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Yun-Su Kim

Publications and source records attributed to Yun-Su Kim.

16 recordsLinked to original sources
arXiv2026

The GIST Korea Test System: A Public-Data Synthetic Model of the Korean Power Grid

No model of the Korean transmission system at native resolution is publicly available, hindering reproducible research on one of the world's most distinctive grids - an islanded interconnection with extreme separation between generation and the Seoul Metropolitan Area load center and heavy reliance on extra-high-voltage transmission. Working strictly from public data, we present the GIST Korea test system, a geographically grounded synthetic model of the Korean grid. Unlike fully synthetic cases, whose lines match no real corridor, and aggregated public Korean models, it derives its 345 and 154 kV layout from the OpenStreetMap power layer by a multi-source shortest-path reassembly of overhead-line and underground-cable geometry, gap-fills unmapped substations by a geographic minimum spanning tree, and calibrates aggregate circuit length to published statistics (94/100/104% at 765/345/154 kV). The current release spans 2265 buses, 614 generation and renewable sources (151 GW), 3185 AC circuits with explicit underground sections, four HVDC converter links, 3413 transformers, and reactive resources, in a PSS/E-compatible CSV schema with zero-sequence and grounding data for unbalanced-fault studies. The model is distributed as a frozen operating point - taps, setpoints, and bus voltages settled once offline - so a single deterministic Newton-Raphson pass reproduces a 91GW evening peak snapshot anchored to the observed 2025 summer peak (2.3% losses, no overloads), consistent with the public KPG-193 model. Standard-parameter dynamic, protection, and unit commitment layers, and a library of 24 hourly operating points derived by security-constrained unit commitment, extend the dataset beyond a single power flow case. The dataset, maps, and tooling are released as a citable, continuously maintained platform for power flow, planning, and decarbonization studies.

eess.SY↗
arXiv2013

Curvature invariant and generalized canonical operator models - II

In [11] the authors investigated a family of quotient Hilbert modules in the Cowen-Douglas class over the unit disk constructed from classical Hilbert modules such as the Hardy and Bergman modules. In this paper we extend the results to the multivariable case of higher multiplicity. Moreover, similarity as well as isomorphism results are obtained.

math.FA↗
arXiv2012

Curvature invariant and generalized canonical Operator models - I

One can view contraction operators given by a canonical model of Sz.-Nagy and Foias as being defined by a quotient module where the basic building blocks are Hardy spaces. In this note we generalize this framework to allow the Bergman and weighted Bergman spaces as building blocks, but restricting attention to the case in which the operator obtained is in the Cowen-Douglas class and requiring the multiplicity to be one. We view the classification of such operators in the context of complex geometry and obtain a complete classification up to unitary equivalence of them in terms of their associated vector bundles and their curvatures.

math.FA↗
arXiv2009

The relationships between Invertible Module Maps X and X_z

If $R$ and $M$ are Hilbert modules (in the sense of R. G. Douglas and V. I. Paulsen), we study the relationship between invertible module maps $X:R\to{M}$ and $X_{z}:R/R_{z}\to{M/M_{z}}$. In particular, for quasi-free Hilbert modules $R$ and $M$, we provide a condition of a module map $X:R\to{M}$, such that if $X_{z}:R/R_{z}\to{M/M_{z}}$ is invertible for every $z$ in a domain $Ω$ in the complex plane, then $X$ is also invertible.

math.FA↗
arXiv2009

Reducing Subspaces on the Annulus

We study reducing subspaces for an analytic multiplication operator M_{z^{n}} on the Bergman space L_{a}^{2}(A_{r}) of the annulus A_{r}, and we prove that M_{z^{n}} has exactly 2^n reducing subspaces. Furthermore, in contrast to what happens for the disk, the same is true for the Hardy space on the annulus. Finally, we extend the results to certain bilateral weighted shifts, and interpret the results in the context of complex geometry.

math.FA↗
arXiv2009

Every transcendental operator has a non-trivial invariant subspace

In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely non-unitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary contractions without a non-trivial algebraic element, or (Case 3) contractions which are not completely non-unitary. We know that every operator of (Case 3) has a non-trivial invariant subspace. In this paper, we answer to the invariant subspace problem for the operators of (Case 2). Since (Case 1) is simpler than (Case 2), we leave as a question.

math.GM↗
arXiv2008

Banach Spaces with respect to Operator-Valued Norms

We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples of Hilbert spaces with respect to L(H)-valued inner products.

math.FA↗
arXiv2008

A Generalization of Beurling's Theorem and Quasi-Inner Functions

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(Ω,K)$ is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-inner divisors.

math.FA↗
arXiv2007

N^p Spaces

We introduce a new norm, called $N^{p}$-norm $(1\leq{p}<\infty)$ on a space $N^{p}(V,W)$ where $V$ and $W$ are abstract operator spaces. By proving some fundamental properties of the space $N^{p}(V,W)$, we also obtain that if $W$ is complete, then the space $N^{p}(V,W)$ is also a Banach space with respect to this norm for $1\leq{p}<\infty$.

math.OA↗
arXiv2007

C_{0}-Hilbert Modules

We provide the definition and fundamental properties of algebraic elements with respect to an operator satisfying hypothesis (h). Furthermore, we analyze Hilbert modules using C_0-operators relative to a bounded finitely connected region Omega in the complex plane.

math.OA↗
arXiv2007

Operator-Valued Norms

We introduce two kinds of operator-valued norms. One of them is an $L(H)$-valued norm. The other one is an $L(C(K))$-valued norm. We characterize the completeness with respect to a bounded $L(H)$-valued norm. Furthermore, for a given Banach space $\textbf{B}$, we provide an $L(C(K))$-valued norm on $\textbf{B}$. and we introduce an $L(C(K))$-valued norm on a Banach space satisfying special properties.

math.FA↗
arXiv2006

A Shift Operator on L(H^2)

We give definitions and some properties of the shift operator S_{L(H^2)} and multiplication operator on L(H^2). In addition, we obtain some properties of the commutant of the shift operator S_{L(H^2)} and characterize S_{L(H^2)}-invariant subspaces.

math.FA↗
arXiv2006

Modular Lattice for $C_{o}$-Operators

We study modularity of the lattice Lat $(T)$ of closed invariant subspaces for a $C_0$-operator $T$ and find a condition such that Lat $(T)$ is a modular. Furthermore, we provide a quasiaffinity preserving modularity.

math.KT↗