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THE DIFFERENTIAL PROPERTY OF ODD AND EVEN HYPERPOWER FUNCTIONS
Cho, Yunhi The Kangwon-Kyungki Mathematical Society 2004 한국수학논문집 Vol.12 No.1
Let $h_e(y)$, $h_o(y)$ denote the limits of the sequences {$^{2n}x$}, {$^{2n+1}x$}, respectively. From these two functions, we obtain a function $y=p(x)$ as an inverse function of them. Several differential properties of $y=p(x)$ are induced.
AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA
Cho, Yunhi Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.4
We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and Santal$\acute{o}$'s formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Su$\acute{a}$rez-Peir$\acute{o}$ [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. Thereafter, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.
PARTIALLY ABELIAN REPRESENTATIONS OF KNOT GROUPS
Cho, Yunhi,Yoon, Seokbeom Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1
A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called w-variables. In this paper, we consider the case when pinched octahedra appear as a boundary parabolic solution in this decomposition. The w-solution with pinched octahedra induces a solution for a new knot obtained by changing the crossing or inserting a tangle at the pinched place. We discuss this phenomenon with corresponding holonomy representations and give some examples including ones obtained from connected sum.
GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE
Cho, Yunhi,Kim, Hyuk Korean Mathematical Society 2013 대한수학회지 Vol.50 No.6
We give a geometric proof of the analyticity of the volume of a tetrahedron in extended hyperbolic space, when vertices of the tetrahedron move continuously from inside to outside of a hyperbolic space keeping every face of the tetrahedron intersecting the hyperbolic space. Then we find a geometric and analytic interpretation of a truncated orthoscheme and Lambert cube in the hyperbolic space from the viewpoint of a tetrahedron in the extended hyperbolic space.
ϵ-PERTURBATION METHOD FOR VOLUME OF HYPERCUBES CLIPPED BY TWO OR THREE HYPERPLANES
( Eungchun Cho ),( Yunhi Cho ) 호남수학회 2021 호남수학학술지 Vol.43 No.4
The first author suggested an exact volume formula of the hypercubes [0, 1]<sup>n</sup> clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using ϵ-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.