• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.749-774
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• 2011

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.528-537
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• 2003

This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic Joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. After the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure Is carried out using Min-Max theory. Finally. one example using the optimal design is presented.

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.455-460
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• 2004

There have been many speculations about the presence of cosmic ray protons (CRps) in galaxy clusters over the past two decades. However, no direct evidence such as the characteristic $\gamma$-ray signature of decaying pions has been found so far. These pions would be a direct tracer of hadronic CRp interactions with the ambient thermal gas also yielding observable synchrotron and inverse Compton emission by additionally produced secondary electrons. The obvious question concerns the type of galaxy clusters most likely to yield a signal: Particularly suited sites should be cluster cooling cores due to their high gas and magnetic energy densities. We studied a nearby sample of clusters evincing cooling cores in order to place stringent limits on the cluster CRp population by using non-detections of EGRET. In this context, we examined the possibility of a hadronic origin of Coma-sized radio halos as well as radio mini-halos. Especially for mini-halos, strong clues are provided by the very plausible small amount of required CRp energy density and a matching radio profile. Introducing the hadronic minimum energy criterion, we show that the energetically favored CRp energy density is constrained to $2\%{\pm}1\%$ of the thermal energy density in Perseus. We also studied the CRp population within the cooling core region of Virgo using the TeV $\gamma$-ray detection of M 87 by HEGRA. Both the expected radial $\gamma$-ray profile and the required amount of CRp support this hadronic scenario.