• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.481-491
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• 2019

In the present paper, we investigate the upper bounds on third order Hankel determinants for certain class of close-to-convex functions in the unit disk. Furthermore, we obtain estimates of the Zalcman coefficient functional for this class.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.201-216
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• 2024

The aim of this paper is to study a new and unified class 𝓡^α_Cosh of analytic functions associated with cosine hyperbolic function in the open unit disc E = {z ∈ ℂ : |z| < 1}. Some interesting properties of this class such as initial coefficient bounds, Fekete-Szegö inequality, second Hankel determinant, Zalcman inequality and third Hankel determinant have been established. Furthermore, these results have also been studied for two-fold and three-fold symmetric functions.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.781-794
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• 2020

In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.81-90
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• 2022

The present investigation is concerned with the estimation of initial coefficients, Fekete-Szegö inequality, second Hankel determinants, Zalcman functionals and third Hankel determinants for certain subclasses of Sakaguchi type functions defined with subordination in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results derived in this paper will pave the way for the further study in this direction.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.231-242
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• 2018

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.901-908
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• 2010

A geometrical description method is proposed to represent the process of the forward selection and backward elimination methods among many variable selection methods for multiple regression models. This graphical method shows the process of the forward selection and backward elimination on the first and second quadrants, respectively, of half circle with a unit radius. At each step, the SSR is represented by the norm of vector and the extra SSR or partial determinant coefficient is represented by the angle between two vectors. Some lines are dotted when the partial F test results are statistically significant, so that statistical analysis could be explored. This geometrical description can be obtained the final regression models based on the forward selection and backward elimination methods. And the goodness-of-fit for the model could be explored.

• Journal of the Korean Society of Costume
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• v.25
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• pp.41-62
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• 1995

This research was intended to investigate how risk perception and risk reduction behavior by consumers differ according to different product characteristics of clothing. The responses of 318 female college students living in Seoul and surrounding vicinities were collected and analyzed. Inner wear, blue-jean pants, coat were selected as representing each clothing product characteristics. Frequencies distribution, regression and correlation coefficient were utilized for statistical analysis. Results are as follows. 1. The type of perceived risk and risk reduction behavior differed according to product characteristics of clothing. Physical and performance risk were more highly perceived for the purchase of innerwear. However, for the purchase of jean pants and coat, socio-psycho-logical and economic risk were also perceived highly because the rate of fashion change, social symbolism, and coordination with other clothing items become more important characteristics. To reduce perceived risk, dependency on past purchase experiences and shop-ping were mostly preferred method regardless of product characteristics of clothing. 2. Risk type as determinant variables for predicting overall risk differed according to product characteristics of clothing. But fashionability and usefulness were common determinant risk variables, which identifies typical characteristics of clothing product.

• 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 Statistical Society
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• v.26 no.3
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• pp.397-405
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• 1997

Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.

• Wind and Structures
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• v.35 no.6
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• pp.395-403
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• 2022

The present research is concerned with the study of Stoneley wave propagation at the interface of two dissimilar homogeneous orthotropic magneto-thermoelastic solids with fractional order theory of type GN-III with three phase-lags and combined effect of hall current and rotation. With the help of appropriate boundary conditions the secular equations of Stoneley waves are obtained in the form of determinant. The characteristics of wave such as phase velocity, attenuation coefficient and specific loss are computed numerically. The effect of rotation on the Stoneley wave's phase velocity, attenuation coefficient, specific loss, displacement components, stress components and temperature change has been depicted graphically. Some particular cases are also derived in this problem.