• East Asian mathematical journal
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• 제39권1호
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• pp.11-21
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• 2023

Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the projective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classification by the distance function of the Poincaré metric on the interior of the unit disc.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.1005-1015
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• 2000

In the unit disc, we find a sufficient condition to bound the Bergman norm by the weighted Poisson integral where the given weighted is $\mid$t$\mid$dt.

• The Journal of Korean Physical Therapy
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• 제2권1호
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• pp.103-112
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• 1990

The intervertebral disc in the anterior portion of the function unit gives the spine its flexibility. The disc is attached closely to the vertebral endplates. Between these endplates and the annulus fibrosus, the nucleus pulposus of the lumbar disc is enclosed in a circle of unyielding tissues. Compressive pressure placed on the disc is dissipated circumferentially in a passive manner In response to the greater axial forced exerted on the lumbar spine in comparison to the cervical and thoracic spines, the nucleus pulposus has its greatest surface area in the lumbar spine. The intervertebral disc is not only structure that helps diss pate stresses placed on the spine. With flexion, extension, rotation, or shear stress, the load distribution on the function unit is shared by the intervertebral disc, anterior and posterior longitudinal ligaments, the facet joints and capsules, and other ligamentous structures like the ligamentum flavum, interspinous and supraspinous ligaments, which attach to the posterior elements of the functional unit.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.219-227
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• 2014

In this note we study the Schwarz lemma and inequalities for some holomorphic functions on the unit disc. Also, we obtain the inequality of the derivative of holomorphic maps at a boundary point of the unit disc and find a holomorphic map to satisfy the equality.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.155-165
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• 2009

We investigate the growth of solutions of complex linear differential equations in the unit disc. We obtain properties of solutions of differential equations with entire coefficients. We use the concept of the hyper order to estimate the growth of solutions.

• East Asian mathematical journal
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• 제37권3호
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• pp.307-317
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• 2021

In this paper, we deal with a problem to determine the type of automorphisms of the unit disc in ℂ in terms of intrinsic geometry. We will characterize the hyperbolicity and parabolicity of automorphism by the distance function of the Poincaré metric.

• 대한수학회보
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• 제59권5호
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• pp.1119-1129
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• 2022

We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.

• 호남수학학술지
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• 제43권4호
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• pp.691-700
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• 2021

In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.

• KIEE International Transactions on Electrophysics and Applications
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• 제3C권5호
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• pp.165-170
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• 2003

This paper presents development of solid core suspension disc insulators (cap and cap suspension disc insulator) for replacing cap and pin suspension disc insulators in overhead transmission and distribution lines which expose to lightning discharges. By this means the punctured problem caused by steep front surge voltage created by lightning discharge on the lines can be solved. The solid core suspension insulator was designed and constructed based on the dimensions of conventional suspension disc insulators (cap and pin insulators). The insulators are made of alumina porcelain. The electrical and mechanical characteristics of the solid core suspension insulators were carried out. The puncture test was performed in the air by applying steep front impulse voltage with amplitude about 2.5 per unit of 50% flashover (CFO) of the insulator unit at negative standard lightning impulse $1.2/50\;\mu\textrm{s}$ with steepness up to $9200\;kV/\mu\textrm{s}$. The testing results show that solid core suspension disc insulators are not punctured eventhough the steepness of the steep front impulse voltage was increased up to $9200\;kV/\mu\textrm{s}$.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination