• East Asian mathematical journal
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• v.22 no.2
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• pp.131-149
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• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.251-259
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• 2015

Let $\mathbb{F}^d_q$ be a d-dimensional vector space over a finite field $\mathbb{F}^d_q$ with q elements. We endow the space $\mathbb{F}^d_q$ with a normalized counting measure dx. Let ${\sigma}$ be a normalized surface measure on an algebraic variety V contained in the space ($\mathbb{F}^d_q$, dx). We define the restricted averaging operator AV by $A_Vf(X)=f*{\sigma}(x)$ for $x{\in}V$, where $f:(\mathbb{F}^d_q,dx){\rightarrow}\mathbb{C}$: In this paper, we initially investigate $L^p{\rightarrow}L^r$ estimates of the restricted averaging operator AV. As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on $\mathbb{F}^2_q$ play a crucial role in proving our results.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

• Journal of Multimedia Information System
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• v.9 no.2
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• pp.93-102
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• 2022

Dependency parsing is a decision problem of the syntactic relation between words in a sentence. Recently, deep learning models are used for dependency parsing based on the word representations in a continuous vector space. However, it causes a mislabeled tagging problem for the proper nouns that rarely appear in the training corpus because it is difficult to express out-of-vocabulary (OOV) words in a continuous vector space. To solve the OOV problem in dependency parsing, we explored the proper noun embedding method according to the embedding unit. Before representing words in a continuous vector space, we replace the proper nouns with a special token and train them for the contextual features by using the multi-layer bidirectional LSTM. Two models of the syllable-based and morpheme-based unit are proposed for proper noun embedding and the performance of the dependency parsing is more improved in the ensemble model than each syllable and morpheme embedding model. The experimental results showed that our ensemble model improved 1.69%p in UAS and 2.17%p in LAS than the same arc-eager approach-based Malt parser.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.767-787
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• 2019

In this paper, we give some characterizations of p-adic central Campanato spaces via the boundedness of commutators of p-adic Hardy type operators. Besides, some further boundedness of p-adic Hardy operators and their commutators is also presented.

• Korean Journal of Applied Biomechanics
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• v.28 no.4
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• pp.213-218
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• 2018

Objective: The purpose of this study was to examine the effect of the core muscle strength enhancement of the elderly on 8 weeks training using the core exercise equipment for the elderly on the ability to control the whole-body center of mass in posture stabilization. Method: 16 females (10 exercise group, 6 control group) participated in this study. Exercise group took part in the core strength training program for 8 weeks with total of 16 repetitions (2 repetitions per week) using a training device. External perturbation during standing as pulling force applied at the pelvic level in the anterior direction was provided to the subject. In a UCM model, the controller selects within the space of elemental variables a subspace (a manifold, UCM) corresponding to a value of a performance variable that needs to be stabilized. In the present study, we were interested in how movements of the individual segment center of mass (elemental variables) affect the whole-body center of mass (the performance variable) during balance control. Results: At the variance of task-irrelevant space, there was significant $test^*$ group interactions ($F_{1,16}=7.482$, p<.05). However, there were no significant main effect of the test ($F_{1,16}=.899$, p>.05) and group ($F_{1,16}=1.039$, p>.05). At the variance of task-relevant space, there was significant $test^*$ group interactions ($F_{1,16}=7.382$, p<.05). However, there were no significant main effect of the test ($F_{1,16}=.754$, p>.05) and group ($F_{1,16}=1.106$, p>.05). Conclusion: The results of this study showed that the 8 weeks training through the core training equipment for the elderly showed a significant decrease in the $Vcm_{TIR}$ and $Vcm_{TR}$. This result indicates that the core strength training affects the trunk stiffness control strategy to maintain balance in the standing position by minimizing total variability of individual segment CMs.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.78.2-78.2
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• 2019

We develop an Alcock-Paczynski (AP) test method that uses the evolution of redshift-space two-point correlation function (2pCF) of galaxies. The method improves the AP test proposed by Li et al. (2015) in that it uses the full two-dimensional shape of the correlation function. Similarly to the original method, the new one uses the 2pCF in redshift space with its amplitude normalized. Cosmological constraints can be obtained by examining the redshift dependence of the normalized 2pCF. This is because the 2pCF should not change apart from the expected small non-linear evolution if galaxy clustering is not distorted by incorrect choice of cosmology used to convert redshift to comoving distance. Our new method decomposes the redshift difference of the 2-dimensional correlation function into the Legendre polynomials whose amplitudes are modelled by radial fitting functions. The shape of the normalized 2pCF suffers from small intrinsic time evolution due to non-linear gravitational evolution and change of type of galaxies between different redshifts. It can be accurately measured by using state of the art cosmological simulations. We use a set of our Multiverse simulations to find that the systematic effects on the shape of the normalized 2pCF are quite insensitive to change of cosmology over \Omega_m=0.21 - 0.31 and w=-0.5 - -1.5. Thanks to this finding, we can now apply our method for the AP test using the non-linear systematics measured from a single simulation of the fiducial cosmological model.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.151-159
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• 2015

This paper investigates temporal regularity of solutions for the incompressible Euler equations in a critical Besov space $B^{\frac{d}{p}+1}_{p,1}(\mathbb{R}^d)$ for $1{\leq}p{\leq}d$.