• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.35-42
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• 2012

In this paper we first introduce a Carleson inequality and study the generalized form of Carleson inequality in the context of spaces of homogeneous type. The previous inequality is known to play important roles in harmonic analysis.

• Progress in Superconductivity and Cryogenics
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• v.14 no.1
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• pp.14-19
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• 2012

Shimming, active and/or passive, is indispensable for most MR (magnetic resonance) magnets where homogeneous magnetic fields are required within target spaces. Generally, shimming consists of two steps, field mapping and correcting of fields, and they are recursively repeated until the target field homogeneity is reached. Thus, accuracy of the field mapping is crucial for fast and efficient shimming of MR magnets. For an accurate shimming, a "magnetic" center, which is a mathematical origin for harmonic analysis, must be carefully defined, Although the magnetic center is in general identical to the physical center of a magnet, it is not rare that both centers are different particularly in HTS (high temperature superconducting) magnets of which harmonic field errors, especially high orders, are significantly dependent on a location of the magnetic center. This paper presents a new algorithm, based on a field mapping theory with harmonic analysis, to define the best magnetic center of an MR magnet in terms of minimization of pre-shimming field errors. And the proposed algorithm is tested with simulation under gaussian noise environment.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.1003-1016
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• 2016

In this paper, we introduce a new kind of slant helix for null curves called null $W_n$-slant helix and we give a definition of new harmonic curvature functions of a null curve in terms of $W_n$ in (n + 2)-dimensional Lorentzian space $M^{n+2}_1$ (for n > 3). Also, we obtain a characterization such as: "The curve ${\alpha}$ s a null $W_n$-slant helix ${\Leftrightarrow}H^{\prime}_n-k_1H_{n-1}-k_2H_{n-3}=0$" where $H_n,H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $k_1,k_2$ are the Cartan curvature functions of the null curve ${\alpha}$.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.649-659
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• 1995

The purpose of this paper is to generalize the Carleson inequality, which is known to play important roles in harmonic analysis. The result given here is a generalization of Coifmann, Meyer, Stein [CMS]. A similar result is shown by Deng [D].

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.599-627
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• 2020

In this paper, we characterize a class of biharmonic maps from and between doubly product manifolds in terms of theie warping function. Examples are constructed when all of the factors are Euclidean spaces.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.649-650
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• 2022

In this erratum, we offer a correction to [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435-1449]. Theorem 1 in the original paper has three assertions (i)-(iii), but we add (iv) after having clarified the argument.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.319-344
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• 2004

In this paper, we define conditional integrals on abstract Wiener and Hilbert spaces and then obtain a formula for evaluating the integrals. We use this formula to establish the existence of conditional Feynman integrals for the classes $A^{q}$(B) and $A^{q}$(H) of functions on abstract Wiener and Hilbert spaces and then specialize this result to provide the fundamental solution to the Schrodinger equation with the forced harmonic oscillator.tor.

• Korean Institute of Interior Design Journal
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• v.19 no.1
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• pp.217-225
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• 2010

As life quality have grown today, People have been greatly interested in health. Moreover, new knowledge and concepts are being applied in the medical facility field and that makes the field expand constantly. Hereby, this research is a study on design elements of dental clinics and the research goals are to understand interior design of current dental clinics by investigation and analysis on furniture, closing materials, colors and so on, and to investigate esthetic and functional environments for dental clinics through analyzing upcoming trends of inner spaces of dental clinics. The investigation was conducted by visits to four clinics per each research area, where are in Busan area and opened after year 2000 and are located in Seoul and Busan. Though the spaces of dental clinics vary according to the characteristics of each clinic, it generally has a consultation room, a waiting room and an X-ray room. The closing materials that make patients feel at ease are used in the waiting room, and ones that make patients feel tidy and fresh are used in consultation spaces, spare spaces, and management spaces. In Seoul area, antique and harmonic colors are used, and modernistic colors are used in Busan area. Reception desks, chair units, sofas and sink storage shelfs are the common furniture in the clinic. We have learned what are mentioned above by research and investigation on the component characteristics of dental clinic spaces. Based on these, more systematical and in-depth research should be continued.