• Journal of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.17-30
• /
• 2012

Let D be an arbitrary domain in $\mathbb{C}^n$, n > 1, and $M{\subset}{\partial}D$ be an open piece of the boundary. Suppose that M is connected and ${\partial}D$ is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood of $\bar{M}$. Let f : $D{\rightarrow}\mathbb{C}^n$ be a holomorphic correspondence such that the cluster set $cl_f$(M) is contained in a smooth closed real-algebraic hypersurface M' in $\mathbb{C}^n$ of finite type. It is shown that if f extends continuously to some open peace of M, then f extends as a holomorphic correspondence across M. As an application, we prove that any proper holomorphic correspondence from a bounded domain D in $\mathbb{C}^n$ with smooth real-analytic boundary onto a bounded domain D' in $\mathbb{C}^n$ with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood of $\bar{D}$.

• Proceedings of the IEEK Conference
• /
• 2000.07b
• /
• pp.803-806
• /
• 2000

The correspondence problem is known to be difficult to solve because false positives and false negatives almost always exist in real image sequences. In this paper, we propose a robust feature tracking algorithm considering incomplete trajectories such as entering and/or vanishing trajectories. We solve the correspondence problem as the optimal graph search problem, by considering false feature points and by properly reflecting motion characteristics. The proposed algorithm finds a local optimal correspondence so that the effect of false feature points can be minimized in the decision process. The time complexity of the proposed graph search algorithm is given by O(mn) in the best case and O(m$^2$n) in the worst case, where m and n are the number of feature points in two consecutive frames. The proposed algorithm can find trajectories correctly and robustly, which has been shown by experimental results.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
• /
• 2010.04a
• /
• pp.11-13
• /
• 2010

Combined with the indeterminate boundaries of spatial objects, n:m correspondences makes an object-based matching be a complex problem. In this study, we model the boundary of a polygon object with fuzzy model and describe their overlapping relations as a weighted bipartite graph. Then corresponding pairs including 1:0, 1:1, 1:n and n:m relations are identified using a spectral singular value decomposition.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.513-518
• /
• 2007

There is a one to one correspondence between Artinian algebras $k[x_1,...,x_n]/Ann(M)$ and finitely generated $k[x_1,...,x_n]-submodules$ M of $k[y_1,...,y_n]$ by Inverse System. In particular, any Artinian level algebra $k[x_1,...,x_n]/Ann(M)$ can be obtained when M is finitely generated by only maximal degree generators. We prove that H = (1, 4, 8, 13,..., 27, 8, 2) is not a level Artinian O-sequence using this inverse system.

• Kyungpook Mathematical Journal
• /
• v.61 no.4
• /
• pp.679-710
• /
• 2021

We study the tensor product algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m), where P_k(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P_k(n₁) ⊗ P_k(n₂) ⊗ ⋯ ⊗ P_k(n_m) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ_k^m, Γ_k^m = {[λ] = (λ₁, λ₂, …, λ_m)|λ_i ∈ Γ_k, i ∈ {1, 2, …, m}} where Γ_k = {λ_i ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f^[λ]m_k^[λ] where m_k^[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f^[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.37 no.6
• /
• pp.25-37
• /
• 2000

The trajectories of feature points can be defined by the correspondences between points in consecutive frames. The correspondence problem is known to be difficult to solve because false positives and false negatives almost always exist in real image sequences. In this paper, we propose a robust feature tracking algorithm considering incomplete trajectories such as entering and/or vanishing trajectories. The trajectories of feature points are determined by calculating the matching measure, which is defined as the minimum weighted Euclidean distance between two feature points. The weights are automatically updated in order to properly reflect the motion characteristics. We solve the correspondence problem as an optimal graph search problem, considering that the existence of false feature points may have serious effect on the correspondence search. The proposed algorithm finds a local optimal correspondence so that the effect of false feature point can be minimized in the decision process. The time complexity of the proposed graph search algorithm is given by O(mn) in the best case and O($m^2n$) in the worst case, where m and n arc the number of feature points in two consecutive frames. By considering false feature points and by properly reflecting motion characteristics, the proposed algorithm can find trajectories correctly and robustly, which has been shown by experimental results.

• Communications of the Korean Mathematical Society
• /
• v.19 no.2
• /
• pp.211-217
• /
• 2004

In a ring $R_n(K,\;J)$ where K is a commutative ring with identity and J is an ideal of K, all prime ideals of $R_n(K,\;J)$ are of the form either $M_n(P)\;o;R_n(P,\;P\;{\cap}\;J)$. Therefore there is a one to one correspondence between prime ideals of K not containing J and prime ideals of $R_n(K,\;J)$.

• The Bulletin of The Korean Astronomical Society
• /
• v.40 no.2
• /
• pp.29.3-30
• /
• 2015

We introduce an advanced one-to-one galaxy correspondence method that populates dark matter halos with galaxies by tracing merging histories of most bound member particles (MBPs) identified in simulated virialized halos. To estimate the survival time of a satellite galaxy, we adopt several models of tidal-destruction time derived from an analytic calculation, isolated galaxy simulations, and cosmological simulations. We build mock galaxy samples for each model by using a merging tree information of MBPs from our new Horizon Run 4 N-body simulation from z = 12 to 0. For models of galaxy survival time derived from cosmological and isolated galaxy simulations, about 40% of satellites galaxies merged into a certain halo are survived until z = 0. We compare mock galaxy samples from our MBP-galaxy correspondence scheme and the subhalo-galaxy scheme with SDSS volume-limited galaxy samples around z = 0 with $M_r-5{\log}h$ < -21 and -20. Compared to the subhalo-galaxy correspondence method, our method predicts more satellite galaxies close to their host halo center and larger pairwise peculiar velocity of galaxies. As a result, our method reproduces the observed galaxy group mass function, the number of member galaxies, and the two-point correlation functions while the subhalo-galaxy correspondence method underestimates them.

• Proceedings of the Korean Society of Crop Science Conference
• /
• 1993.10a
• /
• pp.12-13
• /
• 1993

• Anxiety and mood
• /
• v.9 no.1
• /
• pp.31-37
• /
• 2013

Objective : The PDSQ is a brief and psychometrically strong self-report scale designed to screen for common DSM-IV Axis I disorders in clinical settings. In this study, the K-PDSQ was compared with the M.I.N.I.-Plus (Mini-International Neuropsychiatric Interview-Plus) for diagnostic validity and availability of the K-PDSQ as a part of standardization of the K-PDSQ. Methods : The 640 patients were evaluated with the K-PDSQ and the M.I.N.I.-Plus. Diagnosing with the M.I.N.I.-Plus, the diagnostic correspondence, administering time, sensitivity, specificity, ROC curve, and AUC of the K-PDSQ were evaluated. Results : For the diagnostic correspondence of the K-PDSQ, Cohen's kappa coefficient was .66 between the K-PDSQ and the M.I.N.I.-Plus. The administering time of the K-PDSQ was $18.2{\pm}11.80$ minutes. Both sensitivity and specificity of the K-PDSQ were higher: the mean sensitivity across 10 subscales of K-PDSQ was 86%; the mean specificity was 84%. All AUCs of each subscale were above .80, which were statistically significant. Conclusion : The K-PDSQ is valid and available as a diagnostic screening tool. It will be widely used in clinical settings for screening DSM-IV Axis I diagnosis because of its simplicity and high reliability.