• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.401-430
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• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.9-11
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• 2002

We improve the free-space optical interconnection efficiency by using circular aperture computer-generated hologram (CGH). In free-space optical interconnection system using CGH, the single CGH is composed of sub-CGHs, which can change the direction of input beams to desired output positions, by Fourier transform. Each sub-CGH is rectangular shape, so the input beams through each sub-CGH are transformed to sinc functions in output plane. The side lobes of each sinc function are superimposed in output plane and they result in detection error in output plane, so the detection efficiency is low. We use the circular shaped sub-CGHs in order to reduce the side lobe value in output plane instead of rectangular shaped sub-CGHs. The each input beam is transformed to first-order Bessel functions through circular shaped sub-CGHs in output plane. The side lobes of first-order Bessel functions us low values compared with side lobes of sinc function, so we can improve the detection efficiency in output plane. We use binary phase modulated CGH, and confirm this improvement results by simulation.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.46-48
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• 1995

An efficient technique for the analysis of a general class of microstrip structures with a substrate is applied in this paper using newly-derived closed-form spatial domain Green's functions employed in conjunction with the Method of Moments(MoM). The computed current distributions on the microstrip structures are used to determine the scattering parameters of microstrip discontinuties and the input impedances of microstrip patch antennas. It is shown that the use of the closed-form Green's functions in the context of the MoM provides a computational advantage in terms of the CPU time by almost two orders of magnitude over the conventional spectral domain approach employing the transformed version of the Green's functions.

• Journal of the Korean Institute of Rural Architecture
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• v.14 no.2
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• pp.27-34
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• 2012

This study aims to examine and classify plane types of Hanok at Haengbok village, analyze changes, area distribution and space structures of space components and sort plane types and their characteristics. Plane types were divided into four; living room, kitchen, dining room, etc. These plane types were labelled as LK type, L+K type, L+DK type and LDK type. LK type and L+K type were mainly found at single-wing house and made of living room and kitchen centered space structure, but substantially they were designed to ensure guest room, room and living room. Therefore, hanok built at Haengbok village were designed to combine the functions of residential function and lodging. Plane type was preferred to be used for double functions of residence and lodging. On the other side, L+DK type and LDK type were mainly found in house with several wings and they were designed centering around living room for family space. In addition entrance was placed to simplify entry from the outside and each room and guest room were arranged to be accessed from living room. It means that the functions of house focused on residence rather than lodging and all rooms had the structure to be used as residential space in case of emergency.

• Journal of Society of Preventive Korean Medicine
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• v.8 no.1
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• pp.59-74
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• 2004

We have conducted questionnaire and measured serum liver function tests on 153 patients whom have received a treatment at a local Oriental medicine clinic in Seoul from Sept. 1, 2002 to Dec. 31, 2002. Patients were categorized into the groups of control(10), decoction group(41), herbal group(5), western medicine group(45), and the group taking both herbal and western medicines(55) concurrently or separately. This study was conducted to investigate how these treatment methods can affect the liver functions. Following results were obtained : 1) Most of the research subjects were male(l03 individuals) living in large urban area, with drinking habit, highly educated, and with normal marriage. For the treatment history, 45 individuals received western medicine treatment(28.85%), 46 with Oriental medicine (29.49%), and 55 patients(35.26%) experienced both forms of treatment. 2) Measuring SD of serum liver functions for all the research subjects, T-protein was 6.95(0.73)g/dl, 4.07(0.51)g／dl for albumin, 0.44(0.19)mg／dl for T-bilirubin, 23.18(18.68)U／L for ALT, 27.42(27.43)U／L for AST, and 22l.27(64.58)mg／dl for LDH. 3) Among the research subjects with the liver functions outside of normal range were 0.64% for T-protein, 3.21% for T-bilirubin and ALT, 36.62% for AST, 0.64% for LDH, and none for Albumin. 4) Confusion variables which may affect the liver functions such as age, smoking, drinking, occupation, and residence were eliminated in calculation and no significant differences were witnessed between the control and experiment groups. 5) In measuring affects of treatment duration on the liver functions, no statistical significances were shown in multiple regression's ,${\beta}$(SE) values. 6) The values of odd ratio in the experiment groups compared to the control were in the range of $0.26(0.22){\sim}0.62(1.23)$. but T-bilirubin of the group receiving both Oriental and western medicine was 1.47(1.90) which showed statistical increase(p<0.001). 7) Factors affecting the liver functions are drinking volume per round duration of alcohol intake, western medicine treatment, gender, and age difference caused significant influences. 8) 57 individuals with serum liver functions out of normal range were mostly male, living in large urban area, median age of 38.89, with normal marriage, highly educated drinking less than once a week with less than 2 bottles per round, and with prior treatment in either western or Oriental medicine. Summarizing above results, we can carefully deduce that taking herbal medicine (both decoction and pills) or western medicine doesn't cause much affect in the liver functions. But taking two forms of medication simultaneously or altering dosage affect significant increase in the T-bilirubin level, thus one needs to take precaution when taking both. Further research is needed in this field to verify this evidence.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.183-194
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• 1998

Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.325-338
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• 2022

In this paper, a new identity is given. On the basis of this identity, we establish some new estimates of Milne's quadrature rule, for functions whose first derivative is s-convex. We discuss the cases where the derivatives are bounded as well as Lipschitzian. Some illustrative applications are given.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.797-812
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• 1997

For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss-Radau and the Gauss-Lobatto rules with end points of multiplicity r and prove the convergence of the kernel we obtained. The error bound are obtained for the type $$\mid$R_n(f)$\mid$ \leq \frac{1}{\pi}l(\Gamma) max_{z \in \Gamma} $\mid$K_n(z)$\mid$ max_{z \in \Gamma} $\mid$f(z)$\mid$$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.507-514
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• 1998

The minimum distance estimation based on the L$_2$ distance between a model density and a density estimator is studied from M-estimation point of view. We will show that how a model density and a density estimator are incorporated in order to create an M-estimation function. This method enables us to create an M-estimating function reflecting the natures of both an assumed model density and a given set of data. Some new types of M-estimation functions for estimating a location and scale parameters are introduced.