• Honam Mathematical Journal
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• v.45 no.2
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• pp.316-324
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• 2023

The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P_𝛼𝛽. It is established that the divergence of tensor G_𝛼𝛽 defined with the help of P_𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V₄ satisfying Einstein like field equations, the tensor P_𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.173-176
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• 2000

Finite element model based on the Naghdi's shell theory in the general tensor-based form is formulated in the present study. Partial mixed variational functional for assumed strain is formulated in order to avoid the severe locking troubles known as transverse shear and membrane locking. The proposed assumed strain element in general tensor Naghdi's shell model provides very accurate solutions for thin shells in benchmark problems. In additions, linear elastic constitutive equations are given in the general curvilinear coordinate system including anisotropic layered structures. Thus laminated composited shell structures are easily analyzed in the present formulation.

• 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.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.163-173
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• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.361-375
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• 2018

The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.587-600
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• 2021

Some problems in engineering and science can be equivalently transformed into solving multi-linear systems. In this paper, we propose two preconditioned AOR iteration methods to solve multi-linear systems with -tensor. Based on these methods, the general conditions of preconditioners are given. We give the convergence theorem and comparison theorem of the two methods. The results of numerical examples show that methods we propose are more effective.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.13 no.5
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• pp.432-435
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• 2020

The elasticity tensor for water may be employed to model the fully saturated porous material. Mostly water is assumed to be incompressible with a bulk modulus, however, the upper and lower bounds of off-diagonal components of the elasticity tensor of porous materials filled with water are violated when the bulk modulus is relatively high. In many cases, the generalized Hill inequality describes the general bounds of Voigt and Reuss for eigenvalues, but the bounds for the component of elasticity tensor are more realistic because the principal axis of eigenvalues of two phases, matrix and water, are not coincident. Thus in this paper, for anisotropic material containing pores filled with water, the bounds for the component of elasticity tensor are expressed by the rule of mixture and the upper and lower bounds of fully saturated porous materials are violated for low porosity and high bulk modulus of water.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.283-284
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• 1996

Wormhole solutions of general theory of relativity are known to violate energy conditions. We have considered the possibility of having wormhole solutions in Brans-Dicke theory which is the prototype of scalar-tensor theories of gravity.

• Smart Media Journal
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• v.1 no.2
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• pp.23-33
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• 2012

In this paper, the characteristics of tensor voting, which are used extensively in image processing and computer vision, have been surveyed. In general, tensor voting can infer the structural features like junctions, curves, regions and surfaces from n-dimensional data given as points, curve elements or surface patch elements. Currently various perceptual grouping methods based on such structural inference are studied and are used for diverse applications on images or scenes. Tensor voting provides robustness to noises and demonstrates itself efficient in many applications.

• Journal of Korean Neurosurgical Society
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• v.63 no.4
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• pp.504-512
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• 2020

Objective : An important factor during pituitary adenoma surgery is to preserve pituitary stalk (PS) as this plays a role in reduction of the risk of postoperative diabetes insipidus. The hypothalamic-hypophyseal tract (HHT) projects through the PS to the posterior pituitary gland. To reconstruct white matter fiber pathways, methods like diffusion tensor imaging (DTI) tractography have been widely used. In this report we attempted to predict the position of PS using DTI tractography and to assess its intraoperative correlation during surgery of pituitary adenomas. Methods : DTI tractography was used to tract the HHT in nine patients before craniotomy for pituitary adenomas. The DTI location of the HHT was compared with the PS position identified at the time of surgery. DTI fiber tracking was carried out in nine patients prior to the planned craniotomy for pituitary adenomas. In one patient, the PS could not be identified during the surgery. In the other eight patients, a comparison was made between the location of the HHT identified by DTI and the position of the PS visualized at the time of surgery. Results : The position of the HHT identified by DTI showed consistency with the intraoperative position of the PS in seven patients (88.9% concordance). Conclusion : This study shows that DTI can identify the position of the HHT and thus the position of the PS with a high degree of reliability.