Results 11 to 20 of about 56 (56)
Extensions of the Eneström-Kakeya theorem for matrix polynomials
Special Matrices, 2019 The classical Eneström-Kakeya theorem establishes explicit upper and lower bounds on the zeros of a polynomial with positive coefficients and has been generalized for positive definite matrix polynomials by several authors.
Melman A.
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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
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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
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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
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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
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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
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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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On the zeros and critical points of a rational map
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 4, Page 243-246, 2001., 2001 Let f : ℙ1 → ℙ1 be a rational map of degree d. It is well known that f has d zeros and 2d − 2 critical points counted with multiplicities. In this note, we explain how those zeros and those critical points are related.
Xavier Buff
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On the location of the zeros of analytic functions
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 1, Page 67-72, 1990., 1990 In this paper we obtain regions containing all the zeros of a class of analytic functions whose coefficients are subject to certain conditions. Our results sharpen some of the results known in this direction. Also we give some examples to show that in some cases the regions obtained by our results are considerably sharper than the regions obtained by ...
K. K. Dewan, N. K. Govil
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Some theorems on generalized polars with arbitrary weight
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 4, Page 757-776, 1987., 1987 The present paper, which is a continuation of our earlier work in Annali di Mathematica [1] and Journal Math. Seminar [2] (EγEUθPIA), University of Athens, Greece, deals with the problem of determining sufficiency conditions for the nonvanishing of generalized polars (with a vanishing or nonvanishing weight) of the product of abstract homogeneous ...
Neyamat Zaheer, Aijaz A. Khan
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