• Tunnel and Underground Space
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• v.31 no.1
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• pp.66-81
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• 2021

The effects of directional fracture tensor components and first invariant of fracture tensor on deformation moduli and shear moduli of fractured rock masses is analyzed based on regression analysis performed between 3-D fracture tensor parameters and deformability of DFN blocks. Using one or two deterministic joint sets, a total of 224 3-D discrete fracture network (DFN) cube blocks were generated with various configurations of deterministic density and probabilistic size distribution. The fracture tensor parameters were calculated for each generated DFN systems. Also, deformability moduli with respect to three perpendicular direction of the DFN cube blocks were estimated based on distinct element method. The larger the first invariant of fracture tensor, the smaller the values for the deformability moduli of the DFN blocks. These deformability properties present an asymptotic pattern above the certain threshold. It is found that power-law function describes the relationship between the directional deformability moduli and the corresponding fracture tensor components estimated in same direction.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.341-354
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• 2016

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m₀, m₁, ⋯ , m_r−1 are obtained.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.21-28
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• 2010

In the unified field theory(UFT), many works on the solutions of Einstein's equation have been published. The main goal in the present paper is to obtain some geometric results on a particular solution of Einstein's equation under some condition in even-dimensional UFT $X_n$.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.309-319
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• 1995

Let (M,g) be an m-dimensional compact orientable Riemannian manifold(connected and $C^\infty$) with metric tensor g.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-319
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• 2008

The object of the paper is to study a Sasakian manifold with quasi-conformal curvature tensor.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.337-343
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• 1998

In this paper we show that every contact metric manifold with vanishing contact conformal curvature tensor is a Sasakian space form.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.55-65
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• 2005

We find the expression of the curvature tensor field for a manifold with is endowed with an almost contact structure satisfying the condition (1.7). By using this condition we obtain some properties of the Ricci tensor and scalar curvature (d. Theorem 3.2 and Proposition 3.2).

• East Asian mathematical journal
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• v.22 no.1
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• pp.111-130
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• 2006

We study cosymplectic submersions with vanishing cosymplectic Bochner curvature tensor.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.91-100
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• 2013

This paper is a direct continuation of [1] and [2]. In this paper we investigate some properties of ES-curvature tensor and contracted ES-curvature tensor of g - $ESX_n$. Also, we study the field equations in the n-dimensional ES manifold g - $ESX_n$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.269-277
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• 2005

The tensor product $A{\bigotimes}B$ of Hilbert space operators A and B will be shown to be log-hyponormal if and only if A and Bare log-hyponormal. Some general comments about generalized hyponormality are also made.