arXiv subjects
Publications and source records attributed to Youngik Lee.
Determining the existence of $k$-clique in the arbitrary graph is one of the NP problems. We suggest a novel way to determine the existence of $k$-clique in the clique complex $G$ under specific conditions, by using the normal mode and eigenvector of the Laplace matrix of $G$.
This research focuses on the possibility of the surjective relation between symmetric potential function and its scattering matrix in 1-dimension. The theory bases on the property of wave function symmetry and boundary conditions. This research shows the surjective relation in some particular cases, delta function potential, and finite square wall potential, and disproves the injective relation of the arbitrary potential function and its S-matrix.
This research focuses on the Numerical approach for Fermat's Last theorem. We can induce an Alternative form of Fermat's last theorem by using particular geometric mapping $\mathcal{M}$ on a Cartesian plane to a Torus. It transforms the Fermat's Last Theorem to finding a rational cross point between two parametric curves on the torus. In the end, this research shows the movement of the point, on the line $x^n+y^n=1$, has an acceleration phase transition near ($x,n$)=(0,2). Moreover, the studies about the relationship between this acceleration transition and the solution for the Fermat's Diophantine equation in the case of $n>$2, need further investigation.
This research focuses on identifying high redshift galaxies from LABOCA(LArge APEX BOlometer CAmera) and SPIRE(The Spectral and Photometric Imaging Receiver) maps towards proto-cluster candidates initially selected from the SPT (South pole telescope) survey. Based on the Multi-Gaussian fitting algorithm, we cross-match all significant LABOCA sources at SPIRE wavelengths based on their coordinates and signal to noise ratio to derive their photometry at 250, 350, 500 and 870 $μm$. We use this information to calculate a photometric redshift for SPT sources towards cluster fields. The code was developed in the Python programming environment.