• Korean Journal of Mathematics
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• v.32 no.2
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• pp.285-295
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• 2024

In this work, we consider the function $${\Psi}(z)=\frac{z}{\ln(1+z)}=1+\sum\limits_{n=1}^{\infty}\,G_nz^n$$ whose coefficients G_n are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass ${\mathcal{G}}^{{\lambda},{\mu}}_{\Sigma}(\Psi)$ of analytic bi-univalent functions subordinate to the function Ψ. For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1253-1263
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• 2023

Let 𝓤⁺ be the class of analytic functions f such that ${\frac{z}{f(z)}}$ has real and positive coefficients and f^-1 be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for f, as well as, sharp estimates of the second and the third Hankel determinant for f and f^-1. We also show that the Zalcman conjecture holds for functions f from 𝓤⁺.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1509-1533
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• 2020

We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1123-1148
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• 2016

The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1357-1377
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• 2017

In this article, we first give the $L^p$ boundedness of the operator $D^2L^{-1}$ with BMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator L with VMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.1-16
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• 2007

In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.15
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• pp.33-59
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• 1974

A series of experiments were conducted at Crop Experiment Station from 1968 to 1971 to obtain basic information on effects of selection on yield of wheat varieties. Heritability estimates, correlation and path coefficients computed for yield and yield related characters from fixed variety groups-Korean, U.S., and Japan; early and late-$F_2$ and $F_3$ generations were studied. The same estimates for fixed variety groups grown under different fertilizer levels and years were also studied. The results were summarized as follow: 1. Three variety groups classified by their origins as Korea, United States and Japan showed high heritability estimates for heading date, plant height and spike length. The heritability estimates for grain number per spike and 1, 000 grain weight were moderate and those for the number of spikes per plant and grain yield were low. Very low estimates of heritability were obtained for grain number per spike and yield of variety group from the Unites States. 2. High genotypic correlation coefficients between 1, 000 grain weight and yield were obtained for all variety groups originated from Korea, United States and Japan and early variety group, except late variety group. The genotypic correlation coefficients between grain number per spike and yield were also high for all variety groups except variety group originated from the United States. 3. The direct effects of 1, 000 grain weight in terms of path-coefficients to yield were high for all variety groups except late variety group. 4. High genotypic correlation coefficients were obtained between 1, 000 grain weight and yield in $F_2$ from. two crosses. The same degree of genotypic correlation coefficients were obtained between grain number per spike and yield, although slight differences in its magnitude were found depending upon the cross combination. 5. The analysis of path-coefficients in $F_2$ shows that the direct effects of yield components to yield were negligible. 6. The characters that showed high genotypic correlation coefficients with yield in $F_3$ were 1, 000 gnain weight and grain number per spike. These characters showed also high direct effects to yield. 7. No great variations of heritability estimates for heading date, plant height and spike length were obtained for either fertilizer responsive or non responsive variety group due to fertilizer levels applied. 8. Heritability estimates of 1, 000 grain weight in fertilizer responsive group and yield in fertilizer nonresponsive group were high as level of fertilizer increased. 9. Heritability estimates for grain number per spike and 1, 000 grain weight of fertilizer non-responsive-group were higher than those of fertilizer. responsive group. 10. Genotypic corretation coefficients between yield and 1, 000 grain weight in fertilizer responsive group were getting lower as the level of fertilizer increased and those in fertilizer non-responsive group were vice versa. 11. Genotypic correlation coefficient between yield and spike number per plant in fertilizer responsive group was high. However, the genotypic correlation coefficient between yield and spike number per plant in fertilizer non-responsive group was low. 12. The direct effects of 1, 000 grain weight to yield were higher than other yield components either in fertilizer responsive or non-responsive group regardless of levels of fertilizer applied. The spike number per plant, however, was high only when high level of fertilizers were applied to fitilizer responsive group. 13. Slight variations of heritability estimates for heading dates, plant height, spike length, grain number per spike and 1, 000 grain weight were obtained between years. However, the spike number per plant with low heritabilility showed great variation between years. 14. The character that showed high genotypic correlation coefficients with yield in two years was 1, 000 grain weight, and this character was also high in direct effect to yield in terms of path-coefficients. 15. From the above experimental results, it might be concluded that 1, 000 grain weight would be one of the most important characters to increase the effects of selection for yield in wheat breeding in Korea.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.703-712
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• 2016

In this article, we derive a sharp estimates for the Taylor-Maclaurin coefficients of functions in some certain subclasses of spirallike functions which are defined by generalized Srivastava-Attiya operator. Several corollaries and consequences of the main result are also considered.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.389-397
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• 2017

In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on ${\Delta}=\{z{\in}{\mathbb{C}}$ : 1 < |z| < ${\infty}\}$. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.405-413
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• 2018

In this work, we use the Faber polynomial expansions to find upper bounds for the coefficients of analytic bi-univalent functions in subclass $\Sigma({\tau},{\gamma},{\varphi})$ which is defined by subordination conditions in the open unit disk ${\mathbb{U}}$. In certain cases, our estimates improve some of those existing coefficient bounds.