• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.495-502
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• 2017

Let R be a 2-torsion free prime ring and J be a nonzero Jordan ideal of R. Let F and G be two generalized derivations with associated derivations f and g, respectively. Our main result in this paper shows that if F(x)x - xG(x) = 0 for all $x{\in}J$, then R is commutative and F = G or G is a left multiplier and F = G + f. This result with its consequences generalize some recent results due to El-Soufi and Aboubakr in which they assumed that the Jordan ideal J is also a subring of R.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1375-1390
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• 2023

In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.691-703
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• 2021

Reinforced concrete (RC) beams can be subjected to a complex combination of shear forces (V), torsional moments (T), flexural moments (M) and axial loads (N). This paper proposes a unified approach for the analysis of these elements. An existing model for the analysis of orthogonally reinforced concrete membrane elements subjected to in-plane shear and normal stresses is generalized to apply to the case of beams subjected to the complex loading. The combination of V and T can be critical. Torsion is modelled using the hollow-tube analogy. A direct equation for the calculation of the thickness of the equivalent hollow tube is proposed, and the shear stresses caused by V and T are combined using a simple approach. The development and the evaluation of the model are described. The calculations of the model are compared to experimental data from 350 beams subjected to various combinations of stress-resultants and to the calculations of the ACI and the CSA codes. The proposed model provides the most favorable results. It is also shown that it can accurately model the interaction between V and T. The proposed model provides a unified treatment of shear in beams subjected to complex stress-resultants and in thin membrane elements subjected to in-plane stresses.

• Journal of the Korean Magnetic Resonance Society
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• v.17 no.1
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• pp.11-18
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• 2013

Rapid advances of computational power and method have made it practical to apply the time-consuming calculations with all-atom force fields and sophisticated potential energies into refining NMR structure. Added to the all-atom force field, generalized-Born implicit solvent model (GBIS) contributes substantially to improving the qualities of the resulting NMR structures. GBIS approximates the effects that explicit solvents bring about even with fairly reduced computational times. Although GBIS is employed in the final stage of NMR structure calculation with experimental restraints, the effects by GBIS on structures have been reported notable. However, the detailed effect is little studied in a quantitative way. In this study, we report GBIS refinements of ubiquitin and GB1 structures by six GBIS models of AMBER package with experimental distance and backbone torsion angle restraints. Of GBIS models tested, the calculations with igb=7 option generated the closest structures to those determined by X-ray both in ubiquitin and GB1 from the viewpoints of root-mean-square deviations. Those with igb=5 yielded the second best results. Our data suggest that the degrees of improvements vary under different GBIS models and the proper selection of GBIS model can lead to better results.

• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.291-310
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• 2014

An advanced model for the linear flutter analysis is introduced in this paper. Higher-order beam structural models are developed by using the Carrera Unified Formulation, which allows for the straightforward implementation of arbitrarily rich displacement fields without the need of a-priori kinematic assumptions. The strong form of the principle of virtual displacements is used to obtain the equations of motion and the natural boundary conditions for beams in free vibration. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to carry out free vibration analyses. According to the doublet lattice method, the natural mode shapes are subsequently used as generalized motions for the generation of the unsteady aerodynamic generalized forces. Finally, the g-method is used to conduct flutter analyses of both isotropic and laminated composite lifting surfaces. The obtained results perfectly match those from 1D and 2D finite elements and those from experimental analyses. It can be stated that refined beam models are compulsory to deal with the flutter analysis of wing models whereas classical and lower-order models (up to the second-order) are not able to detect those flutter conditions that are characterized by bending-torsion couplings.

• Journal of the Korean Chemical Society
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• v.57 no.5
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• pp.554-559
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• 2013

In this study, we have investigated potential energy of ${\beta}$-D-glucopyranose in vacuum and implicit water condition. By Comparing two conditions we find that how solvation energy influence ${\beta}$-D-glucopyranose structure. We use AMBER package program and GLYCAM_06 force field. Solvation model was used for the generalized Born model with Hawkins, Cramer, Truhlar has been proposed. We conclude that difference of contour map of two conditions is caused by solvation effect by reducing hydrogen bonding interaction.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.503-514
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• 2012

The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.

• East Asian mathematical journal
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• v.21 no.1
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• pp.1-7
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• 2005

The object of this paper is to study($\sigma,\;\tau$)-Lie ideals in semi-prime rings with derivation. Main result is the following theorem: Let R be a semi-prime ring with 2-torsion free, $\sigma$ and $\tau$ two automorphisms of R such that $\sigma\tau=\tau\sigma$=, U be both a non-zero ($\sigma,\;\tau$)-Lie ideal and subring of R. If $d^2(U)=0$, then d(U)=0 where d a non-zero derivation of R such that $d\sigma={\sigma}d,\;d\tau={\tau}d$.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.21-38
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• 2023

Let R be a commutative ring with identity. Let R be an integral domain and M a torsion-free R-module. We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebari [1], and generalized the concept of homology, and establish a relation between e-exact sequences and homology of modules. We modify some applications of e-exact sequences in homology and reprove some results of homology with e-exact sequences such as horseshoe lemma, long exact sequences, connecting homomorphisms and etc. Next, we generalize two special drived functor T or and Ext, and study some properties of them.

• Journal of the Korean Magnetic Resonance Society
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• v.19 no.1
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• pp.1-10
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• 2015

Refinements with atomistic molecular dynamics (MD) simulation have contributed to improving the qualities of NMR structures. In most cases, the calculations with atomistic MD simulation for NMR structures employ generalized-Born implicit solvent model (GBIS) to take into accounts solvation effects. Developments in algorithms and computational capacities have ameliorated GBIS to approximate solvation effects that explicit solvents bring about. However, the quantitative comparison of NMR structures in the latest GBIS and explicit solvents is lacking. In this study, we report the direct comparison of NMR structures that atomistic MD simulation coupled with GBIS and water molecules refined. Two model proteins, GB1 and ubiquitin, were recalculated with experimental distance and torsion angle restraints, under a series of simulated annealing time steps. Whereas the root mean square deviations of the resulting structures were apparently similar, AMBER energies, the most favored regions in Ramachandran plot, and MolProbity clash scores witnessed that GBIS-refined structures had the better geometries. The outperformance by GBIS was distinct in the structure calculations with sparse experimental restraints. We show that the superiority stemmed, at least in parts, from the inclusion of all the pairs of non-bonded interactions. The shorter computational times with GBIS than those for explicit solvents makes GBIS a powerful method for improving structural qualities particularly under the conditions that experimental restraints are insufficient. We also propose a method to separate the native-like folds from non-violating diverged structures.