• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.347-355
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• 2001

Let ($X, \omega$) be a closed symplectic 4-manifold. Let a finite cyclic group G act semifreely, holomorphically on X as isometries with fixed point set $\Sigma$(may be empty) which is a 2-dimension submanifold. Then there is a smooth structure on the quotient X'=X/G such that the projection $\pi$:X$\rightarrow$X' is a Lipschitz map. Let L$\rightarrow$X be the Spin$^c$ -structure on X pulled back from a Spin$^c$-structure L'$\rightarrow$X' and b_2^$+(X')>1. If the Seiberg-Witten invariant SW(L')$\neq$0 of L' is non-zero and $L=E\bigotimesK^-1\bigotimesE$ then there is a G-invariant pseudo-holomorphic curve u:$C\rightarrowX$,/TEX> such that the image u(C) represents the fundamental class of the Poincare dual $c_1$(E). This is an equivariant version of the Taubes' Theorem.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.173-182
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• 2014

The mixed convolved action principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation, convolution, and fractional calculus. In this paper, its potential in the development of numerical methods for transient problems in various dynamical systems when adopting temporally second order approximation is investigated. For this, the classical single-degree-of-freedom linear elastic dynamical systems are primarily considered to investigate computational characteristics of the developed algorithms. For the undamped system, all the developed algorithms are symplectic with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.