• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.187-199
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• 2024

In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the C^v-reducible and generalized C^v-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is C^v-reducible if and only if it is C-reducible and satisfies the 𝕋-condition. We study the generalized C^v-reducible Finsler manifold with a scalar π-form 𝔸. We show that a Finsler manifold (M, L) is generalized C^v-reducible with 𝔸 if and only if it is C-reducible and 𝕋 = 𝔸. Moreover, we prove that a Landsberg generalized C^v-reducible Finsler manifold with a scalar π-form 𝔸 is Berwaldian. Finally, we consider a special C^v-reducible Finsler manifold and conclude that a Finsler manifold is a special C^v-reducible if and only if it is special semi-C-reducible with vanishing 𝕋-tensor.

• Journal of the Korean Chemical Society
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• v.36 no.1
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• pp.44-50
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• 1992

The ability to account for magnetic and spectra properties of complexes was investigated for the splitting of the degenerate d-orbitals and with nonaqueous solution by UV/vis-spectrophotometric method. The correlation of the magnetitude of 10Dq obtained from the spectra, the pairing energy, and the spin state of the complexes. The electrochemical behavior of complexes were investigated by the use of cyclic voltammetry in aprotic media. These reduction peak of $[(C_6H_5)3_P]_2Pd(II)(CH_3COO)_2$ and $[(C_6H_5)_3Pd]_2Pd(II)Cl_2$ were irreversible one-electron processes at peak $E_{pc1} = -1.32 V,\;E_{pc2} = -1.56 V$ and $E_{pc1} = -1.74 V,\;E_{pc2} = -1.88 V$ of these complexes vs. Ag/AgCl, but nickel complexes were not to be reducible.