• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.185-195
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• 2020

This paper aims to study the 𝒲^⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲^⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲^⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲^⁎-curvature tensor is Einstein. A 𝒲^⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲^⋆-curvature tensor are considered.

• Geophysics and Geophysical Exploration
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• v.12 no.4
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• pp.328-337
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• 2009

To investigate the relation between pore fluid conductivity and bulk resistivity of a rock sample it is assumed that electrolyte solution perfectly substitute the pore fluid that occupied the pore space within the sample in general. In this study, it is investigated that how much can the electrolyte solution substitute the pore fluid by repeating the same saturation process. Four kinds of NaCl solutions of 8, 160, 3200, 64000 ${\mu}S$/cm are used. The saturation process has repeated four times for each electrolyte in increasing conductivity order first then four times each in decreasing order. The more the saturation process repeated with the same electrolyte, the more electrolyte solution substitute the pore fluid. Geometric mean of bulk resistivity in increasing and decreasing orders with the same electrolyte solution is assumed to be mostly close to the bulk resistivity with perfect substitution. Bulk resistivity measurements for both increasing and decreasing order differs within 10% to the geometric mean when repeating the saturation process 4 times while maximum 40% difference is observed when single saturation process for each electrolyte solution with increasing order. The modified parallel resistant model can generally represent the relations between pore fluid resistivity and bulk resistivity in the experiment, but more experimental data with various rock samples with different porosity is needed to generalize the model.