NUMBER OF ZEROS OF POLAR DERIVATIVES OF POLYNOMIALS

2020 ◽  
Vol 15 (2) ◽  
pp. 81-91
Author(s):  
P. Ramulu ◽  
G. L. Reddy
Keyword(s):  
Number Of Zeros ◽  
Polar Derivatives ◽  
Derivatives Of

THE NUMBER OF ZEROS OF POLAR DERIVATIVES OF POLYNOMIALS WITH SPECIAL COEFFICIENTS

2015 ◽  
Vol 27 (2) ◽  
pp. 95-107
Author(s):  
P. Ramulu ◽  
G. L. Reddy ◽  
C. Gangadhar
Keyword(s):  
Number Of Zeros ◽  
Polar Derivatives ◽  
Derivatives Of

Poly(methyl-phenylsilylene) Derivatives as Photoconductors

1993 ◽  
Vol 58 (10) ◽  
pp. 2337-2348 ◽  
Author(s):  
Ivan Kmínek ◽  
Stanislav Nešpůrek ◽  
Eduard Brynda ◽  
Jiří Pfleger ◽  
Věra Cimrová ◽  
...  
Keyword(s):  
Spectral Properties ◽  
Long Wavelength ◽  
Langmuir Blodgett ◽  
Ultrathin Layers ◽  
Polar Derivatives ◽  
Derivatives Of

The attachment of long wavelength absorbing π-conjugated chromophores to poly(methyl-phenylsilylene) (PMPSi) via reactions of its formylated derivative is described. Some of the obtained polymers exhibit improved photostability in comparison with the parent polymer. Their spectral properties and photoconductivity are discussed. Ultrathin layers and multilayers were prepared from polar derivatives of PMPSi by the Langmuir-Blodgett technique and their photoconductive behaviour was studied.

Certain inequalities for the polar derivatives of polynomials

2009 ◽  
Vol 12 (1) ◽  
pp. 29-39 ◽  
Author(s):  
K. K. Dewan ◽  
Naresh Singh ◽  
Sunil Hans
Keyword(s):  
Polar Derivatives ◽  
Derivatives Of

scholarly journals Synthesis of novel polar derivatives of the antimalarial endoperoxides ascaridole and dihydroascaridole

ARKIVOC ◽  
2006 ◽  
Vol 2007 (8) ◽  
pp. 124-135 ◽  
Author(s):  
Emmanuel Hatzakis ◽  
Igor Opsenica ◽  
Bogdan A. Solaja ◽  
Manolis Stratakis
Keyword(s):  
Polar Derivatives ◽  
Derivatives Of

Bernstein-Type Inequalities with Bombieri Norm

1996 ◽  
Vol 39 (2) ◽  
pp. 151-163
Author(s):  
Franck Beaucoup ◽  
Catherine Souchon
Keyword(s):  
Binomial Coefficient ◽  
Bernstein Type ◽  
Univariate Polynomial ◽  
Polar Derivatives ◽  
Image Position ◽  
Bernstein Type Inequalities ◽  
Derivatives Of

AbstractIf is an univariate polynomial with degree n then Bombieri norm of P is defined bywhere denotes the binomial coefficient.In the present paper we give, under assumptions on the roots of P, optimal Bernsteintype inequalities for the ratio between Bombieri norm of P and that of its derivative P′.We also give such inequalities for the polar derivatives of P defined by

Polar derivatives of the [closo-1-CB9H10]− cluster as positive Δε additives to nematic hosts

2009 ◽  
Vol 19 (48) ◽  
pp. 9204 ◽  
Author(s):  
Bryan Ringstrand ◽  
Piotr Kaszynski ◽  
Adam Januszko ◽  
Victor G. Young
Keyword(s):  
Polar Derivatives ◽  
Derivatives Of

Loci of complex polynomials, part II: polar derivatives

2015 ◽  
Vol 159 (2) ◽  
pp. 253-273 ◽  
Author(s):  
BLAGOVEST SENDOV ◽  
HRISTO SENDOV
Keyword(s):  
Higher Order ◽  
Complex Polynomial ◽  
Complex Polynomials ◽  
Point Sets ◽  
Closed Set ◽  
Measurable Set ◽  
Closed Point ◽  
Polar Derivatives ◽  
Lebesgue Measurable Set ◽  
Derivatives Of

AbstractFor every complex polynomial p(z), closed point sets are defined, called loci of p(z). A closed set Ω ⊆ ${\mathbb C}$* is a locus of p(z) if it contains a zero of any of its apolar polynomials and is the smallest such set with respect to inclusion. Using the notion locus, some classical theorems in the geometry of polynomials can be refined. We show that each locus is a Lebesgue measurable set and investigate its intriguing connections with the higher-order polar derivatives of p.

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