• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1047-1053
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• 1996

In this paper, we obtain a solution of Einstein's unified field equations on a generalized n-dimensional Riemannian manifold $X_n$.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.10a
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• pp.145-151
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• 1994

Welded connections have been designed on basis of allowable stresses, wherein the response to loading is assumed to be totally elastic. This is the vector analysis method, which resolves the stresses determined from the direct stress formula and the torsion formula into a vector combination to obtain a solution. It has been known that this method gives conservative answers and typically a very high factor of safety. An analytical method based on the Instantaneous Center of Rotation has been developed which predicts the ultimate strength of an eccentically loaded fillet welded connection. The method of Instantaneous Center of Rotation results in weld resistance capacities greater than the vector analysis method, by recognizing the variation in fillet weld strength with respect to the direction of the applied loading and actual load-deformation response of elemental fillet welds. The procedure of numerical analysis is iterative and complex. The relations between vector analysis method and the method of Instantaneous Center of Rotation on eccentrical distance subjected to variation of load direction are presented in this paper. Considering of the effects on configuration of weld groups, the method of Instantaneous Center of Rotation are provided a more exact results of the numerical analysis.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1147-1165
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• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.225-236
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• 2021

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

• Geotechnical Engineering
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• v.13 no.4
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• pp.149-162
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• 1997

A series of torsion shear tests were performed to study the strength characteristics of sand under various stress paths during rotation of principal stress. These results can be classified into two groups of 25cm and 40cm according to the height of specimen, and toy que was applied only in the clockwise direction. In this study, strength characteristics of sand for the principal stress ratio in torsion sheartests were investigated and their results were compared with Lade's failure criterion. And the effect for specimen was considered. From the results of tests, friction angle of sand was affected by the deviatoric principal stress ratio $b:(\sigma_2 -\sigma_s)/(\sigma_2, -\sigma_3)$Failure strength of sand was determined not by the stress paths but by the current stress state. From comparison of specimens on 25cm and 40cm height, effect of end restraint could not be found. In the test where b is over 0.5 due to extension force, necking phenomenon by the strain localization was found.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.265-280
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• 2018

In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curvature and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.9-16
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• 2000

An A-module M is catenary if for each pair of prime submodules K and L of M with $K{\subset}L$ all saturated chains of prime submodules of M from K to L have a common finite length. We show that when A is a Noetherian domain, then every finitely generated A-module is catenary if and only if A is a Dedekind domain or a field. Moreover, a torsion-free divisible A-module M is catenary if and only if the vector space M over Q(A) (the field of fractions of A) is finite dimensional.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.87-95
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• 2019

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.637-647
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• 2017

Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.