• Journal of the Chungcheong Mathematical Society
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• v.17 no.2
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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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• v.22 no.1
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• pp.21-34
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• 2005

The initial conditions that generate bounded motion in eccentric reference orbit are determined for satellite formation flying. Because Hill's equations cannot describe the relative motion between two satellites in eccentric orbit, a new relative dynamics utilizing the nonlinearity and eccentricity correction for Hill's initial conditions is implemented. The constraint that matches angular rates of chief and deputy satellites is used to obtain the bounded motion between them. The constraint can be applied to satellite formation motions in eccentric orbit, since it implicates J2 perturbation due to the central body's aspherical gravitational forces. The periodic bounded motions are analyzed for the orbit with the eccentricity of less than 0.05 and about 0.5 km relative distance between chief and deputy satellites. It is mainly illustrated that the satellite formations in small eccentric orbits can have hounded motions; consequently, the formation can be kept by matching angular rates of the satellites. These results demonstrate an useful method that reduces the cost for operating satellites by providing effective initial conditions for satellite formation flying in eccentric orbit.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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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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• v.12 no.3
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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.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.2
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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.

• Communications of Mathematical Education
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• v.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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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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• v.22 no.1
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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.