• Kyungpook Mathematical Journal
• /
• 제14권1호
• /
• pp.7-14
• /
• 1974

• 대한수학회지
• /
• 제18권2호
• /
• pp.149-166
• /
• 1982

• Journal of Astronomy and Space Sciences
• /
• 제37권2호
• /
• pp.131-142
• /
• 2020

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, F^αβ, which implies both electric field ${\overrightarrow{E}}$ and magnetic field ${\overrightarrow{B}}$ rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor F^αβ and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.

• Fibers and Polymers
• /
• 제2권1호
• /
• pp.163-172
• /
• 2001

To determine three-dimensional fiber orientation states in injection-molded short fiber composites a CLSM (Confocal Laser Scanning Microscope) is used. Since the CLSM optically sections the composites, more than two cross-sections either on or below the surface of the composite can be obtained. Three dimensional fiber orientation states can be determined with geometric parameters of fibers on two parallel cross-sections. For experiment, carbon fiber reinforced polystyrene is examined by the CLSM. Geometric parameters of fibers are measured by image analysis. In order to compactly describe fiber orientation states, orientation tensors are used. Orientation tensors are determined at different positions of the prepared specimen. Three dimensional orientation states are obtained without the difficulty in determining the out-of-plane angles by utilizing images on two parallel planes acquired by the CLSM. Orientation states are different at different positions and show the shell-core structure along the thickness of the specimen.

• 한국산업융합학회 논문집
• /
• 제3권4호
• /
• pp.329-336
• /
• 2000

A geometric and material nonlinear finite element analysis is developed for the layered elastomeric bearings. In this study, a mixed variational approach with separate variables is used to describe the displacement and volume change of rubber. To represent finely deformed behavior, Kirchoff stress tensors are used and converted Eulerian stress tensors to describe real physical meanings. Newton's method is utilized to solve the governing nonlinear finite element equations. Numerical test are performed in the case of compression and shear to verify the theory and to illustrate the application of this analysis. And the results of this study were compared to the results of Moore's discrete finite element analysis.

• Bulletin of the Korean Chemical Society
• /
• 제17권5호
• /
• pp.457-460
• /
• 1996

The principal elements of the 31P NMR chemical shielding tensors have been determined for three binuclear platinum diphosphite complexes, K4[Pt2(P2O5H2)4·2H2O ("Pt2"), K4[Pt2(P2O5H2)4Cl2]·2H2O ("Pt2Cl2"), and K4[Pt2(P2O5H2)4Br2]·2H2O ("Pt2Br2"), by using a Herzfeld-Berger graphical method for interpreting the 31P MAS spectrum. The orientations of 31P chemical shielding tensor relative to the molecular axis system are partially assigned with combination of the longitudinal relaxation study of HPO32- and the reference to known tensor orientations of related sites; the most chemical shielding component, δ33, is directed along the P-Pt bond axis. A discussion is given in which the experimental principal elements of the 31P chemical shielding tensor are related with the Pt-Pt bond distances in binuclear platinum diphosphite complexes.

• 호남수학학술지
• /
• 제45권2호
• /
• pp.215-230
• /
• 2023

In this article, generalized Sasakian space forms are investigated on W₀ -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W₀-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W₀-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W₀-pseudosymmetry and W₀ -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

• Nonlinear Functional Analysis and Applications
• /
• 제27권2호
• /
• pp.433-448
• /
• 2022

The Cartan's second curvature tensor Pⁱ_jkh is a positively homogeneous of degree-1 in yⁱ, where yⁱ represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pⁱ_jkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.

• East Asian mathematical journal
• /
• 제10권1호
• /
• pp.25-34
• /
• 1994

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 2005년도 학술발표회(1)
• /
• pp.534-534
• /
• 2005