Results 31 to 40 of about 79,547 (300)
Inequalities concerning polar derivative of polynomials [PDF]
, 2016 In this paper we obtain certain results for the polar derivative of a polynomial \(p(z) = c_nz^n +\sum_{j=\mu}^n c_{n-j}z^{n-j}\), \(1\leq\mu\leq n\), having all its zeros on \(|z| = k\), \(k\leq 1\), which generalizes the results due to Dewan and Mir ...
Ahuja, Arty, Hans, Sunil, Dewan, K. K.
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Inequalities for the polar derivative of a polynomial [PDF]
The Journal of Analysis, 2020 Let P(z) be a polynomial of degree n having all its zeros in $$|z|\le 1$$ , then according to Turan (Compositio Mathematica 7:89–95, 2004) $$\begin{aligned} \max \limits _{|Z|=1}|P'(z)|\ge ...
M. H. Gulzar, B. A. Zargar, Rubia Akhter
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Bernstein-Type Inequalities Involving Polar Derivative of a Polynomial [PDF]
, 2020 In this paper, we extend some polynomial inequalities to the polar derivative of a polynomial having all its zeros inside or outside a circle of radius k, k > 0 and thereby present some compact generalizations and improvements of certain well-known ...
Qasim, Idrees
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A new fractional derivative and its application to explanation of polar bear hairs [PDF]
, 2016 A new fractional derivative is defined through the variational iteration method, and its application in explaining the excellent thermal protection of polar bear hairs is elucidated.
Qing-li Wang +5 more
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Bernstein Type Inequalities for Polar Derivative of Polynomial [PDF]
, 2021 If is a polynomial of degree n such that in , , then Govil [ Proc. Nat. Acad. Sci., Vol. 50, pp. 50-52, 1980. ] proved provided and attain their maxima at the same point on the circle ,
Chanam, Barchand
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Journal of Inequalities and Applications, 2020 Some Zygmund-type integral inequalities for the polar derivatives of complex polynomials, inspired by the classical Bernstein-type inequalities that relate the uniform norms of polynomials and their derivatives on the unit circle, are investigated.
Gradimir V. Milovanović, Abdullah Mir
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On Extremal Properties for the Polar Derivative of Polynomials
Analysis in Theory and Applications, 2011 Summary: If \(p(z)\) is a polynomial of degree \(n\) having all its zeros on \(|z|=k\), \(k\leq 1\), then it is known that \[ \max\limits_{|z|=1}|p'(z)|\leq \frac n {k^{n-1}+k^n}\max\limits_{|z|=1}|p(z)|. \] In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type \(p(z)=c_nz^n +\sum\limits ...
Dewan, K. K., Ahuja, Arty
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BODIPY-based dye for no-wash live-cell staining and imaging
BioTechniques, 2017 In nonpolar solvents, hydrophobic organic fluorophores often show bright fluorescence, whereas in polar media, they usually suffer from aggregation-caused quenching (ACQ).
Alexey A. Pakhomov +7 more
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Deriving polarity from granularity
Semantics and Linguistic Theory, 2021 In this paper, we present a way to unify Positive Polarity Items formed with some NP and minimizers, such as lift a finger. The connection is made via granularity properties of the two classes of polarity sensitive expressions. We begin with an observation in Strawson 1974 that the use of some NP involves an inference about the availability of a more ...
Goncharov, Julie, Wolf, Lavi
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Some Inequalities for the Polar Derivative of a Polynomial
Kragujevac Journal of Mathematics, 2003 Summary: Let \(P(z)\) be a polynomial of degree \(n\) which has no zeros in \(|z|
Gulzar, M. H. +2 more
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