• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.683-692
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• 2024

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to that of the usual projective plane. Recent explicit constructions of fake projective planes embed them via their bicanonical embedding in ℙ⁹. In this paper, we study Keum's fake projective plane (a = 7, p = 2, {7}, D₃2₇) and use the equations of [1] to construct an embedding of fake projective plane in ℙ⁵. We also simplify the 84 cubic equations defining the fake projective plane in ℙ⁹.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1027-1034
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• 2017

In this paper, we propose a new function embedding method that can measure mathematical projections of probability amplitude, probability, average expectation and matrix elements of stationary-state unit matrix at all control operation points of quantum gates. The function embedding method in this paper is to embed orthogonal normalization condition of probability amplitude for each control operating point into a binary scalar operator by using Dirac symbol and Kronecker delta symbol. Such a function embedding method is a very effective means of controlling the arithmetic power function of a unitary gate in a unitary transformation which expresses a quantum gate function as a tensor product of a single quantum. We present the results of evolutionary operation and projective measurement when we apply the proposed function embedding method to the ternary 2-qutrit cNOT gate and compare it with the existing methods.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1231-1252
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• 2006

In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichmiiller space ${\Im}(M)$ into the Goldman space g(M). From this algebraic presentation, we shall show that the Goldman's length parameter on g(M) is an isometric extension of the Fenchel-Nielsen's length parameter on ${\Im}(M)$.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.253-267
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• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.129-134
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• 2005

Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.661-681
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• 2004

We research properties of the space of measurable functions square integrable with weight exp$2\nu $\mid$x$\mid$$, and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the space of analytic functions extended to any strip in $C^n$ which are estimated with the aid of a special exponential function exp($\mu$｜x｜).

• East Asian mathematical journal
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• v.34 no.1
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• pp.21-28
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• 2018

For a nondegenerate irreducible projective variety, it is a classical problem to study the defining equations of a variety with respect to the given embedding. In this paper we precisely determine the defining equations of certain types of rational curves in ${\mathbb{P}}^3$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.751-763
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• 2016

The properties of the nonabelian tensor products are interesting in different contexts of algebraic topology and group theory. We prove two theorems, dealing with the nonabelian tensor products of projective limits of finite groups. The first describes their topology. Then we show a result of embedding in the second homology group of a pro-p-group, via the notion of complete exterior centralizer. We end with some open questions, originating from these two results.

• East Asian mathematical journal
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• v.38 no.3
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• pp.347-355
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• 2022

For a nondegenerate projective variety, it is a classical problem to study its defining equations with respect to a given embedding. In this paper, we precisely determine minimal sets of generators of the defining ideals of some curves of maximal regularity in ℙ⁵.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1090-1093
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• 2004

In this paper, a problem of geometrically distorted images is considered. In particular, the paper discusses the detection of a watermark from a photographed image of the watermarked picture. The image is possibly obtained by using a digital camera. This watermark detection problem is made difficult by various geometric distortions added to the original picture through the printing and photographing processes. In particular, the paper focuses on the geometric distortion due to a projective transformation, as part of a camera 3D-to-2D imaging process. It is well-known that a cross ratio of collinear points is invariant under a perspective projection. By exploiting this fact, a projective-invariant digital watermarking technique is developed. By detecting the picture's corners, and the image center point at the intersection of two main diagonal lines, predefined cross ratios are used to compute the watermark embedded locations. From those identified embedding pixel locations, a watermark can be detected by performing a correlation between a watermark pattern and the image over those pixels. The proposed method does not require an inverse transformation on the distorted image, thus simplifying the detection process. Performance of the proposed method has been analyzed through computer experiments