Results 21 to 30 of about 196 (100)
Roots and polynomials as Homeomorphic spaces [PDF]
, 2005 We provide a unified, elementary, topological approach to the classical results stating the continuity of the complex roots of a polynomial with respect to its coefficients, and the continuity of the coefficients with respect to the roots.
Branko Ćurgus, V. Mascioni
semanticscholar +1 more source
Veterinary Dermatology, Volume 27, Issue 5, Page 391-e98, October 2016., 2016 Background– Pseudomonas aeruginosa (PA) may cause suppurative otitis externa with severe inflammation and ulceration in dogs. Multidrug resistance is commonly reported for this organism, creating a difficult therapeutic challenge. Objective– The aim of this study was to evaluate the in vitro antimicrobial activity of a gel containing 0.5 µg/mL of ...
Giovanni Ghibaudo +6 more
wiley +1 more source
An integral that counts the zeros of a function
Open Mathematics, 2018 Given a real function f on an interval [a, b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f, f′ and f″.
Hungerbühler Norbert, Wasem Micha
doaj +1 more source
Unification of the Bernstein-type polynomials and their applications
, 2013 In this paper, we investigate some new identities related to the unification of the Bernstein-type polynomials, Bernoulli polynomials, Euler numbers and Stirling numbers of the second kind. We also give some remarks and applications of the Bernstein-type
Y. Şimşek
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Zero distribution of sequences of classical orthogonal polynomials
Abstract and Applied Analysis, Volume 2003, Issue 17, Page 985-993, 2003., 2003 We obtain the zero distribution of sequences of classical orthogonal polynomials associated with Jacobi, Laguerre, and Hermite weights. We show that the limit measure is the extremal measure associated with the corresponding weight.
Plamen Simeonov
wiley +1 more source
Pairs of paths and critical points
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 3, Page 189-192, 2001., 2001 Two sufficient conditions are presented, in terms of the values taken by a holomorphic function f(z) on a pair of smooth paths intersecting at a point z0 in its domain, implying that f′(z0) = 0.
Florin Caragiu, Ioana Caragiu
wiley +1 more source
Integral mean estimates for polynomials whose zeros are within a circle
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 4, Page 231-235, 2001., 2001 Let p(z) be a polynomial of degree n having all its zeros in |z| ≤ k; k ≤ 1, then for each r > 0, p > 1, q > 1 with p−1 + q−1 = 1, Aziz and Ahemad (1996) recently proved that n{∫02π|p(eiθ)|rdθ} 1/r≤{∫02π|1+keiθ|prdθ} 1/pr{∫02π|p′(eiθ)|qrdθ} 1/qr. In this paper, we extend the above inequality to the class of polynomials p(z)=anzn+∑v=μnan−vzn−v;1≤μ≤n ...
K. K. Dewan, Abdullah Mir, R. S. Yadav
wiley +1 more source
The number of connected components of certain real algebraic curves
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 11, Page 693-701, 2001., 2001 For an integer n ≥ 2, let p(z)=∏k=1n(z−αk) and q(z)=∏k=1n(z−βk), where αk, βk are real. We find the number of connected components of the real algebraic curve {(x, y) ∈ ℝ2 : |p(x + iy)| − |q(x + iy)| = 0} for some αk and βk. Moreover, in these cases, we show that each connected component contains zeros of p(z) + q(z), and we investigate the locus of ...
Seon-Hong Kim
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Growth of the Maximum Modulus of Polynomials With Prescribed Zeros
Sarajevo Journal of MathematicsIf $p(z)$ be a polynomial of degree $n$ which does not vanish in the disk $\left|z\right|
K. K. Dewan, S. Hans
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On sharpening of a Theorem of T. J. Rivlin
, 2018 Let p(z) = a0 +a1z+a2z +a3z + · · ·+anz be a polynomial of degree n . According to a well-known theorem of Rivlin [11], if p(z) is a polynomial of degree n having no zeros inside the unit circle, then for 0 < r 1, max |z|=r |p(z)| ( r +1 2 )n max |z|=1 ...
N. Govil, S. Hans
semanticscholar +1 more source