• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.27-36
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• 2010

We give a simple proof of certain mapping properties of the p-adic Riesz potential and Bessel potential, and the p-adic version of the Sobolev embedding theorem obtained in [6].

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-195
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• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• Journal of KIISE
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• v.44 no.4
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• pp.399-410
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• 2017

We present a system that automatically annotates unverified Web sentences with information from credible sources. The system turns to neural theorem proving for an annotating task for cancer related Wikipedia data (1,486 propositions) with Korean National Cancer Center data (19,304 propositions). By switching the recursive module in a neural theorem prover to a word embedding module, we overcome the fundamental problem of tremendous learning time. Within the identical environment, the original neural theorem prover was estimated to spend 233.9 days of learning time. In contrast, the revised neural theorem prover took only 102.1 minutes of learning time. We demonstrated that a neural theorem prover, which encodes a proposition in a tensor, includes a classic theorem prover for exact match and enables end-to-end differentiable logic for analogous words.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.517-523
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• 1998

In this paper we prove that a normed almost linear space \hat{X} can be embedded in a normed linear space X when a normed almost linear space X has a basis and splits as X=V+W. Also we have a metric induced by a norm on a normed almost linear space as a corollary.

• Communications of the Korean Mathematical Society
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• v.9 no.1
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• pp.67-77
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• 1994

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.171-182
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• 2009

In this paper, we consider the parameter space of the rational plane curves with uni-branched singularity. We show that such a parameter space is decomposable into irreducible components which are rational varieties. Rational parametrizations of the irreducible components are given in a constructive way, by a repeated use of Abhyankar-Moh Epimorphism Theorem. We compute an enumerative invariant of this parameter space, and include explicit computational examples to recover some classically-known invariants.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.643-651
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• 2005

In the first part of this paper we investigate several statements concerning infinite maximal planar graphs which are equivalent in finite case. In the second one, for a given induced $\theta$-path (a finite induced path whose endvertices are adjacent to a vertex of infinite degree) in a 4-connected VAP-free maximal planar graph containing a vertex of infinite degree, a new $\theta$-path is constructed such that the resulting fan is tight.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.319-331
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• 2019

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

• 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.19 no.1
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• pp.133-150
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• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.