• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.369-378
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• 2004

A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.

• The korean journal of orthodontics
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• v.19 no.2
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• pp.7-24
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• 1989

The physical properties of seven sizes of control groups and experimental group in stainless steel orthodontic wires were studied in tension, hardness, bending, torsion and observation of microstructure. The wires (0.40-0.90mm dia.) of round type were tested in the as-received condition. The wires of control groups were TRU-CHROME and REMANIUM, and experimental group was SK wire which was developed by ourselves and made in Korea. The results were as follows; 1. The chemical compositions of control groups and experimental group were austenite stainless steel wires of SOS 304. 2. Higher values of tensile and yield strength in tension were control group I, experimental group, control group II. Maximum tensile and yield strength of experimental group were $203.63{\pm}1.41kg/mm^2$ in 0.70mm diameter and $148.96{\pm}4.88kg/mm^2$ in 0.60mm diameter, and maximum elongation was $5.20{\pm}0.57%$ in 0.45mm diameter. 3. Hardness values of experimental group were similar to control groups. Maximum hardness values were $596.2{\pm}13.66Hv$ in 0.45mm diameter wire of control group I, $590.5{\pm}20.08Hv$ in 0.50mm diameter wire of control group II, and $563.6{\pm}5.35Hv$ in 0.70mm diameter wire of experimental group. 4. Torsion properties of experimental group were similar to control group I and more than control group II. Maximum torsion cycles were $31.8{\pm}2.48$ in 0.45mm diameter of control group I, $17.4{\pm}4.84$ in 0.60mm diameter of control group II, and $24.6{\pm}3.04$ in 0.45mm diameter of experimental group. 5. Maximum bending cycles of experimental group were smaller than control groups. Maximum bending cycles were $9.00{\pm}0.00$ in 0.50mm diameter wire of control group I, $10.0{\pm}0.82$ in 0.40mm diameter wire of control group II, and $8.0{\pm}1.26$ in 0.50mm diameter wire of experimental group. 6. Microstructures of experimental and control groups co-existed with martensited austenite structure and elongated austenite structure. 7. The direction of wire fracture was propagated parallel to torsion direction typically and there was no probability showing wire fracture at inclusions and surface scratches. 8. The type of wire fracture was brittle fracture at initiation site and ductile fracture at core.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.177-183
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• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.