• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.643-657
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• 2022

Let R be a ring and S a multiplicative subset of R. An R-module T is called u-S-torsion (u-always abbreviates uniformly) provided that sT = 0 for some s ∈ S. The notion of u-S-exact sequences is also introduced from the viewpoint of uniformity. An R-module F is called u-S-flat provided that the induced sequence 0 → A ⊗_R F → B ⊗_R F → C ⊗_R F → 0 is u-S-exact for any u-S-exact sequence 0 → A → B → C → 0. A ring R is called u-S-von Neumann regular provided there exists an element s ∈ S satisfying that for any a ∈ R there exists r ∈ R such that sα = rα². We obtain that a ring R is a u-S-von Neumann regular ring if and only if any R-module is u-S-flat. Several properties of u-S-flat modules and u-S-von Neumann regular rings are obtained.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.333-344
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• 2023

In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if Tor^R₁ (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed.

• Structural Engineering and Mechanics
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• v.60 no.6
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• pp.1039-1061
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• 2016

Based on Vlasov's torsional theory of open thin-walled members and the nonlinear constitutive relations of materials, a nonlinear analysis model to predict response of open thin-walled RC members subjected to pure torsion is proposed in the current study. The variation of the circulatory torsional stiffness and warping torsional stiffness over the entire loading process and the impact of warping shear deformation on the torsion-induced rotation of the member are considered in the formulation. The torque equilibrium differential equation is then solved by Runge-Kutta method. The proposed nonlinear model is then applied to predict the behavior of five U-shaped thin-walled RC members under pure torsion. Four of them were tested in an earlier experimental study by the authors and the testing data of the fifth one were reported in an existing literature. Results show that the analytical predictions based on the proposed model agree well with the experimental data of all five specimens. This clearly shows the validity of the proposed nonlinear model analyzing behavior of U-shaped thin-walled RC members under pure torsion.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.31-43
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• 2024

Let $R_e\,=\,\frac{{\mathbb{F}}_{p^m}[u]}{{\langle}u^e{\rangle}}$, where p is a prime number, e is a positive integer and u^e = 0. In this paper, we first characterize the structure of cyclic codes of length p^s over R_e. These codes will be classified into 2^e distinct types. Among other results, in the case that e = 4, the torsion codes of cyclic codes of length p^s over R₄ are obtained. Also, we present some examples of cyclic codes of length p^s over R_e.

• Journal of the korean veterinary medical association
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• v.19 no.6
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• pp.18-22
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• 1983

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.577-587
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• 2002

Let A be a commutative ring and M an Artinian .A-module. Let $\sigma$ be a torsion radical functor and (T, F) it's corresponding partition of Spec(A) In [1] the concept of Cohen-Macauly modules was generalized . In this paper we shall define $\sigma$-co-Cohen-Macaulay (abbr. $\sigma$-co-CM). Indeed this is one of the aims of this paper, we obtain some satisfactory properties of such modules. An-other aim of this paper is to generalize the concept of cograde by using the left derived functor $U^{\alpha}$$_{I}$(-) of the $\alpha$-adic completion functor, where a is contained in Jacobson radical of A.A.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.803-808
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• 2000

This thesis studied whether friction welding of SPSS, localized torsion bar material could be accomplished or not. And then optimum welding conditions were examined and leaded through tensile, impact, torsion and hardness test after postweld heat treatment of the actual field condition. Obtained results were as follows; Linear relationship was existed between heating time and total upset, and a quadratic equation model could be made between tensile strength and heating time. Optimum welding conditions with fine structure were as follows in case total upset(U)=8.5mm; the number of rotations(n)=2,000 rpm, heating pressure($p_1$)=80MPa, upset pressure($p_2$)=200MPa, heating time($t_1$)=4sec, upset time($t_2$)=3 sec.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.2
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• pp.16-29
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• 1995

In this study a tracked vehicle is idealized as a 2-dimensional 9-degrees-of-freedom model which takes into account the effects of HSU units, torsion bars, and track. For the model equations of motion are derived using Kane's method. By using the equations of motion, a numerical example is solved and results are compared to those obtained by using a general purpose multi body dynamic analysis program. The comparison study shows the reasonable coherence between the two results. which confirms the effectiveness of the model. With the model, dynamic response optimization is carried out. The objective function is the peak value of the vertical acceleration of the vehicle at the driver's seat, and the constraints are the wheel travel limits, the ground clearance. and the limits of other design variables. Three different sets of design variables are chosen and used for the optimization. The results show the attenuation of the acceleration peak value. Thus the procedure presented in this study can be utilized for the design improvement of the real system.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.159-167
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• 2011

We consider a curve $\alpha$= $\alpha$(s) in Minkowski 3-space $E_1^3$ and denote by {T, N, B} the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction U of $E_1^3$ such that the function is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in $E_1^3$.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.10a
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• pp.33-36
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• 2000

The dynamic recrystallization (DRX) of medium carbon steels (SCM 440 and POSMA45) was studied with torsion test in the temperature range of $900-1100^{\circ}C$ and the strain rate range of $5.0x10^{-2}\;-\;5.0x10^0/sec$. To establish the quantitative equations for DRX, the evolution of flow stress curve with strain was analyzed. The critical strain (${\varepsilon}_c$) and strain for maximum softening rate ( ${\varepsilon}^{*}$) could be confirmed by the analysis of work hardening rate ($d{\sigma}/d{\varepsilon}\;=\; \theta$). The volume fraction of dynamic recrystallization ($X_{DRX}$) as a function of processing variables, such as strain rate ( $\dot{\varepsilon}$ ), temperature (T), and strain ( $\varepsilon$ ) were established using the ${\varepsilon}_c$ and ${\varepsilon}^{*}$. For the exact prediction, the ${\varepsilon}_c$, ${\varepsilon}^{*}$ and Avrami' exponent (m') were quantitatively expressed by dimensionless parameter, Z/A respectively. The transformation-effective strain-temperature curve for DRX could be composed. It was found that the calculated results were agreed with the experimental data for the steels at any deformation conditions.