Results 21 to 30 of about 85 (80)
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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Elliptic equations in divergence form, geometric critical points of solutions and Stekloff eigenfunctions [PDF]
, 1994 . The Stekloff eigenvalue problem (1.1) has a ’ countable number of eigenvalues (Pn}n = 1,2..... each of finite multiplicity. In this paper the authors give an upper estimate, in terms of the integer n, of the multiplicity of Pn, and the number of ...
ALESSANDRINI, GIOVANNI +4 more
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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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LOCATION OF ZEROS OF A CLASS OF POLYNOMIALS
, 2017 <p>In this paper we consider a certain class of polynomials with certain conditions on their coefficients and find regions containing all or some of their zeros.</p> <p><strong>Mathematics Subject Classification:</strong>
M.H. Gulzar*
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Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
, 2018 We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A study of the asymptotic variance of the number of roots is needed, this result
León, José, Rafael +3 more
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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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Electrostatic models for zeros of polynomials: Old, new, and some open problems [PDF]
, 2007 15 pages, 2 figures.-- MSC2000 codes: Primary, 30C15; Secondary, 34C10; 33C45; 42C05; 82B23.MR#: MR2345246 (2008h:33017)Zbl#: Zbl 1131.30002We give a survey concerning both very classical and recent results on the electrostatic interpretation of the ...
Marcellán, Francisco +6 more
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