Results 21 to 30 of about 342 (67)
Some Inequalities on Polynomials in the Complex Plane Concerning a Linear Differential Operator
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we consider new extremal problems in the uniform norm between a univariate complex polynomial and its associated reciprocal polynomial involving a generalized B‐operator. Our first result deals with inequality for the upper bound of a polynomial having s‐fold zero at the origin governed by generalized B‐operator, and as applications of ...
Mayanglambam Singhajit Singh +3 more
wiley +1 more source
Veterinary Dermatology, Volume 36, Issue 4, Page 453-461, August 2025.Background – Canine atopic dermatitis (cAD) is a chronic, inflammatory, multifactorial and pruritic disease. The presence of skin barrier impairment (e.g. filaggrin alterations), along with abnormal immune responses, can negatively impact cutaneous barrier function.
Wendie Roldan Villalobos +5 more
wiley +1 more source
Veterinary Dermatology, Volume 36, Issue 2, Page 148-158, April 2025.Background – Biofilm production by canine otitis externa (COE) pathogens and resistance development to multiple antimicrobials are commonly reported problems in veterinary practice. The use of adjuvants to disrupt biofilms may be a viable adjunctive therapy.
Bhumika F. Savaliya +3 more
wiley +1 more source
Complex Analogues of the Rolle's Theorem [PDF]
, 2007 2000 Mathematics Subject Classification: 30C10.Classical Rolle’s theorem and its analogues for complex algebraic polynomials are discussed.
Sendov, Blagovest
core
Hair fragility (trichorrhexis nodosa) in alopecic Pomeranian dogs
Veterinary Dermatology, Volume 36, Issue 1, Page 64-73, February 2025.Background – Alopecia associated with hair cycle arrest (HCA, Alopecia X) is well‐recognised in Pomeranian dogs. The authors are unaware of reports of hair fragility in affected dogs. Hypothesis/Objectives – Following the observation of frequent hair shaft abnormalities in alopecic Pomeranians, we hypothesised that hair fragility events would be more ...
Erin Brennan +6 more
wiley +1 more source
Open MathematicsIn this article, we extend inequalities concerning the polar derivative of a polynomial to integral mean for the class of polynomials with s-fold zero at the origin and the remaining zeros inside some closed disk of radius kk for k≥1k\ge 1 and k≤1k\le 1,
Singha Nirmal Kumar, Chanam Barchand
doaj +1 more source
Sendov conjecture for high degree polynomials [PDF]
, 2011 Sendov conjecture tells that if $P$ denotes a complex polynomial having all his zeros in the closed unit disk and $a$ denote a zero of $P$, the closed disk of center $a$ and radius 1 contains a zero of the derivative $P'$.
Dégot, Jérôme
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Refinements of inequalities on extremal problems of polynomials
Open MathematicsLet H(z) be a polynomial of degree n, and for any complex number α, let D α H(z) = nH(z) + (α − z)H′(z) denote the polar derivative of H(z) with respect to α.
Devi Maisnam Triveni +2 more
doaj +1 more source
A Fascinating Polynomial Sequence arising from an Electrostatics Problem on the Sphere
, 2011 A positive unit point charge approaching from infinity a perfectly spherical isolated conductor carrying a total charge of +1 will eventually cause a negatively charged spherical cap to appear. The determination of the smallest distance $\rho(d)$ ($d$ is
C. E. van de Woestijne +9 more
core +1 more source
Integral mean estimates for the polar derivative of a polynomial [PDF]
, 2013 Let $ P(z) $ be a polynomial of degree $ n $ having all zeros in $|z|\leq k$ where $k\leq 1,$ then it was proved by Dewan \textit{et al} that for every real or complex number $\alpha$ with $|\alpha|\geq k$ and each $r\geq 0$ $$ n(|\alpha|-k)\left\{\int\
Gulzar, Suhail, Rather, N. A.
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