• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.497-503
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• 2012

In this paper, we study elliptic curves E over $\mathbb{Q}$ such that the 3-torsion subgroup E[3] is split as ${\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$. For a non-zero intege $m$, let $C_m$ denote the curve $x^3+y^3=m$. We consider the relation between the set of integral points of $C_m$ and the elliptic curves E with $E[3]{\simeq}{\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.645-652
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• 2006

The purpose of this paper is to describe some characterizations on rational and f-rational extensions of modules, to determine the forms of f-rational extensions of given f-torsion free module for a left exact radical t and investigate the maximal t-rational extensions of modules.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.439-456
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• 1994

Let $\tau$ be a given hereditary torsion theory for left R-module category R-Mod. The class of all $\tau$-torsion left R-modules, denoted by T is closed under homomorphic images, submodules, direct sums and extensions. And the class of all $\tau$-torsionfree left R-modules, denoted by $F$, is closed under submodules, injective hulls, direct products, and isomorphic copies ([3], Proposition 1.7 and 1.10).

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1759-1786
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• 2017

We examine the moduli space of oriented locally homogeneous manifolds of Type ${\mathcal{A}}$ which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at least 3. These exhibit phenomena that is very different than in the case of surfaces. In dimension 3, we determine all the possible symmetry groups in the torsion free setting.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.323-336
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• 2004

We consider the application of complex variable method to elastic problem and investigate the nonlinear effect of finite torsion of a compressible elastic composite layer. We obtain that as a result of finite deformation approach, a tube subjected to torsion decreases in radius giving rise to a “hold effect”.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.121-133
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• 1998

We find some properties of the pro-torsion products. Under the suitable conditions, we also show that the map ${\bar{H}}_P({\chi};G){\rightarrow}{\bar{H}}_p^{s(r)}({\chi};G)$ is an isomorphism and the n-th homotopy group of X is isomorphic to the n-th ${\check{C}}ECH$ homology group.

• Journal of the Semiconductor & Display Technology
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• v.3 no.3
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• pp.27-29
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• 2004

The responses of hypothetical silicon nanotubes under torsion have been investigated using an atomistic simulation based on the Tersoff potential. A torque, proportional to the deformation within Hooke's law, resulted in the ribbon-like flattened shapes and eventually led to a breaking of hypothetical silicon nanotubes. Each shape change of hypothetical silicon nanotubes corresponded to an abrupt energy change and a singularity in the strain energy curve as a function of the external tangential force, torque, or twisted angle. The dynamics of silicon nanotubes under torsion can be modelled in the continuum elasticity theory.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.75-82
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• 2020

In this study, the problem of torsion of bars with open cross section surrounded by corrugated boundaries is analyzed. An approximate analytical solution is given using perturbation technique. First, the stress analysis for circular open cross-section for arbitrary opening angle is formulated and the problem is analytically solved. Second, the open cross-section with corrugated cross section is analyzed using perturbation method. First order contributions to the stresses and the torques have been added. The results have been exemplified and compared by considering special examples.

• Journal of Integrative Natural Science
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• v.14 no.3
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• pp.139-146
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• 2021

The purpose of this paper is to classify the torsion-free extensions 1→ℤ³→𝛱→ℤ_𝜱→1 with injective abstract kernel 𝜙 : ℤ_𝜱→Aut(ℤ³). From this classification, we handle the sufficient conditions so as to classify the crystallographic groups of Sol⁴_m,n.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.23-29
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• 2019

Rings in which all accessible subrings are ideals are called filial. A ring R is called fully filial if all its subrings are filial (that is rings in which the relation of being an ideal is transitive). The present paper is devoted to the study of fully filial torsion rings. We prove a classification theorem for semiprime fully filial torsion rings.