• Honam Mathematical Journal
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• v.45 no.1
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• pp.130-145
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• 2023

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.9
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• pp.930-937
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• 2009

The estimation method of the fracture resistance curve for the pipe specimen was proposed using the load ratio method for the standard specimen. For this, the calculation method of the load - CMOD curve for the pipe specimen with the common format equation(CFE) was proposed by using data of the CT specimen. The proposed method agreed well with experimental data. The J-integral value and the crack extension were calculated from the estimated load - CMOD data. The fracture resistance curve was estimated from the calculated J-integral and the crack extension. From these results, it have been seen that the proposed method is reliable to estimate the J-R curve of the pipe specimen.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.209-224
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• 2013

The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.603-616
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• 2017

In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.

• Structural Engineering and Mechanics
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• v.3 no.6
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• pp.541-553
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• 1995

The determination of the stress intensity factors is investigated by using the surface integral defined around the crack tip of the structure. In this work, the integral method is derived naturally from the standard path integral J. But the use of the surface integral is also extended to the case where body forces act. Computer program for obtaining the stress intensity factors $K_I$ and $K_{II}$ is developed, which prepares input variables from the result of the conventional finite element analysis. This paper provides a parabolic smooth curve function. By the use of the function and conventional element meshes in which the aspect ratio (element length at the crack tip/crack length) is about 25 percent, relatively accurate $K_I$ and K_{II}$ values can be obtained for the outer integral radius ranging from 1/3 to 1 of the crack length and for inner one zero.

• Structural Engineering and Mechanics
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• v.34 no.1
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• pp.85-95
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• 2010

In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

• The Journal of Advanced Prosthodontics
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• v.10 no.3
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• pp.227-235
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• 2018

PURPOSE. Implant site preparation may be adjusted to achieve the maximum possible primary stability. The aim of this investigation was to study the relation among bone-to-implant contact at insertion, bone density, and implant primary stability intra-operatively measured by a torque-measuring implant motor, when implant sites were undersized or tapped. MATERIALS AND METHODS. Undersized (n=14), standard (n=13), and tapped (n=13) implant sites were prepared on 9 segments of bovine ribs. After measuring bone density using the implant motor, 40 implants were placed, and their primary stability assessed by measuring the integral of the torque-depth insertion curve. Bovine ribs were then processed histologically, the bone-to-implant contact measured and statistically correlated to bone density and the integral. RESULTS. Bone-to-implant contact and the integral of the torque-depth curve were significantly greater for undersized sites than tapped sites. Moreover, a correlation between bone to implant contact, the integral and bone density was found under all preparation conditions. The slope of the bone-to-implant/density and integral/density lines was significantly greater for undersized sites, while those corresponding to standard prepared and tapped sites did not differ significantly. CONCLUSION. The integral of the torque-depth curve provided reliable information about bone-to-implant contact and primary implant stability even in tapped or undersized sites. The linear relations found among the parameters suggests a connection between extent and modality of undersizing and the corresponding increase of the integral and, consequently, of primary stability. These results might help the physician determine the extent of undersizing needed to achieve the proper implant primary stability, according to the planned loading protocol.

• Journal of the Korean Society for Precision Engineering
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• v.6 no.3
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• pp.78-89
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• 1989

Applicability of tearing modulus based on J-integral proposed by Paris et al is investigated using compact tension specimens of strutural alloy steel (SCM4). Both general fracture test and instability fracture test are performed. The applied tearing modulus, ( $T_{j}$)app estimated from the real load vs. crack growth curve measured from experiments are compared with that estimated from the limit load vs. crack growth curve. The results are : (1) the $T_{j}$parameter could be applied to predict crack growth instability : (2) The use of ( $T_{j}$)app estimated from the load vs. crack growth curve, proposed in this study could be well predicted crack growth instability instead of that estimated form the limit load vs. crack growth curve.e.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.89-95
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• 2002

In this paper, we obtain an integral formula relating the measure of great spheres $S^{n-2}$ and arc length of a curve on the unit sphere $S^{n-1$ As an application of the formula, we develop a geometric inequality for a spherical curve and prone generalized version of Fenchel＇s theorem in $S^n$.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.107-118
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• 2017

In this paper we study CR-submanifolds of maximal CR-dimension by investigating extrinsic behaviors of integral curves of characteristic vector field on them. Also we consider the notion of ruled CR-submanifold of maximal CR-dimension which is a generalization of that of ruled real hypersurface and find some characterizations of ruled CR-submanifold of maximal CR-dimension concerning extrinsic shapes of integral curves of the characteristic vector field and those of CR-Frenet curves.