• 호남수학학술지
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• 제45권2호
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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.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 추계학술발표대회 논문집
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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.

• 대한수학회보
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• 제42권2호
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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.

• 대한수학회논문집
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• 제10권1호
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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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• 제58권2호
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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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• 제39권3_4호
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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.

• 한국정보전자통신기술학회논문지
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• 제13권5호
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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.

• 천문학회지
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• 제29권spc1호
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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.

• 스마트미디어저널
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• 제1권2호
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• pp.23-33
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• 2012

본 논문에서는 영상처리 및 컴퓨터비전 분야에서 다양하게 응용되고 있는 텐서보팅(tensor voting)의 특징을 고찰하고자 한다. 일반적으로 텐서보팅은 점 (points), 곡선 성분 (curve elements), 그리고 표면 조각 성분 (surface patch elements)로 주어진 n-차원의 데이터들로부터 교차점 (junction), 곡선 (curve), 영역 (region), 그리고 표면 (surface)과 같은 구조 특징을 추론할 수 있다. 영상 및 장면에서 구조적 추론을 이용한 지각기반 그룹핑 (perceptual grouping) 방법들이 다양한 분야에서 연구되어 응용되고 있다. 텐서보링은 잡음에 강건한 특징을 제공하며 다양한 응용을 통하여 효율성을 보여주고 있다.

• Journal of Korean Neurosurgical Society
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• 제63권4호
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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.