• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.697-709
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• 2018

In the present paper, we introduce and investigate two new subclasses, namely; the class of strongly ${\alpha}$-bi-spirallike functions of order ${\beta}$ and ${\alpha}$-bi-spirallike functions of order ${\rho}$, of the function class ${\Sigma};$ of normalized analytic and bi-univalent functions in the open unit disk $$U=\{z:z{\in}C\;and\;{\mid}z{\mid}<1\}$$. We find estimates on the coefficients ${\mid}a_2{\mid}$, ${\mid}a_3{\mid}$ and ${\mid}a_4{\mid}$ for functions in these two subclasses.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• 대한수학회논문집
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• 제37권4호
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• 대한원격탐사학회지
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• 제34권6_2호
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• pp.1251-1260
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• 2018

항공영상으로 제작한 고품질의 해빙표면모델은 인공위성 기반 원격탐사 기술 개발을 위한 현장자료 뿐만 아니라 북극 해빙의 정밀한 형상학적 변동 특성 분석에도 효과적으로 사용될 수 있다. 그러나 해빙 표면의 부족한 텍스쳐 정보는 영상정합을 어렵게 만드는 요인으로 작용한다. 이에 본 논문에서는 고품질 해빙표면 모델 생성을 위한 일환으로 균질한 해빙 표면에 대한 정합비용함수들의 성능 비교 분석을 수행한다. 정합비용함수로는 영상 도메인의 SSD(sum of squared differences), NCC(normalized cross-correlation), ZNCC(zero-mean normalized cross-correlation), 주파수 도메인의 PC(phase correlation), OC(orientation correlation), GC(gradient correlation)를 분석하였다. 텍스쳐 정보량에 따른 정합 성능을 보다 명확하고 객관적으로 분석하기 위해 객체 공간 기반 정합 기법의 원리를 바탕으로 하는 새로운 평가 방법을 도입하였다. 실험결과는 해빙 표면과 같이 텍스쳐 정보가 희박한 지역에 대해서는 정합 지역에 따라 적합한 크기의 탐색창을 가변적으로 적용해야만 정합의 신뢰성 및 정확도 확보가 가능함을 보여주었다. 정합비용함수들 사이에서는 NCC와 ZNCC가 텍스쳐 정보 변화에 대해서 가장 우수한 성능을 나타냈다.

• 대한수학회논문집
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• 제35권3호
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• pp.953-966
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• 2020

In this article we study the evolution and monotonicity of the first non-zero eigenvalue of weighted p-Laplacian operator which it acting on the space of functions on closed oriented Riemannian n-manifolds along the extended Ricci flow and normalized extended Ricci flow. We show that the first eigenvalue of weighted p-Laplacian operator diverges as t approaches to maximal existence time. Also, we obtain evolution formulas of the first eigenvalue of weighted p-Laplacian operator along the normalized extended Ricci flow and using it we find some monotone quantities along the normalized extended Ricci flow under the certain geometric conditions.

• Structural Engineering and Mechanics
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• 제32권1호
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• pp.127-145
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• 2009

A novel approach is proposed to effectively estimate the quantile functions of normalized performance indices of reliability constraints in a reliability-based optimization (RBO) problem. These quantile functions are not only estimated as functions of exceedance probabilities but also as functions of the design variables of the target RBO problem. Once these quantile functions are obtained, all reliability constraints in the target RBO problem can be transformed into non-probabilistic ordinary ones, and the RBO problem can be solved as if it is an ordinary optimization problem. Two numerical examples are investigated to verify the proposed novel approach. The results show that the approach may be capable of finding approximate solutions that are close to the actual solution of the target RBO problem.

• 대한수학회보
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• 제33권1호
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• pp.1-16
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• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".

• 대한수학회논문집
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• 제39권3호
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• pp.647-655
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• 2024

In this article, by making use of the λ-pseudo-starlike functions, we introduce a certain family of normalized analytic functions in the open unit disk U and we establish coefficient estimates for the first four determinants of the Toeplitz matrices T₂(2), T₂(3), T₃(2) and T₃(1) for the functions belonging to this family. Further, some known and new results which follow as special cases of our results are also mentioned.

• 대한수학회지
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• 제55권1호
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• pp.175-184
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• 2018

We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions f, analytic and univalent in the unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$, and normalized so that f(0) = 0 = f'(0)-1, and satisfying Re $\left[\left(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\right)^{\gamma}\left({\frac{zf^{\prime}(z)}{f(z)}}\right)^{1-{\gamma}}\right]$ > 0.

• 대한수학회지
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• 제45권3호
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• pp.611-620
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• 2008

The purpose of this present paper is to derive some subordination and superordination results involving Carlson-Shaffer operator for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.