• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.691-702
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• 1994

Let X be a normed linear space, M a subspace of X, and V a subspace of the dual space $X^*$. In [3], we studied the Hahn-Banach extension property in V. Here we give the definition and a characterization of the Hahn-Banach extension property in V.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.245-254
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• 2009

In this paper, one kind of subgroup in arbitrary group which similar to the linear subspace was constructed, and the generalization of the Hahn-Banach theorem on this kind of subgroup in arbitrary groups was obtained.

• Journal of Korea Multimedia Society
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• v.20 no.11
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• pp.1720-1728
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• 2017

Active shape model is widely used in the field of image processing especially on arbitrary meaningful shape extraction from single gray level image. Cootes et. al. showed efficient detection of variable shape from image by using covariance and mean shape from learning. There are two stages of learning and testing. Hahn applied enhanced shape alignment method rather than using Cootes's rotation and scale scheme. Hahn did not modified the profile itself. In this paper, the method using directional one dimensional profile is proposed to enhance Cootes's one dimensional profile and the shape alignment algorithm of Hahn is combined. The performance of the proposed method was superior to Cootes's and Hahn's. Average landmark estimation error for each image was 27.72 pixels and 39.46 for Cootes's and 33.73 for Hahn's each.

• Economic and Environmental Geology
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• v.37 no.2
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• pp.153-171
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• 2004

This study was carried out to define the geochemical and mineralogical relationship between stream sediments and regional geology on upstream of Hahn river area. Geochemical characteristic including for major elements, trace elements and rare earth elements of the South and North Hahn river bed sediments are similar to those of acid igneous rocks which are distributed around both Hahn river basin. The chemical variation of major elements against SiO$_2$ and trace elements contents between South and North Hahn river bed sediments doesn't show the difference. REE patterns of both area show a distinct negative Eu anomaly, but total contents of rare earth elements are higher in North Hahn river sediments than South Hahn river sediments. The heavy minerals in the river bed sediments in this study area are identified as tremolite-actinolite, hematiteㆍmagnetite, common hornblende, ilmenite, garnet, epidote, rutile and sphene. In conclusion, it is elucidated that South and North Hahn river bed sediments are being originated from igneous rocks or metamorphic rocks which contains medium-high grade metamorphic minerals and components of originated from sedimentary rocks those of politic or calcareous rocks are eroded away as solution or suspended load.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.63-79
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• 1997

Consider an oparator equation of the form : $$ (1.1) H[y](x) = \alpha(x)\delta^2 y(x) + \beta(x)\delta y(x) = \lambda_n y(x), $$ where $\alphs(x)$ and $\beta(x)$ are polynomials of degree at most two and one respectively, $\lambda_n$ is the eigenvalue parameter, and $\delta$ is Hahn's operator $$ (1.2) \delta f(x) = \frac{(q - 1)x + \omega}{f(qx + \omega) - f(x)}, $$ for real constants $q(\neq \pm 1)$ and $\omega$.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.401-414
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• 2019

Let ${\mathcal{F}}$ denote an algebraically closed field with characteristic not two. Fix an integer $d{\geq}3$, let $Mat_{d+1}({\mathcal{F}})$ denote the ${\mathcal{F}}$-algebra of $(d+1){\times}(d+1)$ matrices with entries in ${\mathcal{F}}$. An ordered pair of matrices A, $A^*$ in $Mat_{d+1}({\mathcal{F}})$ is said to be LB-TD form whenever A is lower bidiagonal with subdiagonal entries all 1 and $A^*$ is irreducible tridiagonal. Let A, $A^*$ be a Leonard pair in $Mat_{d+1}({\mathcal{F}})$ with fundamental parameter ${\beta}=2$, with this assumption there are four families of Leonard pairs, Racah, Hahn, dual Hahn, Krawtchouk type. In this paper we show from these four families only Racah and Krawtchouk have LB-TD form.

• Korean Architects
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• s.634
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• pp.82-83
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• 2022

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2005.10a
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• pp.121-121
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• 2005

• Journal of Preventive Medicine and Public Health
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• v.29 no.3 s.54
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• pp.521-527
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• 1996

The Hahn double 15 hue test is used for social and vacational aptitude test to separate strongly and mildly affected subjects among the colour vision defective persons, detected using colour vision test. However, the assessment of colour vision defect type and severity is based on the hue confusions which are represented diagrammatically on Hahn double 15 hue score sheet, this qualitative assessment of the test results have not provide a numerical score suitable for methematical analysis. This paper presented a new proposal for quantitatively scoring the Hahn double 15 hue test based on those hue confusions made by the subject. With this program large numbers of double 15 hue test results can be processed easily and rapidly, and program helps to compare the severity of specific type colour vision defect and monitor acquired colour vision defect which has various disease process, continuously.