• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.525-538
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• 1998

Recently, a stability theorem for the Feynman integral as a bounded linear operator on$ L_2$($R^{d}$ /) with respect to measures whose positive and negative variations are in the generalized Kato class was proved. We study a stability theorem for the Feynman integral with respect to measures whose positive variations are in the class of $\sigma$-finite smooth measures and negative variations are in the generalized Kato class. This extends the recent result in the sense that the class of $\sigma$-finite smooth measures properly contains the generalized Kato class.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.15-24
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• 2008

Let $N{\geq}1$ and p > 1. Let ${\Omega}$ be a domain of $\mathbb{R}^N$. In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form $A_pu$ = divA(x,$\nabla$u) for $u{\in}K_p({\Omega})$, ), where $K_p({\Omega})$ is an admissible class and $A(x,\xi)\;:\;{\Omega}{\times}\mathbb{R}^N{\rightarrow}\mathbb{R}^N$ is a mapping satisfying some structural conditions. If p = 2 for example, then we have $K_2({\Omega})\;= \;\{u\;{\in}\;L_{loc}^1({\Omega})\;:\;\partial_ju,\;\partial_{j,k}^2u\;{\in}\;L_{loc}^1({\Omega})\;for\;j,k\;=\;1,2,{\cdots},N\}$. Then we shall prove that $A_p{\mid}u{\mid}\;\geq$ (sgn u) $A_pu$ and $A_pu^+\;\geq\;(sgn^+u)^{p-1}\;A_pu$ in D'(${\Omega}$) with $u\;\in\;K_p({\Omega})$. These inequalities are called Kato's inequalities provided that p = 2. The class of operators $A_p$ contains the so-called p-harmonic operators $L_p\;=\;div(\mid{{\nabla}u{\mid}^{p-2}{\nabla}u)$ for $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.9
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• pp.4665-4667
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• 2012

Cervical cancer is the most common cancer in Laos women and a screening programme, even with the PAP smear test (PAP test), has yet to be established for routine use. The Pap test is accepted as the most appropriate for cervical cancer screening in some settings but it is not commonly available in Laos hospitals, because there are few cytopathologists and gynecologists have little experience. As a pilot program, seminars for the PAP test were given in 2007 and 2008, and then PAP tests were carried out using self-sampling instrument (Kato's device) with 200 healthy volunteers in Setthathirath hospital, Laos, in 2008. The actual examination number was 196, divided into class I 104 (53.1%), class II 85 (43.3%), class IIIa 4 (2.0%), class IIIb 1 (0.5%), and class V 1 (0.5%) by modified Papanicolau classification. Four cases had menstruation. There were 6 cases with epithelial cell abnormalities including malignancy. There were 7 cases with fungus and 2 cases with trichomonas in Class II. More than 70% volunteers felt comfortable with the Kato's device and wanted to use it next time, because of the avoidance of the embarrassment and a low cost as compared with pelvic examination by gynecologists. This first trial for PAP test for healthy Laos women related to a hospital found three percent to have abnormal cervical epithelial cells. Therefore, this appraoch using a self-sampling device suggests that it should be planned for cervical cancer prevention in Laos.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.79-86
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• 2000

In this paper, we introduce the classes H(p,q,k),K(p;k) of operators determined by the Heinz-Kato-Furuta inequality and Holer-McCarthy inequality. We characterize relationship between p-quasihyponormal, $\kappa$-quasihyponormal and $\kappa$-p-quasihyponormal operators. And it is proved that every operator in K(p;1) for some $0 is paranormal.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.689-699
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• 2001

We discuss the class of projective systems whose supports are the complement of the union of three linear subspaces in general position. We proves these codes are uniquely dtermined up to equivalence by their weight enumerators. Our result is a generalization of the result given in [1].

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.559-577
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• 2002

It is known that the analytic operator-valued Feynman integral exists for some "potentials" which we so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.65-72
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• 2015

In this paper we show that the spectrum is continuous on the class of ${\star}$-paranormal operators but the approximate point spectrum generally is not continuous at ${\star}$-paranormal operators.

• ETRI Journal
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• v.29 no.6
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• pp.769-778
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• 2007

This paper proposes a multiplication algorithm for $F_{p^m}$, which can be efficiently applied to many pairs of characteristic p and extension degree m except for the case that 8p divides m(p-1). It uses a special class of type- Gauss period normal bases. This algorithm has several advantages: it is easily parallelized; Frobenius mapping is easily carried out since its basis is a normal basis; its calculation cost is clearly given; and it is sufficiently practical and useful when parameters k and m are small.

• The Korean Journal of Ceramics
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• v.6 no.2
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• pp.168-171
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• 2000

VO$_2$ceramics exhibiting a negative temperature coefficient (NTC) of resistivity have been widely used as temperature dependence resistors. The NTC effect similar to $VO_2$ceramics was observed when a low-thermal-expansion ceramic matrix was loaded near the percolation threshold with conductive metal particles. The resistivity in a composite made from silica glass and 20 vol% Ag filler suddenly decreased from $10^{-7}$ to $10^3\;\Omega$cm at about $300^{\circ}C$.

• Journal of Microbiology
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• v.34 no.4
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• pp.300-304
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• 1996

To define the effects of zooplankton and phytoplankton to bacteria, bacterial numbers, frequency of dividing cells (FDC) and size distribution were performed with image analysis in the surface layer of Lake Soyang. In August 1992, when Anabaena was blooming, the bacterial number increased at daytime. Bacterial numbers and FDC value had a negative correlation (r = 0.83, P < 0.01). Bacterial size spectrums were dynamically changed during the day and night, especially the small bacteria less than $0.5\;{\mu}m^3$. Meanwhile, in October, after the bloom, the bacterial number was only one third of that in August, even though the FDC was higher than that in August. The bacterial numbers of small size class dropped at 13:00. But the size spectrums were relatively constant during the night time. These results suggest that the bacterial growth was tightly coupled with phytoplankton during Anabaena bloom. And after the bloom, the bacterial number was controlled grazing activity of zooplankton at daytime.