• Journal of applied mathematics & informatics
• /
• v.41 no.3
• /
• pp.603-613
• /
• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.1-5
• /
• 2006

We will introduce tensor product spectrums on the tensor product spaces. And we will show that ${\sigma}[P(T_1,T_2,{\ldots},T_n)]=P[({\sigma}(T_1),{\sigma}(T_2){\ldots},{\sigma}(T_n)]={\sigma}(T_1,T_2{\ldots},T_n)$.

• Bulletin of the Korean Chemical Society
• /
• v.8 no.4
• /
• pp.338-340
• /
• 1987

The single-frequency two-photon absorption tensor is carefully rederived and examined. It is pointed out that the conventionally used tensor, which has been formally deduced from the different-frequency two-photon absorption tensor, can give an incorrect absolute two-photon absorption rate. The identity forbidded selection rule and the polarization ratio expressions are also examined with the new tensor.

• Journal of the Korean Mathematical Society
• /
• v.44 no.1
• /
• pp.211-235
• /
• 2007

In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians $G_2(\mathbb{C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $G_2(\mathbb{C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$.

• Journal of Astronomy and Space Sciences
• /
• v.37 no.2
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.601-609
• /
• 2011

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.

• Journal of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.391-413
• /
• 2018

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.249-256
• /
• 2009

Let $G{\otimes}G$ be the tensor square of a group G. The set of all elements a in G such that $a{\otimes}g\;=\;1_{\otimes}$, for all g in G, is called the tensor centre of G and denoted by $Z^{\otimes}^$(G). In this paper some properties of the tensor centre of G are obtained and the capability of the pair of groups (G, G') is determined. Finally, the structure of $J_2$(G) will be described, where $J_2$(G) is the kernel of the map $\kappa$ : $G{\otimes}\;{\rightarrow}\;G'$.

• Honam Mathematical Journal
• /
• v.40 no.2
• /
• pp.347-354
• /
• 2018

Let ${\mathcal{C}}$, ${\mathcal{M}}$, ${\mathcal{L}}$ be concircular curvature tensor, M-projective curvature tensor and conharmonic curvature tensor, respectively. We obtain that if a non-Kenmotsu ($k,{\mu}$)'-almost Kenmotsu manifold satisfies ${\mathcal{C}}{\cdot}{\mathcal{S}}=0$, ${\mathcal{R}}{\cdot}{\mathcal{M}}=0$ or ${\mathcal{R}}{\cdot}{\mathcal{L}}=0$, then it is locally isometric to the Riemannian product ${\mathds{H}}^{n+1}(-4){\times}{\mathds{R}}^n$.

• The Journal of Korean Academy of Orthopedic Manual Physical Therapy
• /
• v.19 no.2
• /
• pp.39-46
• /
• 2013

Background: The purpose of this study was to realize the relations between gluteus medius, tensor fascia lata of pelvic muscles and functional leg length in women's university students. This study is examined the change of electromyographic activation on gluteus medius and tensor fascia lata according to the leg length discrepancy. Methods: All of the female of freshman and sophomore in 'D'college were gathered and separated fourteen of healthy women in two groups by functional leg length discrepancy. and The subjects divided into two groups that the difference with less than 2cm or more would have structural defects by tapeline. The electromyographic activation on the gluteus medius and tensor fascia lata muscles were recorded by surface electrodes at maximal voluntary isometric contraction (MVIC) during lunge posture. The collected datas were analyzed using Independent t-test with SPSS win19.0. Results: In intergroup comparison of electromyographic activation levels for gluteus medius and tensor fascia lata in short or long leg, the influence of electromyographic activation on tensor fascia lata is shown to be more statically higher than gluteus medius according to functional leg length discrepancy in coeds. Even though both muscles are shown to be statistically higher in comparison of electoromyographic activation levels for tensor fascia lata and gluteus medius between short leg and long leg in Group I, Differences of electoromyographic activation levels for tensor fascia lata is shown to be statistically higher than gluteus medius. Conclusion: Through this study, we realized that tensor fascia lata than the long leg, and also, tensor fascia lata is significantly effective for functional leg length discrepancy than gluteus medius. It leads to pelvic lateral instability. This means that cause tensor fascia lata to have a leg length discrepancy.