• 한국해양학회지
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• v.14 no.1
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• pp.32-38
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• 1979

The original concept and theory of Shannon's function H=-$\Sigma$(i-1,n)Pi, log$\_$2/Pi and its applicable domains in ecology are discussed. The confusions exist in use and interpretation of this function are due to: 1. Mixing the idea of proper ecological diversity with that of Shannon's information theory. 2. Confusion of physical or thermodynamical systems with ecological systems. 3. Confusion of the system from which one had calculated function H with the system of which function H is interpreted. It's proposed to use function H for the comparison of community's structure and so, for the distinction of community's evolution (succession) steps.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.927-944
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• 2022

Let $\vec{p}{\in}(0,\;1]^n$ be an n-dimensional vector and A a dilation. Let $H^{\vec{p}}_A(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H^{\vec{p}}_A(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f{\in}H^{\vec{p}}_A(\mathbb{R}^n)$ coincides with a continuous function F on ℝⁿ in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H^{\vec{p}}_A(\mathbb{R}^n)$.

• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.7-21
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• 2015

We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.211-215
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• 1978

In the present paper, we obtain two new and interesting finite summation formulae for the H-function of two variables in a very neat and elegant form. The novel feature of the paper is that the method used here in deriving these formulae is simple and direct and does not impose heavy restrictions on the parameters involved. On account of the most general nature of the H-function of two variables, a number of related finite summation formulae for a number of other useful functions can also be obtained as special cases of our results. As an illustration, we have obtained here from our main results, the corresponding finite summation formulae for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function. Appell's function and Gauss' hypergeometric function which are also believed to be new.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1043-1059
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• 2019

In this paper, we use some theta function identities involving two parameters h_n,k and h'_n,k for the theta function φ to establish new evaluations of Ramanujan's cubic continued fraction.

• Bulletin of the Korean Chemical Society
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• v.8 no.5
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• pp.406-408
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• 1987

It has been shown that the distribution of relaxation times, H(ln $\tau$), in semi-logarithmic time scale can easily be calculated numerically from the derivative of the relaxation function in semilogarithmic scale. In that, ln$\tau$, the abscissa, is divided into N different segments of equal size, then H is considered to be a linear function of ln $\tau$within each segment. The technique has been applied to a Williams-Watts function as well as to the relaxation function obtained by photon correlation spectroscopy from atactic polystyrene glass. It has been demonstrated that the relaxation functions can be precisely reproduced from the calculated distribution functions.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.936-938
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• 1996

The $H_{\infty}$ robust controller is designed for on-line adaptive control application by using polynomial approach. The $H_{\infty}$ robust controllers for adaptive system were designed first by Grimble. But they have a problem that two minimum costs can exist and did not minimize the conventional $H_{\infty}$ cost function which is the $H_{\infty}$ sum of weighted sensitivity and complementary sensitivity terms. In this paper, the two minimum costs problem can be avoided and the conventional $H_{\infty}$ cost function is minimized by employing the Youla parameterization and polynomial approach at the same time. In addition pole placement is possible without any relation with weighting function.

• The Journal of Korean Medicine
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• v.28 no.4
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• pp.18-26
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• 2007

Objective : To study the effect of the Insamyangyoung-tang(ISYT) extract on the skin barrier function, the skin pH, skin humidity and transepidermal water loss(TEWL) were measured and histological changes were observed in DNCB(2,4-dinitrochloro-benzen)-induced contact dermatitis(CD) hairless mice. Methods : The male hairless mice were divided into three groups. Each group consisted of 15 mice. The normal group which had acetone- olive oil applied. The control group which had intentionally induced CD by DNCB and it was fed normal saline orally. The ISYT group which had intentionally induced CD by DNCB and it was fed ISYT extract orally for 7 days. The three groups were checked 24h, 48h and 72h later after inducing CD, and the skin pH, skin humidity and TEWL were observed. Tissue samples were taken, and damage to the epithelial cell was observed. Statistical analysis was performed by using one way-ANOVA: significance was set at p values less than 5% (p<0.05). Results : ISYTextract efficiently maintained the pH balance, it kept the skin humidity at a normal level, and it inhibited TEWL of the DNCB-induced CD hairless mouse. The damage to the epithelium was decreased and the regeneration power of the skin was increased in the ISYT group. Conclusion : Insamyangyoung-tang has a good effect on the skin barrier function of DNCB induced contact dermatitis hairless mice.

• Proceedings of the Korean Society of Plant Pathology Conference
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• 2003.10a
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• pp.67.2-68
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• 2003

A rice cultivar, Taebaegbyeo, is highly resistant to rice blast and moderately resistant to bacterial leaf blight (BLB) caused by Magnaporthe grisea and Xanthomonas oryzae pv. oryzae, respectively. To study the rice disease resistance mechanism, we generated rice deletion M3 mutants by gamma-ray irradiation. Blast and BLB responses of 16,000 M3 mutants were screened by inoculating mixtures of 4 races (KJ-201, H-1113a, KI-313, KI-409) of M. grisea and 3 Korean races of X. oryzae pv. oryzae. We selected so far 21 M3 mutants of Taebaegbyeo showing high susceptibility to the diseases. One of the mutants, KCT-6417, was susceptible to KI-1113a race of M. grisea, suggesting the deletion of a race-specific blast resistance gene in the mutant. To isolate rice genes involved in blast resistance and defense response, we take a PCR-based suppression subtractive hybridization approach using cDNAs of blast-inoculated wild type and the KCT-6417 as a tester and a driver, respectively. Genes specifically expressed in the wild type will be presented. The selected genes would give us a clue to understand mechanism for the race specific resistance and defense responses against M. grisea H-1113a in Taebaegbyeo.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.537-543
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• 2015

In [9], the authors determine an infinite class of non-unimodal Gorenstein sequence, which includes the example $$\bar{h}_1\text{ = (1, 125, 95, 77, 71, 77, 95, 125, 1)}$$. They raise a question whether there is a Gorenstein algebra with Hilbert function $$\bar{h}_2\text{= (1, 125, 95, 77, 70, 77, 95, 125, 1)}$$, which has remained an open question. In this paper, we prove that there is no Gorenstein algebra with Hilbert function $\bar{h}_2$.