• Title, Summary, Keyword: homogeneous functions

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COEFFICIENT BOUNDS FOR CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH VERTICAL STRIP DOMAIN

  • Bulut, Serap
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.789-797
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    • 2020
  • By considering a certain univalent function in the open unit disk ��, that maps �� onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We determine the coefficient bounds for functions in this new class. Relevant connections of some of the results obtained with those in earlier works are also provided.

[ $L^p$ ] NORM INEQUALITIES FOR AREA FUNCTIONS WITH APPROACH REGIONS

  • Suh, Choon-Serk
    • East Asian mathematical journal
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    • v.21 no.1
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    • pp.41-48
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    • 2005
  • In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

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ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS

  • Bhoosnurmath, Subhas S.;Kulkarni, Milind Narayanrao;Yu, Kit-Wing
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.427-435
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    • 2008
  • In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree $\bar{d}$(P) and lower degree $\underline{d}$(P).

UNIQUENESS OF HOMOGENEOUS DIFFERENTIAL POLYNOMIALS CONCERNING WEAKLY WEIGHTED-SHARING

  • Pramanik, Dilip Chandra;Roy, Jayanta
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.439-449
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    • 2019
  • In 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between "CM" and "IM". In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of nonconstant homogeneous differential polynomials P[f] and P[g] generated by meromorphic functions f and g, respectively. Our results generalize the results due to S. Lin and W. Lin, and H.-Y. Xu and Y. Hu.

Natural Frequency of a Rectangular Plate on Non-homogeneous Elastic Foundations (비균질 탄성 기초위에 놓여있는 직사각형 평판의 고유 진동수)

  • Hwang, Ju-Ik;Kim, Yong-Cheol;Lee, Taek-Sun
    • Journal of Ocean Engineering and Technology
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    • v.3 no.2
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    • pp.70-76
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    • 1989
  • The natural frequencies of a rectangular plate on non-homogeneous elastic foundations were obtained by using the Ritz method and Galerkin method. The results of both methods using the different type of trial functions were also compared. Furthermore, the effects of the variation of boundary conditions, the stiffness of the foundation spring, the dimension ratio of the plate were investigated. As a result, the Galerkin method can be used to obtain the accurate solution and can be effectively used to design the foundation bed.

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HOMOGENEOUS MULTILINEAR FUNCTIONS ON HYPERGRAPH CLIQUES

  • Lu, Xiaojun;Tang, Qingsong;Zhang, Xiangde;Zhao, Cheng
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.1037-1067
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    • 2017
  • Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.