• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.105-122
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• 2023

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by Clifford multiplication over the standard sphere in odd dimension. In the even dimensional case, we give the spectra of the square of such operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form cases, respectively. We also give eigenvalue formulas for the conformally invariant differential operators of all odd orders on the subbundle of the bundle of spinor-valued forms that are annihilated by Clifford multiplication in both even and odd dimensions on the sphere.

• Journal of KIISE
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• v.43 no.8
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• pp.910-918
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• 2016

A tensor is a multi-dimensional array that represents many data such as (user, user, time) in the social network system. A tensor generator is an important tool for multi-dimensional data mining research with various applications including simulation, multi-dimensional data modeling/understanding, and sampling/extrapolation. However, existing tensor generators cannot generate sparse tensors like real-world tensors that obey power law. In addition, they have limitations such as tensor sizes that can be processed and additional time required to upload generated tensor to distributed systems for further analysis. In this study, we propose TeT, a distributed tera-scale tensor generator to solve these problems. TeT generates sparse random tensor as well as sparse R-MAT and Kronecker tensor without any limitation on tensor sizes. In addition, a TeT-generated tensor is immediately ready for further tensor analysis on the same distributed system. The careful design of TeT facilitates nearly linear scalability on the number of machines.

• Bulletin of the Korean Chemical Society
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• v.33 no.9
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• pp.3039-3042
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• 2012

Pressure tensors at the planar surface of liquid-vapor argon are evaluated from the virial theorem, Irving-Kirkwood, and Harasima versions using a test-area molecular dynamics simulation method through a Lennard-Jones intermolecular potential at two temperatures. We found that the normal and transverse components of the pressure tensor, $p_N(z)$ and $p_T(z)$, obtained from the virial theorem and Harasima version are essentially the same. The normal component of the pressure tensor from Irving-Kirkwood version, $p_N^{IK}(z)$, is shown to be a nearly constant at the lower temperature, independent of z, as agreed in a previous study, but not for $p_N^H$(z), while the transverse components, $p_T^{IK}(z)$ and $p_T^H(z)$, are almost the same. The values of surface tension for both versions computed from $p_N(z)-p_T(z)$ are also the same and are fully consistent with the experimental data.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.56-59
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• 2008

This paper presents results of a parametric study for a constitutive model (Lee et ai, 1989) for particle-reinforced composites considering weakened interfaces and crack nucleation. Eshelby's tensors for particles with imperfect interfaces (Ju and Chen, 1994) and microcracks (Sun and Ju, 2004) are incorporated into a micromechanical formulation. A parametric study for the microcrack nucleation parameter ${\phi}_{{\upsilon}0}$ and ${\epsilon}^{th}$ is conducted to investigate the sensitivity of the parameter to the constitutive model.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• Computers and Concrete
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• v.15 no.5
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• pp.709-733
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• 2015

This work deals with a damage model formulation taking into account the unilateral effect of the mechanical behaviour of brittle materials such as concrete. The material is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity induced by damage evolution. Two damage tensors governing the stiffness in tension or compression regimes are introduced. A new damage tensor in tension regimes is proposed in order to model the diffuse damage originated in prevails compression regimes. Accordingly with micromechanical theory, the constitutive model is validate when dealing with unilateral effect of brittle materials, Finally, the proposed model is applied in the analyses of reinforced concrete framed structures submitted to reversal loading. The numerical results have shown the good performance of the modelling and its potentialities to simulate practical problems in structural engineering.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.863-881
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• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.327-340
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• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.10
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• pp.1461-1468
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• 1993

In this paper the propagation problem of waves obliquely incident upon an anisotropic medium with arbitrary permittivity tensors is analyzed through a partial variational finite element method. First, a variational equation is derived from the new approach based on the induction theorem, reactions, and reciprocity. Next, by using the finite element method, the propagation problems are solved from the obtained functional. Also included are numerical results for the problem of waves incident upon a magnetoplasma slab.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.352-361
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• 2003

A fatigue damage accumulation model based on the continuum damage mechanics theory was develope(1 where modules decay ratios in tension and shear on used as indicators for damage variables D . In the model, the damage variables are considered to be second-order tensors. Then the maximum principal damage variable, $D^*$ is introduced According to the similarity to the Principal stress, $D^*$ is obtained as the maximum eigen value of damage tensor [D']. Under proportional tension and torsion loadings, fatigue lives were satisfactorily predicted at any combined stress ratios using the present model in which the fatigue characteristics only under uniaxial tension and pure torsion loadings on needed. Fatigue life prediction under uniaxial tension and pure torsion loadings, was performed based on the damage mechanics using boundary element method.