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Some Bounds for the Polar Derivative of a Polynomial [PDF]
International Journal of Mathematics and Mathematical Sciences, 2018 The polar derivative of a polynomial p(z) of degree n with respect to a complex number α is a polynomial np(z)+α-zp′(z), denoted by Dαp(z). Let 1≤R≤k. For a polynomial p(z) of degree n having all its zeros in z≤k, we investigate a lower bound of modulus of Dαp(z) on z=R.
Jiraphorn Somsuwan +1 more
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Sensors, 2020 Micro absolute distance measurement (MADM) is widely used in industrial and military fields. To achieve high accuracy and frequency response, a polarized low-coherence interferometry (PLCI)-based method for MADM is proposed.
Xun Sun +5 more
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Remote Sensing, 2022 Significant wave height (SWH) is one of the most important descriptors for ocean wave fields. The polynomial regression (PolR) and Gaussian process regression (GPR) models are implemented to explore the effects of polarization and incidence angles on the
Chenqing Fan +5 more
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Determination of Glucose Concentration By Rotation of Polarization Plane of He-Ne Laser [PDF]
مجلة التربية والعلم, 2011 In this research, the optical activity of glucose solution had been studied through the studying of influence of this solution in rotation of polarization plane of laser He-Ne light, the different concentrations of glucose solution were selected for ...
Zead T. Ahmed Ameer F. Hammeed
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On the nonexistence of certain curves of genus two [PDF]
, 2002 We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2.
Howe, Everett W.
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Rocky Mountain Journal of Mathematics, 2010 We introduce a new class of polynomials $\{P_{n}\}$, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with $n+1$ unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect ...
Cabrera, H. Pijeira +2 more
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Lower Bound of the Complexity of Seven-Valued Functions in the Class of Polarized Polynomials
Известия Иркутского государственного университета: Серия "Математика", 2017 One of the directions of the investigation of functions over finite fields is the study of their representations, including polynomial ones. In the area of polynomial representations of functions the problem of estimating the complexity of such ...
A.S. Baliuk, A.S. Zinchenko
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Drones, 2023 Mapping forest canopy height at large regional scales is of great importance for the global carbon cycle. Polarized interferometric synthetic aperture radar is an efficient and irreplaceable remote sensing tool.
Hongbin Luo +4 more
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Inequalities for the Polar Derivative of a Polynomial [PDF]
Abstract and Applied Analysis, 2012 For a polynomial p(z) of degree n, we consider an operator Dα which map a polynomial p(z) into Dαp(z): = (α − z)p′(z) + np(z) with respect to α. It was proved by Liman et al. (2010) that if p(z) has no zeros in |z | < 1, then for all α, β ∈ ℂ with |α | ≥ 1, | β | ≤ 1 and |z | = 1, |zDαp(z) + nβ((|α | − 1)/2)p(z)|≤(n/2){[|α + β((|α | − 1 ...
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Inequalities for the Polar Derivative of A Polynomial [PDF]
Mathematics and Statistics, 2013 IfP (z) = anz n + n P v= a n vz n v , 1 n, has all its zeros onjzj = k, k 1, then it was recently proved by Dewan and Ahuja (3) that for every real or complex number withj j k. maxzj=1 jD P (z)j n(j j +s )s k n +1 (1 +s ) maxzj=1 jP (z)j; In this paper, we improve the above result and obtain new inequality for the polar derivative of a polynomial.
Rather, N. A., Gulzar, Suhail
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