• Journal of the Korean Society for Precision Engineering
• /
• v.20 no.9
• /
• pp.159-165
• /
• 2003

Most engineers interested in stress singularities have focused mainly on the research of power stress singularities for v-notched cracks in dissimilar materials. The logarithmic stress singularity was discussed a little in Bogy's paper. The power-logarithmic stress singularity was reported by Dempsey and Sinclair. It was indicated that the logarithmic singularity is only a special case of power-logarithmic stress singularities. Then, Dempsey reported specific cases which have power-logarithmic singularities even fur homogeneous boundary conditions. It was known that logarithmic stress singularities for v-notched cracks in dissimilar materials occurs when the surfaces of a v-notched crack have constant tractions. In this paper, using the complex potential method, the stresses and displacements having logarithmic stress singularities were obtained and the coefficients vectors were calculated by a numerical program code: Mathematica. It was shown that our analysis models don't have logarithmic stress singularities under the constant tractions, although the coefficient vectors are existing.

• Journal of the Optical Society of Korea
• /
• v.1 no.2
• /
• pp.81-89
• /
• 1997

The formation of phase singularities in optical fibers is theoretically and experimentally investigated. In particular, their structural characteristics and properties are discussed in relation to guided mode patterns. It is found that except for the fundamental linearly polarized(LP) modes, all the mixed modes displayed phase singularities in the transverse plane. The results in the few mode fiber show that superposition of the LP even and odd modes produces isolated dark points and phase singularities. Phase singularities are found to be of the screw type and of first order. The number of phase singularities linearly increases with the number of guided modes.

• Current Optics and Photonics
• /
• v.1 no.2
• /
• pp.85-89
• /
• 2017

It is shown that polarization singularities of a new type, namely U and P singularities, arise at the transverse cross section of a partially coherent beam, instead of the common singularities such as C points and L lines in a completely coherent vector field. A relationship between the two kind of singularities with respect to intensity is proposed. We also present a setup that can generate the new singularities, and any desired distribution of degree of polarization, using intensity control.

• Journal of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1173-1246
• /
• 2019

We find all P-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces (a corrected version of) Jan Steven's list [Manuscripta Math. 1993] of the numbers of P-resolutions of each singularities. We then compute the dimensions and Milnor numbers of the corresponding irreducible components of the reduced base spaces of versal deformations of each singularities. Furthermore we realize Milnor fibers as complements of certain divisors (depending only on the singularities) in rational surfaces via the semi-stable minimal model program for 3-folds. Then we compare Milnor fibers with minimal symplectic fillings, where the latter are classified by Bhupal and Ono [Nagoya Math. J. 2012]. As an application, we show that there are 6 pairs of entries in the list of Bhupal and Ono [Nagoya Math. J. 2012] such that two entries in each pairs represent diffeomorphic minimal symplectic fillings.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1213-1223
• /
• 2015

We examine a family of isolated complex surface singularities whose exceptional curves consist of two complex curves with high genera intersecting transversally. Topological data of smoothings of these singularities are determined. We use these computations to construct symplectic 4-manifolds by replacing neighborhoods of the exceptional curves with smoothings of the singularities.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.2
• /
• pp.17-28
• /
• 1999

A new procedure of the boundary element method(BEM),say, singular BEM for the potential problems with singularities is presented. To obtain the numerical solution of which asymptotic behavior near the singularities is close to that of the analytic solution, we use particular elements on the boundary segments containing singularities. The Motz problem and the crack problem are taken as the typical examples, and numerical results of these cases show the efficiency of the present method.

• Journal of the Korean Mathematical Society
• /
• v.36 no.5
• /
• pp.891-910
• /
• 1999

We classify analytically surface singularities defined by some weighted homogeneous polynomials which are topologically equivalent to the type {{{{ { z}`_{0 } ^{n } }}}} + {{{{ { z}`_{k } ^{1 } }}}} + {{{{ { z}`_{2 } ^{1 } }}}} = 0.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.667-680
• /
• 2003

The mirror conjecture means originally the deep relation between complex and symplectic geometry in Calabi-Yau manifolds. Recently, this conjecture is posed beyond Calabi-Yau, and even to, open manifolds (e.g. $A_{n}$ singularities and its resolution) is discussed. While if we treat open manifolds, we can't avoid the boundary (in our case, CR manifolds). Therefore we pose the more precise conjecture (mirror symmetry with boundaries). Namely, in mirror symmetry, for boundaries, what kind of structure should correspond\ulcorner For this problem, the $A_{n}$ case is studied.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1997.10a
• /
• pp.747-750
• /
• 1997

Using complex potentials and the concept of repeated roots for general solutions, logarithmic stress singularities and coefficient vectors for v-notched cracks in isotropic dissimilar materials are evaluated and demonstrated to have no influence on the logarithmic stress singularities.

• 제어로봇시스템학회:학술대회논문집
• /
• 1989.10a
• /
• pp.138-143
• /
• 1989

In considering the singularities of robot, singularity avoidance control of robot wrist is very important. Because it is more difficult structurally to exclude the wrist singularity than the arm singularity. Since control policies with Jacobian may bring about mathematical singularities, control policies with Euler parameters that never cause mathematical singularities are necessary. In this research, singular status of robot wrist was analyzed and control algorithms for 3 and 4 axes robot wrist were proposed. Application results of the proposed control algorithms to the path including singularity showed us usefulness and validity.