• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1551-1559
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• 2014

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle ${\pi}{\alpha}$, ${\alpha}{\in}(1,2]$, at infinity. We derive the exact interval for the variability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are contained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1937-1943
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• 2015

For $1{\leq}{\alpha}<2$, let $\mathcal{F}({\alpha})$ denote the class of locally univalent normalized analytic functions $f(z)=z+{\Sigma}_{n=2}^{\infty}{a_nz^n}$ in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\left|z\right|}<1\}$ satisfying the condition $Re\(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\)>{\frac{{\alpha}}{2}}-1$. In the present paper, we shall obtain the sharp upper bound for Fekete-$Szeg{\ddot{o}}$ functional $|a_3-{\lambda}a_2^2|$ for the complex parameter ${\lambda}$.

• Advances in nano research
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• v.8 no.1
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• pp.49-58
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• 2020

This paper investigates the vibration characteristics of flexoelectric nanobeams resting on viscoelastic foundation and subjected to magneto-electro-viscoelastic-hygro-thermal (MEVHT) loading. In this regard, the Nonlocal strain gradient elasticity theory (NSGET) is employed. The proposed formulation accommodates the nonlocal stress and strain gradient parameter along with the flexoelectric coefficient to accurately predict the frequencies. Further, with the aid of Hamilton's principle the governing differential equations are derived which are then solved through Galerkin-based approach. The variation of the natural frequency of MEVHT nanobeams under the influence of various parameters such as the nonlocal strain gradient parameter, different field loads, power-law exponent and slenderness ratio are also investigated.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.789-804
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• 2022

Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C^*-algebras and derive the results of Schur and Vybíral. As an application, we state C^*-algebraic version of Novak's conjecture and solve it for commutative unital C^*-algebras. We formulate Pólya-Szegő-Rudin question for the C^*-algebraic Schur product of positive matrices.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.443-460
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• 2023

A binary linear code is said to be a ℤ₂-double cyclic code if its coordinates can be partitioned into two subsets such that any simultaneous cyclic shift of the coordinates of the subsets leaves the code invariant. These codes were introduced in [6]. A ℤ₂-double cyclic code is called reversible if reversing the order of the coordinates of the two subsets leaves the code invariant. In this note, we give necessary and sufficient conditions for a ℤ₂-double cyclic code to be reversible. We also give a relation between reversible ℤ₂-double cyclic code and LCD ℤ₂-double cyclic code for the separable case and we present a few examples to show that such a relation doesn't hold in the non-separable case. Furthermore, we list examples of reversible ℤ₂-double cyclic codes of length ≤ 10.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.787-805
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• 2023

Let (Ω, µ) be a measure space and {τ_α}_α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space 𝓗 of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that $$\sup\limits_{{\alpha},{\beta}{\in}{\Omega},{\alpha}{\neq}{\beta}}\,{\mid}{\langle}{\tau}_{\alpha},\,{\tau}_{\beta}{\rangle}{\mid}^{2m}\,{\geq}\,{\frac{1}{({\mu}{\times}{\mu})(({\Omega}{\times}{\Omega}{\backslash}{\Delta})}\;\[\frac{{\mu}({\Omega})^2}{\({d+m-1 \atop m}\)}-({\mu}{\times}{\mu})({\Delta})\],\;{\forall}m{\in}{\mathbb{N}}.$$ This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

• Communications for Statistical Applications and Methods
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• v.30 no.6
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• pp.531-550
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• 2023

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.

• Journal of the Korean Wood Science and Technology
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• v.51 no.3
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• pp.157-172
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• 2023

Azadirachta excelsa, is a plant belonging to the same genus as Indian neem (Azadirachta indica), and its use as a pesticide is reported by few studies. Despite being a different species, it is expected to have the same biopesticide potential as A. indica. Therefore, this study aims to investigate the anti-termite activity of n-hexane and methanol extracts of A. excelsa seed kernel at various concentrations against Coptotermes curvignathus. The methanol extract demonstrated greater termicidal activity than n-hexane at doses test of 2%, 4%, and 8%. It also showed 100% termite mortality on the third day of administering the 8% dose. According to the gas chromatography with mass spectrometry data, the putative main components of the n-hexane extract were hexadecanoic acid, ethyl ester (18.99%), 9,12-octadecadienoic acid (Z,Z)- (16.31%), and 9-octadecenal (16.23%). In contrast, the principal constituents of methanol extract were patchouli alcohol (28.1%), delta-guaiene (15.15%), and alpha-guaiene (11.93%). Furthermore, limonoids profiling of A. excelsa methanol extract was determined using Ultrahigh-performance liquid chromatography coupled with quadrupole-Orbitrap high-resolution mass spectrometry. The number of limonoids identified tentatively was fifteen, such as 6-deacetylnimbin, nimbolidin C, nimbolide, 6-acetylnimbandiol, 6-deacetyl-nimbinene, salannol, 28-deoxonimbolide, gedunin, nimbandiol, epoxyazadiradione, azadirone, 2',3'-dihydrosalannin, marrangin, nimbocinol, and azadirachtin. They were the same as those reported in the seed and leaves of A. indica, but its largest component in A. excelsa was 6-deacetylnimbin. As a result, the presence of these compounds may be responsible for the anti-termite activity of A. excelsa seed kernel extract. Additionally, column chromatography of methanol extract yielded 6-deacetylnimbin, which was found to be antifeedant and termiticide against C. curvignathus.

• Fisheries and Aquatic Sciences
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• v.26 no.4
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• pp.268-281
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• 2023

Coral reef fisheries are prominent for the archipelagic countries' food sufficiency and security. Studies showed that fish abundance and biomass are affected by biophysical variables. The present study determines which biophysical variables are important predictors of fish diversity, abundance, and biomass. The study used available monitoring data from the Indonesian Research Center for Oceanography, the National Board for Research and Innovation. Data were collected from 245 transects in 19 locations distributed across the Indonesian Archipelago, including the eastern Indian Ocean, Sunda Shelf (Karimata Sea), Wallacea (Flores and Banda Seas), and the western Pacific Ocean. Principal component analysis and multiple regression model were administered to 13 biophysical metrics against 11 variables of coral reef fishes, i.e., diversity, abundance, and biomass of coral reef fishes at three trophic levels. The results showed for the first time that the covers of other fauna, coral rubbles, and soft corals were the three most important predictor variables for nearly all coral reef fish variables. Other fauna cover was the important predictor for all 11 coral reef fish variables. Coral rubble cover was the predictor for ten variables, but carnivore fish abundance. Soft coral cover was a good predictor for corallivore, carnivore, and targeted fishes. Despite important predictors for corallivore and carnivore fish variables, hard coral cover was not the critical predictor for herbivore fish variables. The other important predictor variables with a consistent pattern were dead coral covered with algae and rocks. Dead coral covered with algae was an important predictor for herbivore fishes, while the rock was good for only carnivore fishes.

• Ocean and Polar Research
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• v.25 no.1
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• pp.75-87
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• 2003

The water balance calculation in the IRL shows that fresh groundwater discharge is the primary factor, with surface runoff from gaged and ungaged areas as the second freshwater contributor. Precipitation and evaporation are almost in balance fer the entire IRL. Due to high freshwater discharge from ground-water, the annual net flow is outward from the IRL to the continental shelf of the Atlantic Ocean resulting in a relatively short flushing time, denoted as $T_{0.5}$ (50% flushing time) and $T_{0.99}$ (99% flushing time). $T_{0.5}$, and. $T_{0.99}$ without a tidal effect in the Northern IRL are 17 and 114 days, respectively, during the dry season. During the wet season, they are 10 and 65 days, respectively. Tidal flushing effects are considered in central IRL due to the proximity to Sebastian Inlet. In the Northern Central zone during dry season, $T_{0.5}$, and. $T_{0.99}$ are 6 and 43 days, respectively and during the wet season 5 and 33 days. In the Southern Central zone they are 2 and 16 days for the dry season,2 and 15 days for the wet season. High groundwater seepage into the IRL is considered to be a positive effect in maintaining relatively good water quality condition even with few narrow inlets.