05 이하이고 위성간의 상대거리가 0.5km 정도인 경우만이 주기적으로 일정하게 간격이 유지되는 결과를 얻을 수 있다. 따라서 이심률이 크지 않은 타원궤도에서는 평균각속도 일치의 구속조건을 사용하여 위성간의 상대거리를 유지할 수 있었다. 이러한 결과를 이용하여 타원궤도에서의 위성편대비행을 위한 효율적인 초기조건을 제공할 수 있고, 위성편대비행의 운용에 있어서 비용을 절감할 수 있는 방법을 제시할 수 있다.

• 대한수학회논문집
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• 제32권4호
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• pp.899-908
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• 2017

We call a sequence $(T_n)_n$ of bounded operators on a Banach space X, BSC-Sequence if it is a Cauchy sequence in the strong operator topology and is uniformly bounded below. We determine conditions under which such sequences has a fixed point.

• 충청수학회지
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• 제18권1호
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• pp.51-64
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• 2005

The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.

• Journal of Positioning, Navigation, and Timing
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• 제12권3호
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• pp.215-228
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• 2023

The State Space Representation (SSR) method provides individual corrections for each Global Navigation Satellite System (GNSS) error components. This method can lead to less bandwidth for transmission and allows selective use of each correction. Precise Point Positioning (PPP) - Real-Time Kinematic (RTK) is one of the carrier-based precise positioning techniques using SSR correction. This technique enables high-precision positioning with a fast convergence time by providing atmospheric correction as well as satellite orbit and clock correction. Currently, the positioning service that supports PPP-RTK technology is the Quazi-Zenith Satellite System Centimeter Level Augmentation System (QZSS CLAS) in Japan. A system that provides correction for each GNSS error component, such as QZSS CLAS, requires monitoring of each error component to provide reliable correction and integrity information to the user. In this study, we conducted an analysis of the performance of residual error bounding for each error component. To assess this performance, we utilized the correction and quality indicators provided by QZSS CLAS. Performance analyses included the range domain, dispersive part, non-dispersive part, and satellite orbit/clock part. The residual root mean square (RMS) of CLAS correction for the range domain approximated 0.0369 m, and the residual RMS for both dispersive and non-dispersive components is around 0.0363 m. It has also been confirmed that the residual errors are properly bounded by the integrity parameters. However, the satellite orbit and clock part have a larger residual of about 0.6508 m, and it was confirmed that this residual was not bounded by the integrity parameters. Users who rely solely on satellite orbit and clock correction, particularly maritime users, thus should exercise caution when utilizing QZSS CLAS.

• 천문학회보
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• 제35권2호
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• pp.54-54
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• 2010

Interplanetary space is filled with dust particles originating mainly from comets and asteroids. Such interplanetary dust particles lose their angular momentum by olar radiation pressure, causing the dust grains to slowly spiral inward Poynting-Robertson effect). As dust particles move into the Sun under the influence of Poynting-Robertson drag force, they may encounter regions of resonance just outside planetary orbits, and be trapped by their gravities, forming the density enhancements in the dust cloud (circumsolar resonance ring). The circumsolar resonance ring near the Earth orbit was detected in the zodiacal cloud through observations of infrared space telescopes. So far, there is no observational evidence other than Earth because of the detection difficulty from Earth bounded orbit. A Venus Climate Orbiter, AKATSUKI, will provide a unique opportunity to study the Venusian resonance ring. It equips a near-infrared camera for the observations of the zodiacal light during the cruising phase. Here we consider whether Venus gravity produces the circumsolar resonance ring around the orbit. We thus perform the dynamical simulation of micron-sized dust particles released outside the Earth orbit. We consider solar radiation pressure, solar gravity, and planetary perturbations. It is found that about 40 % of the dust particles passing through the Venus orbit are trapped by the gravity. Based on the simulation, we estimate the brightness of the Venusian resonance ring from AKATSUKI's locations.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제5권
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.

• 대한수학회보
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• 제42권4호
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• pp.807-815
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• 2005

Let R be a ring with identity, X the set of all nonzero, nonunits of Rand G the group of all units of R. We will consider two group actions on X by G, the regular action and the conjugate action. In this paper, by investigating two group actions we can have some results as follows: First, if G is a finitely generated abelian group, then the orbit O(x) under the regular action on X by G is finite for all nilpotents x $\in$ X. Secondly, if F is a field in which 2 is a unit and F $\backslash\;\{0\}$ is a finitley generated abelian group, then F is finite. Finally, if G in a unit-regular ring R is a torsion group and 2 is a unit in R, then the conjugate action on X by G is trivial if and only if G is abelian if and only if R is commutative.

• East Asian mathematical journal
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• 제22권1호
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• pp.35-51
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• 2006

This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.