• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.487-499
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• 2021

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.1 no.1
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• pp.97-101
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• 1991

The polynomial factorization problem is important not only number theorly but chyptology with Discrete logarithm. We factorized polynolmials with integer coefficients by means of factori-zing polynomials on a finite field by Hensel's Lifting Lemma and finding factors of pol;ynomial with integer coeffcients.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1423-1438
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• 2022

In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.113-124
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• 2022

In this paper, we plan to introduce the class of the analytic functions called 𝒫 (b) and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient c₂ in the expansion of f(z) = z+c₂z²+… belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of f(z) function at the boundary point 𝛼 with f'(𝛼) = 1 - b, b ∈ ℂ, by taking into account their first nonzero two Maclaurin coefficients.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.389-400
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• 2023

In this paper, some estimations will be given for the analytic functions belonging to the class 𝓡(α). In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function h(z) and the modulus of the angular derivative of the function ${\frac{zh^{\prime}(z)}{h(z)}}$, respectively. Also, the relationship between the coefficients of the analytical function h(z) and the derivative mentioned above will be shown.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.25-33
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• 2023

This paper's objectives are to present the $\mathcal{H}$ class of analytical functions and explore the many characteristics of the functions that belong to this class. Some inequalities regarding the angular derivative have been discovered for the functions in this class. In addition, the symmetry points on the unit disc are used for the obtained inequalities.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.27 no.1
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• pp.49-54
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• 1982

Experiments were carried out to establish physiological maturity determination criteria with reference to visibly easy measurement in barley in 1980 at Suweon. Thirty-three cultivars and lines from 500 crossing blocks were classified into 4 heading groups, and 5 variables; moisture content, discoloration of awn, exsertion, lemma and flag leaf were measured. There were highly negative correlations between heading date and ripening periods (r=-0.656$^{**}$ ), so early heading types had longer ripening periods. Comparing with the variables used for maturity determination, moisture content and discoloration of lemma were most sensitive to development of grain-filling. Those two variables, alone or in combination could be used to screen many genotypes of barley for physiological maturity. In determination of maturity with reference to visibly easy measurement, color of lemma changed stably and was the most useful way and discolor of flag leaf increased the accuracy of determination. The color of lemma at this time was Grayish yellow, and the mean moisture content was about 33 percent in 33 barley cultivars and lines.

• Plant Resources
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• v.5 no.2
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• pp.95-103
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• 2002

Microscopic techniques were used to observe the microstructure of rice husk. Microscopic examination showed that two main components of husk, lemma and palea consisted of outer epidermis, layers of fibers, vascular bundles, parenchyma cells, and inner epidermis, in sequence from the outer to the inner surface. The outer epidermal walls were extremely thick, highly convoluted and lignified. The underlying fibers were also thick-walled and lignified. Parenchyma cells were thin-walled and unlignified. Inner epidermal cells were also unlignified. The outer surface of both lemma and palea were conspicuously ridged, but the lower surface had a flat appearance. As part of a detailed study to characterize rice husk using microscopic and micro-analytical techniques, distribution of silica was also examined, and is presented elsewhere. Rice husk can potentially be used as a raw material for making composite products and the observations presented here form valuable background information for our future work related to product development.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.325-334
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• 2016

In this paper, a boundary version of the Schwarz lemma is investigated. We take into consideration a function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$ holomorphic in the unit disc and $\|\frac{f(z)}{{\lambda}f(z)+(1-{\lambda})z}-{\alpha}\|$ < ${\alpha}$ for ${\mid}z{\mid}$ < 1, where $\frac{1}{2}$ < ${\alpha}$ ${\leq}{\frac{1}{1+{\lambda}}}$, $0{\leq}{\lambda}$ < 1. If we know the second and the third coefficient in the expansion of the function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$, then we can obtain more general results on the angular derivatives of certain holomorphic function on the unit disc at boundary by taking into account $c_{p+1}$, $c_{p+2}$ and zeros of f(z) - z. We obtain a sharp lower bound of ${\mid}f^{\prime}(b){\mid}$ at the point b, where ${\mid}b{\mid}=1$.

• East Asian mathematical journal
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• v.10 no.2
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• pp.339-343
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• 1994