• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.137-145
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• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• Journal of English Language & Literature
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• v.58 no.1
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• pp.69-91
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• 2012

Marina Carr's By the Bog of Cats.... (1998) is the last play of the trilogy of "the midlands plays" which can be regarded as her re-writing of both Euripides' Medea and J. M. Synge's The Playboy of the Western World by resetting the two plays in the midlands of contemporary Ireland. Carr intends to courageously explore into the dangerous liminal space, i.e., the middle between the past and the present, the high Greek and the Irish folk culture, dealing with the ghosts of the dead writers for her own Irish feminist theatre. Thus, in the middle Carr can build a new Irish theatre by minorating and abjecting the Greek tragedy and subverting and expanding Synge's theatre of grotesque realism. This paper attempts to read By the Bog of Cats... as Carr's final project of exploration into the midland of Ireland to establish a new Irish feminist theatre and at the same time a new Irish folk theatre. By focusing on her strategies of minoration and subversion through grotesque imagery and carnival rituals it argues that Carr put Hester's becoming-ghost in the middle, the bog of the cats as both grave and womb, waiting for the birth of a new Irish people. And it emphasizes that the ghost of Hester, merging with the ghosts of her mother and daughter by the bog of cats will haunt the official society as a threatening abjection, challenging the restoration of the social order.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.245-271
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• 2023

In this paper we discuss some recovery of H(div)-conforming flux approximations from the equilibrated fluxes of Ainsworth and Oden for quadratic finite element methods of second-order elliptic problems. Combined with the hypercircle method of Prager and Synge, these flux approximations lead to a posteriori error estimators which provide guaranteed upper bounds on the numerical error. Furthermore, we prove some superconvergence results for the flux approximations and asymptotic exactness for the error estimator under proper conditions on the triangulation and the exact solution. The results extend those of the previous paper for linear finite element methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.441-448
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• 2000

An investigation into the nonlinear free vibrations of a cantilever beam which can have not only planar motion but also nonplanar motion is made. Using Galerkin's method based on the first mode in each motion, we transform the boundary and initial value problem into an initial value problem of two-degree-of-freedom system. The system turns out to have two normal modes. By Synge's stability concept we examine the stability of each mode. In order to check validity of the stability we obtain the numerical Poincare map of the motions neighboring on each mode.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1993.10a
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• pp.77-83
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• 1993

In this paper, the dynamics of a 2-DOF not 1:1 resonant Hamiltonian system are studied. In the first part of the work, the behaviors of special periodic orbits called normal modes are examined by means of the harmonic balance method and their approximate stability ar analyzed by using the Synge's concept named stability in the kinematico-statical sense. Secondly, the global dynamics of the system for low and high energy are studied in terms of a perturbation analysis and Poincare' maps. In this part, one can see that the unstable normal mode generates chaotic motions resulting from the transverse intersections of the stable and unstable manifolds. Although there exist analytic methods for proving the existence of infinitely many periodic orbits, chaos, they cannot be applied in our case and thus, the Poincare' maps constructed by direct numerical integrations are utilized fot detecting chaotic motions. In the last part of the work, the existence of arbitrarily many periodic orbits of the system are proved by using a subharmonic Melnikov's method. We also study the possibility of the breakdown of invariant KAM tori only when h>h$_{0}$ (h$_{0}$:bifurcating energy) and investigate the generality of the destruction phenomena of the rational tori in the systems perturbed by stiffness and inertial coupling.