• 대한수학회보
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• 제45권1호
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• pp.33-37
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• 2008

Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the fixed point set $M^G\neq\emptyset$ and dim $M^G=0$, then G has a subgroup H with $G/H{\cong}\mathbb{Z}_2$, the cyclic group of order 2. The tangential representation $\tau_x$(M) of G at $x{\in}M^G$ is also regarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.

• 대한수학회보
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• 제25권2호
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• pp.175-178
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• 1988

Let .SIGMA. be a smooth compact manifold without boundary having the same homotopy type as a sphere, which is called a homotopy sphere. Supose a group G acts smoothly on .SIGMA. with the fixed point set .SIGMA.$^{G}$ consists of two isolated fixed points p and q. In this case, tangent spaces $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA. at isolated fixed points, as isotropy representations of G are called Smith equivalent. Moreover .SIGMA. is called a supporting homotopy sphere of Smith equivalent representations $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA.. The study on Smith equivalence has rich history, and for this we refer the reader to [P] or [Su]. The following question of pp.A.Smith [S] motivates the study on Smith equivalence.e.

• East Asian mathematical journal
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• 제35권3호
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• pp.357-363
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• 2019

Let the circle act on a compact almost complex manifold M with a non-empty discrete fixed point set. To each fixed point, there are associated non-zero integers called weights. A positive weight w is called primitive if it cannot be written as the sum of positive weights, other than w itself. In this paper, we show that if every weight is primitive, then the Todd genus Todd(M) of M is positive and there are $Todd(M){\cdot}2^n$ fixed points, where dim M = 2n. This generalizes the result for symplectic semi-free actions by Tolman and Weitsman [8], the result for semi-free actions on almost complex manifolds by the author [6], and the result for certain symplectic actions by Godinho [1].

• Structural Engineering and Mechanics
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• 제31권6호
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• pp.639-662
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• 2009

A comprehensive investigation of the stochastic response of an isolated cable-stayed bridge subjected to spatially varying earthquake ground motion is performed. In this study, the Jindo Bridge built in South Korea is chosen as a numerical example. The bridge deck is assumed to be continuous from one end to the other end. The vertical movement of the stiffening girder is restrained and freedom of rotational movement on the transverse axis is provided for all piers and abutments. The longitudinal restraint is provided at the mainland pier. The A-frame towers are fixed at the base. To implement the base isolation procedure, the double concave friction pendulum bearings are placed at each of the four support points of the deck. Thus, the deck of the cable-stayed bridge is isolated from the towers using the double concave friction pendulum bearings which are sliding devices that utilize two spherical concave surfaces. The spatially varying earthquake ground motion is characterized by the incoherence and wave-passage effects. Mean of maximum response values obtained from the spatially varying earthquake ground motion case are compared for the isolated and non-isolated bridge models. It is pointed out that the base isolation of the considered cable-stayed bridge model subjected to the spatially varying earthquake ground motion significantly underestimates the deck and the tower responses.

• 한국조경학회지
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• 제35권3호
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• pp.105-113
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• 2007

This study was conducted to analyze the effects of environmental factors such as soil moisture, light intensity, temperature and humidity on changes in cambial electrical resistance. To improve data quality, cambial electrical resistance was continuously measured at fixed points by using a data logger isolated from alternating current. The relationship between environmental factors and changes in cambial electrical resistance was also analyzed. The results are as follows: 1. Cambial electrical resistance is highly correlated to the temperature of the measured area(r=-0.934). Therefore, temperature compensation is needed to analyze the effects of other environmental factors on cambial electrical resistance changes. 2. If temperature is compensated for, the change of cambial electrical resistance is highly correlated to water vapor pressure(r=-0.836). 3. If temperature and humidity are compensated for, the change of cambial electrical resistance is highly correlated to intensity of light(r=-0.738). 4. Diurnal deviation of soil water potential is not more significantly related than the change of cambial electrical resistance. However, in the long-term, soil water potential and cambial electrical resistance are highly correlated(r=-0.831). This indicates that soil moisture significantly influences the long-term change of cambial electrical resistance.