• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.127-134
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• 1998

It is proved [6] that there exists a basis of $L^\Gamma$ (the space of meromorphic vector fields on a Riemann surface, holomorphic away from two fixed points) represented by the vector fields which have the expected zero or pole order at the two points. In this paper, we carry out the same task for the quadratic differentials. More precisely, we compute a basis of $Q^\Gamma$ (the sapce of meromorphic quadratic differentials on a Riemann surface, holomorphic away from two fixed points). This basis consists of the quadratic differentials which have the expected zero or pole order at the two points. Furthermore, we show that $Q^\Gamma$ has a Lie algebra structure which is induced from the Krichever-Novikov algebra $L^\Gamma$.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.765-780
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• 2023

In this work, a novel combined logarithmic, secant and tangential 2D and quasi-3D refined higher order shear deformation theory is proposed to examine the buckling analysis of simply supported uniform functionally graded plates under uniaxial and biaxial loading. The proposed formulations contain a reduced number of variables compared to others similar solutions. The combined function employed in this study ensures automatically the zero-transverse shear stresses at the free surfaces of the structure. Various models of the material distributions are considered (linear, quadratic, cubic inverse quadratic and power-law). The differentials stability equations are derived via virtual work principle with including the stretching effect. The Navier's approach is applied to solve the governing equations which satisfying the boundary conditions. Several comparative and parametric studies are performed to illustrates the validity and efficacity of the proposed model and the various factors influencing the critical buckling load of thick FG plate.