• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.679-683
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• 1997

We obtain new upper bound of the area of a constant breath curve. We estimate the area of a constant breadth curve in terms of its breadth and minimal radius and the arc length of its pedal curve.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.15-23
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• 1999

We obtain an efficient upper bound of the area of convex curves of constant relative breadth in the Minkowski plane. The estimation is given in terms of the Minkowski are length of pedal curve of original curve.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.849-866
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• 2011

In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space $E^3_1$. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in $E^3_1$. As an example, the obtained results are applied to the case $\rho$ = const. and $k_2$ = const., and are discussed.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.107-116
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• 1997

In this paper, we get some properties of curves of constant relative breadth in the Minkowski plane.

• Tribology and Lubricants
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• v.19 no.1
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• pp.1-8
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• 2003

Recently, PM-high speed steel(PM-HSS) has reportedly been a good alternative material for rolling mill because of its superior performance to conventional HSS. This paper has been aimed to investigate the possibility for application to rolling contact element for PM-HSS by X-ray diffraction technique. The X-ray elastic constant for PH-HSS has been found by X-ray diffraction during the four-point bending test. Residual stress and half-value breadth on the contact surface during rolling contact fatigue process by X-ray diffraction have also been measured. The result of this study shows that the application of X-ray diffraction technique to PM-HSS could be as possible alternative material as conventional HSS. Half-value breadth on rolling contact surface by X-ray diffraction is not changed during rolling contact fatigue process. On the other hand, the residual stress is changed. This suggests that dislocation reaction has been hardly occurred in rolling contact, depending on super-saturated carbon in PM-HSS.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.78-86
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• 2002

In general, X-ray diffraction method detects the changes of crystal lattice under material surface using the angle of diffraction 2$\theta$. This technique which deals with in the presented paper can be applied to a behavior on the slipped band or the micro crack cause to material degradation. The relation between half-value breadth and cycle numbers shows three stages, which consist of rapid decrease in the initial cycle, slight decrease in the middle cycle, and then rapid decrease in the final cycle. The ratio of half-value breadth has a constant value on B/B$\_$0/ - N diagram under the loading condition except early part of fatigue life. The ratio of half-value breadth B/B$\_$0/ - log N$\_$f/ with respect to number of cycle to failure N$\_$f/ has linear behavior on B/B$\_$0/ - log N$\_$f/ diagram. Therefore, the evaluation of fatigue life by the average gradient has much less mean error than the estimation of fatigue life by log B/B$\_$0/ - log N/N$\_$f/ relation.

• Journal of Ocean Engineering and Technology
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• v.8 no.1
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• pp.114-122
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• 1994

X-ray stress constant, K, was determined for the diffraction line of (211)plane by using Cr-K$\alpha$ radiation. K was -340.87 MPa/deg. Fatigue crack propagation tests of SS41 steel were conducted under stress ratios of 0.1, 0.3 and 0.5. The half-value breadth of X-ray diffraction profile was measured at and beneath the fracture surface. The half-value breadth, B, on the fracture surface was found to increase with increasing $K_max$. The value of B was influenced by stress ratio in SS41 steel. The half-value breadth took the maximum value at the borden of reversed plastic zone, while it approached to the initial (pre-fatigue) value near the boundary of monotonic plastic zone. The maximum depth of the plasticzone was evaluated on the basis of the half-value breadth distribution. The depth $\omega$$_y$ is related to $K_max$by the following equation : $\omega$$_y$ = $\alpha$($K_max$/$\sigma$$_y$$)^2$ where .sigma.$\sigma$$_y$ is the yield strength obtength obtained in tension test .alpha.is 0.136 for SS41 steel.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.145-152
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• 2000

X-ray diffraction method detects change of crystal lattice distance under material surface using diffraction angle 2$\theta$. This technique can be applied to the behavior on slip band and micro crack due to material degradation. The relation between half-value breadth and number of cycle has three stages which constitute rapid decrease in initial number of cycles, slight decrease in middle number of cycles and rapid decrease in final number of cycles. The ratio of half-value breadth takes a constant value on B/B$_{0}$-N diagram with loading condition except early part of fatigue life. The ratio of half-value breadth B/B$_{0}$ with respect to number of cycle to failure N$_{f}$ has linear behavior on B/B$_{0}$-log N$_{f}$ diagram. Therefore, in this paper the estimation of fatigue life by average gradient method has much less estimated mean error than the estimation of fatigue life by log B/B$_{0}$-log N/N$_{f}$ relation.elation.ation.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.735-740
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• 2001

Let K be a convex body of constant relative breadth and let $K^*$ be its polar dual with respect to the Euclidean unit circle. In this paper we obtain the lower bound for the volume of the pedal body $PK^*P $K^{*}$ of K^*.$ Using this, we also obtain the lower bound for the volume product V$(PK^*)$V(PK) for planar bodies.s.

• International Journal of Industrial Entomology and Biomaterials
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• v.6 no.2
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• pp.139-143
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• 2003

Mathematical constants for multiplication with leaf length (I) or breadth (b) or l ${\times}$ b have been worked out for determining leaf area in promising mulberry genotypes viz., Chinese White, S-146, Chak Majra and Sujanpur Local of sub-tropical India. When pooled, the mathematical constants worked out were 8.1132, 10.1019 and 0.5992 for multiplication with leaf length, breadth and l ${\times}$ b, respectively, for genotypes bearing un-lobbed leaves and 6.9447, 8.2761 and 0.5009 for multiplication with leaf length, breadth and l ${\times}$ b, respectively for genotypes bearing lobbed leaves. Leaf area can be worked out by using any constant by multiplying either with leaf length or breadth or both (l ${\times}$ b). Estimated leaf areas worked out were found significantly and positively correlated with actual leaf area (r＝999$^{＊＊}$). The suggested present non-destructive method by using mathematical constants is very quick and alternative to electronic leaf area meter for spot leaf area determination in mulberry which is the only food source for mulberry silkworm in sericulture industry.