• Research in Mathematical Education
• /
• v.8 no.1
• /
• pp.19-30
• /
• 2004

This research applies the discursive approach to investigate the social transformation of students' conceptual model of differential equations. The analysis focuses on the students' use of metaphor in class in order to find kinds of metaphor used, their characteristics, and a pattern in the use of metaphor. Based on the analysis, it is concluded that the students' conceptual model of differential equations gradually becomes transformed with respect to the historical and cultural structure of the communal practice of mathematics. The findings suggest that through participating in the daily practice of mathematics as a historical and cultural product, a learner becomes socially transformed to a certain kind of a cultural being with historicity. This implies that mathematics education is concerned with the formation of historical and cultural identity at a fundamental level.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.253-267
• /
• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• Journal of the Korean Society for Heat Treatment
• /
• v.22 no.2
• /
• pp.101-107
• /
• 2009

Effect of isochronic aging on transformation behavior of Ti-50.85at%Ni alloy were investigated by differential scanning calorimeter (DSC). The martensitic transformation temperature increases with increasing annealing temperature until reaching a maximum, and then decreases with further increasing annealing temperature. This can be rationalized by interaction between the distribution of $Ti_3Ni_4$ precipitates and Ni content in the matrix. The R-phase transformation temperature increases with increasing annealing temperature until reaching a maximum, and then decreases with a further increase of annealing temperature. This is attributed to the change of Ni content in the matrix caused by precipitation of $Ti_3Ni_4$. The occurrence of the multiple-stage martensitic and R-phase transformation is attributed to precipitation-induced inhomogeneity of the matrix, both in terms of composition and of internal stress fields.

• Journal of the Korean Society for Heat Treatment
• /
• v.5 no.3
• /
• pp.149-156
• /
• 1992

Transformation behavior and reversible shape memory effct of Ti-Ni-Cu alloys with various Cu content has been investigated by means of electrical resistivity measurement, differential scanning calorimetry. X-ray diffraction and strain gage sensor. The transformation sequence in Ti-Ni-Cu alloys substituted by Cu for Ni up to 5at.% occurs to $B2{\leftrightarrow}B19^{\prime}$ and it proceeds in two stages by addition of 10 at.%Cu. i.e. $B2{\leftrightarrow}B19{\leftrightarrow}B19^{\prime}$. But the content of Cu increases up to 20at.%, it has been transformed in one stage ; $B2{\leftrightarrow}B19$. The shape change of Ti-40Ni-10Cu alloy which was constrain aged in circular form bended in $B2{\leftrightarrow}B19$ transformation but it spreaded out in $B19{\leftrightarrow}B19^{\prime}$ transformation. The amount of reversible shape change (${\Delta}{\varepsilon}$) of Ti-47Ni-3Cu alloy constrain aged at $400^{\circ}C$ after solution treatment has a maximum value of about $5.6{\times}10^{-3}$, but that of cold rolled and constrain aged specimens exhibits a little value independent of Cu concentrations.

• Transactions on Electrical and Electronic Materials
• /
• v.13 no.1
• /
• pp.19-22
• /
• 2012

Transformation behavior of rapidly solidified Ti-47.3Ni (at%) alloy ribbons and thermal stability of the R phase in the ribbons were investigated by means of differential scanning calorimetry (DSC), X-ray diffraction, and transmission electron microscopy. Rapidly solidified Ti-47.3Ni alloy ribbons showed the two-stage B2-R-B19' martensitic transformation behavior. The B2-R transformation in the ribbons was observed even after annealing at 1,223 K, which was attributed to the fact that a specific orientation relationship between $Ti_2Ni$ and matrix in the ribbons is maintained after annealing at 1,223 K. The DSC peak temperature of the B2-R transformation ($T_R^*$) decreased with raising annealing temperature, which was attributed to the increased volume fraction of $Ti_2Ni$, thus causing an increased Ni content in the matrix.

• Journal of the Korea Computer Industry Society
• /
• v.8 no.3
• /
• pp.155-166
• /
• 2007

In this paper, captured face-image was pre-processing, segmentation, and extracting features from thinning by differential operator and minute-delineation. A straight line in slope-intercept form was transformed at the $r-\theta$ domain using Hough Transform, instead of Housdorff distance are extract feature as length, rotation, displacement of lines from thinning line components by differentiation. This research proposed a new approach compare with Hough Transformation and Housdorff Distance for face recognition so that Hough transform is simple and fast processing of face recognition than processing by Housdorff Distance. Rcognition accuracy rate is that Housdorff method is higher than Hough transformation's method.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.5-15
• /
• 2005

The conharmonic transformation is a conformal trans-formation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishii and we have generalized his results. Twisted product space is a generalized warped product space with a warping function defined on a whole space. In this paper, we partially classified the twisted product space and obtain a sufficient condition for a twisted product space to be locally Riemannian products.

• Journal of the Korean Society of Safety
• /
• v.24 no.1
• /
• pp.26-30
• /
• 2009

Shape memory recoverable stress and strain of Ti-42.5at%Ni-10at%Cu alloys were measured by means of constant temperature tensile tests. The alloys' transformation behavior is B2 - B19 by DSC result. The strain by tensile stress were perfectly recovered by heating at any testing conditions but shape memory recoverable stress increased to 66MPa and then slightly decreased. Transformation temperatures from thermal cycling under constant uniaxial applied tensile loads linearly increased by increasing tensile load and their thermal hysteresis are about 110K and their maximum recoverable strain is 6.5% at 100MPa condition.

• Journal of the Korean Magnetics Society
• /
• v.5 no.5
• /
• pp.511-514
• /
• 1995

The crystallization kinetics of $Fe_{73.5}Si_{13.5}B_{9}Cu_{1}Nb_{3}$ amorphous alloy has been investigated using differential scanning calorimetry (DSC). The crystallization process had two stages, i.e. precipitation of the $\alpha$-Fe(Si) solid solution and the tetragonal borides. The isothermal transformation data of the amorphous alloy has been fitted successfully to the generalized Johnson-Mehl-Avrami equation. The mean time exponent, n, obtained is close to 2.5. The value of n=2.5 may be interpreted as being due to a diffusion-controlled transformation process with a constant nucleation rate, one likely transformation mode for the crystallization of metallic amorphous alloys. The activation energy of the overall crystallization process deduced from the time to 50% crystallization are about 81 kcal/mole. The value is of the same order as those estimated from viscous flow.

• Structural Engineering and Mechanics
• /
• v.58 no.5
• /
• pp.847-868
• /
• 2016

In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton's principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.