• Title/Summary/Keyword: polynomial degree

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INEQUALITIES FOR COMPLEX POLYNOMIAL WITH RESTRICTED ZEROS

  • Istayan Das;Robinson Soraisam;Mayanglambam Singhajit Singh;Nirmal Kumar Singha;Barchand Chanam
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.4
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    • pp.943-956
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    • 2023
  • Let p(z) be a polynomial of degree n and for any complex number 𝛽, let D𝛽p(z) = np(z) + (𝛽 - z)p'(z) denote the polar derivative of the polynomial with respect to 𝛽. In this paper, we consider the class of polynomial $$p(z)=(z-z_0)^s \left(a_0+\sum\limits_{{\nu}=0}^{n-s}a_{\nu}z^{\nu}\right)$$ of degree n having a zero of order s at z0, |z0| < 1 and the remaining n - s zeros are outside |z| < k, k ≥ 1 and establish upper bound estimates for the maximum of |D𝛽p(z)| as well as |p(Rz) - p(rz)|, R ≥ r ≥ 1 on the unit disk.

ON NEW IDENTITIES FOR 3 BY 3 MATRICES

  • Lee, Woo
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1185-1189
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    • 2008
  • In this paper we show that the polynomial of degree 9 called generalized algebraicity is a polynomial identity for $3{\times}3$ matrices. ([5])

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FINITENESS OF COMMUTABLE MAPS OF BOUNDED DEGREE

  • Lee, Chong Gyu;Ye, Hexi
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.45-56
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    • 2015
  • In this paper, we study the relation between two dynamical systems (V, f) and (V, g) with $f{\circ}g=g{\circ}f$. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Preper(f)) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f.

Approximate Conversion of Rational Bézier Curves

  • Lee, Byung-Gook;Park, Yunbeom
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.2 no.1
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    • pp.88-93
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    • 1998
  • It is frequently important to approximate a rational B$\acute{e}$zier curve by an integral, i.e., polynomial one. This need will arise when a rational B$\acute{e}$zier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational B$\acute{e}$zier curves with polynomial curves of higher degree.

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CLASSIFICATION OF FOUR DIMENSIONAL BARIC ALGEBRAS SATISFYING POLYNOMIAL IDENTITY OF DEGREE SIX

  • Kabre Daouda;Dembega Abdoulaye;Conseibo Andre
    • Korean Journal of Mathematics
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    • v.32 no.1
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    • pp.163-171
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    • 2024
  • In this paper, we proceeded to the classification of four dimensional baric algebras strictly satisfying a polynomial identity of degree six. After some results on the structure of such algebras, we show that the type of an algebra of the studied class is an invariant under change of idempotent in the Peirce decomposition. This last result plays a major role in our classification.

SEMI-CYCLOTOMIC POLYNOMIALS

  • LEE, KI-SUK;LEE, JI-EUN;Kim, JI-HYE
    • Honam Mathematical Journal
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    • v.37 no.4
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    • pp.469-472
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    • 2015
  • The n-th cyclotomic polynomial ${\Phi}_n(x)$ is irreducible over $\mathbb{Q}$ and has integer coefficients. The degree of ${\Phi}_n(x)$ is ${\varphi}(n)$, where ${\varphi}(n)$ is the Euler Phi-function. In this paper, we define Semi-Cyclotomic Polynomial $J_n(x)$. $J_n(x)$ is also irreducible over $\mathbb{Q}$ and has integer coefficients. But the degree of $J_n(x)$ is $\frac{{\varphi}(n)}{2}$. Galois Theory will be used to prove the above properties of $J_n(x)$.

Failure Prediction and Behavior of Cut-Slope based on Measured Data (계측결과에 의한 절토사면의 거동 및 파괴예측)

  • Jang, Seo-Yong;Han, Heui-Soo;Kim, Jong-Ryeol;Ma, Bong-Duk
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.10 no.3
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    • pp.165-175
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    • 2006
  • To analyze the deformation and failure of slopes, generally, two types of model, Polynomial model and Growth model, are applied. These two models are focused on the behavior of the slope by time. Therefore, this research is more focused on predicting of slope failure than analyzing the slope behavior by time. Generally, Growth model is used to analyze the soil slope, to the contrary, Polynomial model is used for rock slope. However, 3-degree polynomial($y=ax^3+bx^2+cx+d$) is suggested to combine two models in this research. The main trait of this model is having an asymptote. The fields to adopt this model are Gosujae Danyang(soil slope) and Youngduk slope(rock slope), which are the cut-slope near national road. Data from Gosujae are shown the failure traits of soil slope, to the contrary, those of Youngduk slope are shown the traits of rock slope. From the real-time monitoring data of the slope, 3-degree polynomial is proved as excellent system to analyze the failure and behavior of slope. In case of Polynomial model, even if the order of polynomials is increased, the $R^2$ value and shape of the curve-fitted graph is almost the same.