• Title/Summary/Keyword: tensor

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Dipole Moment Derivatives and Infrared Intensities in Chloromethanes

  • Kim, Kwan;Kim, Hyun-Sik;Kim, Myung-Soo;Kim, Ho-Jing
    • Bulletin of the Korean Chemical Society
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    • v.10 no.2
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    • pp.161-167
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    • 1989
  • The results of ab initio(MP2/6-31G) molecular orbital calculations of the dipole moment derivatives and gas phase IR intensities in chloromethanes are reported. The theoretical polar tensors are analyzed into the net charge, charge-flux, and overlap contributions. The charge-flux contribution was found to be dominant in the Cl atom polar tensor, while the net charge effect was the most prominent contribution for the H atom polar tensor. The Cl atom polar tensor appeared, in a good approximation, to be transferable among various chloro molecules. On the other hand, for the prediction of IR spectra of complex hydrocarbons containing chlorine atoms, some empirical adjustment of the H-atom polar tensor seemed to be made depending on the number of Cl atoms bound to the certain carbon atom.

SASAKIAN 3-MANIFOLDS SATISFYING SOME CURVATURE CONDITIONS ASSOCIATED TO Ƶ-TENSOR

  • Dey, Dibakar;Majhi, Pradip
    • The Pure and Applied Mathematics
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    • v.28 no.2
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    • pp.143-153
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    • 2021
  • In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

HOPF HYPERSURFACES OF THE HOMOGENEOUS NEARLY KÄHLER 𝕊3 × 𝕊3 SATISFYING CERTAIN COMMUTING CONDITIONS

  • Xiaomin, Chen;Yifan, Yang
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.6
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    • pp.1567-1594
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    • 2022
  • In this article, we first introduce the notion of commuting Ricci tensor and pseudo-anti commuting Ricci tensor for Hopf hypersurfaces in the homogeneous nearly Kähler 𝕊3 × 𝕊3 and prove that the mean curvature of hypersurface is constant under certain assumptions. Next, we prove the nonexistence of Ricci soliton on Hopf hypersurface with potential Reeb vector field, which improves a result of Hu et al. on the nonexistence of Einstein Hopf hypersurfaces in the homogeneous nearly Kähler 𝕊3 × 𝕊3.

BACH ALMOST SOLITONS IN PARASASAKIAN GEOMETRY

  • Uday Chand De;Gopal Ghosh
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.763-774
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    • 2023
  • If a paraSasakian manifold of dimension (2n + 1) represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric g has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if r = -6; shrinking if r > -6; expanding if r < -6.

GENERALIZED SASAKIAN SPACE FORMS ON W0-CURVATURE TENSOR

  • Tugba Mert ;Mehmet Atceken
    • Honam Mathematical Journal
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    • v.45 no.2
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    • pp.215-230
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    • 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.

DECOMPOSITION FOR CARTAN'S SECOND CURVATURE TENSOR OF DIFFERENT ORDER IN FINSLER SPACES

  • Abdallah, Alaa A.;Navlekar, A.A.;Ghadle, Kirtiwant P.;Hamoud, Ahmed A.
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.2
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    • pp.433-448
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    • 2022
  • The Cartan's second curvature tensor Pijkh 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 Pijkh 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.

Image Data Classification using a Similarity Function based on Second Order Tensor (2차 텐서 기반 유사도 함수를 이용한 영상 데이터 분류)

  • Yoon, Dong-Woo;Lee, Kwan-Yong;Park, Hye-Young
    • Journal of KIISE:Software and Applications
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    • v.36 no.8
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    • pp.664-672
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    • 2009
  • Recently, studies on utilizing tensor expression on image data analysis and processing have been attracting much interest. The purpose of this study is to develop an efficient system for classifying image patterns by using second order tensor expression. To achieve the goal, we propose a data generation model expressed by class factors and environment factors with second order tensor representation. Based on the data generation model, we define a function for measuring similarities between two images. The similarity function is obtained by estimating the probability density of environment factors using a matrix normal distribution. Through computational experiments on a number of benchmark data sets, we confirm that we can make improvement in classification rates by using second order tensor, and that the proposed similarity function is more appropriate for image data compared to conventional similarity measures.

Determination of the Strike and the Dip of a Line Source Using Gravity Gradient Tensor (중력 변화율 텐서를 이용한 선형 이상체의 주향과 경사 결정)

  • Rim, Hyoungrea;Jung, Hyun-Key
    • Journal of the Korean earth science society
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    • v.35 no.7
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    • pp.529-536
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    • 2014
  • In this paper, the automatic determination algorithm of strike and dip of a line source using gravity gradient on a single profile is proposed. In general, the gravity gradient tensor due to a line source has only two independent components because of its 2-Dimensional (2-D) characteristics. However, if the line source has the strike and dip regarding the observation profile, it comes to have five independent components. The proposed algorithm of the determination both strike and dip is based on the rotational transform that converts full gravity gradient tensor to reduced 2-D gravity gradient tensor. The least-square method is applied in order to find optimum rotational angles that make one of the row components minimalized simultaneously. The two synthetic cases of a line source are represented; one has strike only and the other has both strike and dip. This study finds that the automatic determination method using gravity gradient tensor can find directions of a line source in each case.

Analysis of Relationship between 2-D Fabric Tensor Parameters and Hydraulic Properties of Fractured Rock Mass (절리성 암반의 이차원 균열텐서 파라미터와 수리적 특성 간의 상관성 분석에 관한 연구)

  • Um, Jeong-Gi;Han, Jisu
    • Tunnel and Underground Space
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    • v.27 no.2
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    • pp.100-108
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    • 2017
  • As a measure of the combined effect of fracture geometry, the fabric tensor parameters could quantify the status of the connected fluid flow paths in discrete fracture network (DFN). The correlation analysis between fabric tensor parameters and hydraulic properties of the 2-D DFN was performed in this study. It is found that there exists a strong nonlinear relationship between the directional conductivity and the fabric tensor component estimated in the direction normal to the direction of hydraulic conductivity. The circular radial plots without significant variation of the first invariant ($F_0$) of fabric tensor for different sized 2-D DFN block are a necessary condition for treating representative element volume (REV) of a fractured rock mass. The relative error (ER) between the numerically calculated directional hydraulic conductivity and the theoretical directional hydraulic conductivity decreases with the increase in $F_0$. A strong functional relation seems to exist between the $F_0$ and the average block hydraulic conductivity.