1 citations · 4 across the 13 of their papers we have counts for
16 papers
Improved Upper Bounds for the Rank of the Determinant Tensor via Glynn's Formula
Jeong-Hoon Ju, Hayoung Choi, Taehyeong Kim
In this paper, we improve the upper bound for the tensor rank of the determinant tensor to by finding a new tensor decomposition of the ten…
Twisted Diophantine Approximation II: Uniform Theory
Taehyeong Kim, Vasiliy Neckrasov
We develop a general method for uniform twisted metric Diophantine approximation with an arbitrary fixed real matrix. Using all successive minima of the associated diagonal lattice…
Twisted Diophantine Approximation I: Asymptotic Theory
Taehyeong Kim, Vasiliy Neckrasov
We establish an exact zero-one law for twisted Diophantine approximation with an arbitrary fixed real matrix and a positive non-increasing approximation function satisfying dyadic…
Weighted singular vectors in common-base self-similar sets
Taehyeong Kim, Jaemin Park
We prove a lower bound for the Hausdorff dimension of weighted totally irrational singular vectors in affine-spanning common-base integral self-similar sets satisfying the open set…
Structured matrix factorization length
Jeong-Hoon Ju, Taehyeong Kim
Every (resp. a generic) complex matrix can be expressed as a product of (resp. ) Toeplitz matrices. Motivated by this result, it is natu…
Hamiltonian and Symplectic Tensors in the T-product Algebra
Susana Lopez-Moreno, Taehyeong Kim
We study Hamiltonian and symplectic tensor structures in the T-product algebra. We define T-Hamiltonian and T-symplectic tensors and characterize them through their Fourier-domain…
Infinitely badly approximable affine forms
Taehyeong Kim
A pair of a real matrix and is said to be if \[ \liminf_{\mathbf{q}\in\mathbb{…
Geometric mean for T-positive definite tensors and associated Riemannian geometry
Jeong-Hoon Ju, Taehyeong Kim, Yeongrak Kim +1
In this paper, we generalize the geometric mean of two positive definite matrices to that of third-order tensors using the notion of T-product. Specifically, we define the geometri…
On a Kurzweil type theorem via ubiquity
Taehyeong Kim
Kurzweil's theorem ('55) is concerned with zero-one laws for well approximable targets in inhomogeneous Diophantine approximation under the badly approximable assumption. In this a…
Finding tensor decompositions with sparse optimization
Taehyeong Kim, Jeong-Hoon Ju, Yeongrak Kim
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank tensors. The main ingredient is the Least Absolute Shrinkage and…
A new formula of the determinant tensor with symmetries
Jeong-Hoon Ju, Taehyeong Kim, Yeongrak Kim
In this paper, we present a new formula of the determinant tensor for matrices. In \cite{kim2023newdet4}, Kim, Ju, and Kim found a new formula of …
A new formula for the determinant of matrices
Taehyeong Kim, Jeong-Hoon Ju, Yeongrak Kim
In this paper, we present a new formula for the determinant of a matrix. We approach via the sparse optimization problem and derive the formula through the Least Absol…
On a lower bound of Hausdorff dimension of weighted singular vectors
Taehyeong Kim, Jaemin Park
Let be a -tuple of positive real numbers such that and . A -dimensional vector $x=(x_1,\dots,x_d)\in\mathbb{R}^d…
On Hausdorff dimension in inhomogeneous Diophantine approximation over global function fields
Taehyeong Kim, Seonhee Lim, Frédéric Paulin
In this paper, we study inhomogeneous Diophantine approximation over the completion of a global function field (over a finite field) for a discrete valuation , with af…
Dimension estimates for badly approximable affine forms
Taehyeong Kim, Wooyeon Kim, Seonhee Lim
For given and , we say that a real matrix is -badly approximable for the target if $$\liminf_{q\in\mathbb{Z}^n, \|q\|\to\infty} \|q\|…
Hausdorff measure of sets of Dirichlet non-improvable affine forms
Taehyeong Kim, Wooyeon Kim
For a decreasing real valued function , a pair of a real matrix and is said to be -Dirichlet improvable if the sy…