Results 31 to 40 of about 111,867 (281)
Ufimskii Matematicheskii Zhurnal, 2019 Summary: For a given polynomial \[P\left( z\right) =z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+\cdots +a_1z+a_0\] with real or complex coefficients, the Cauchy bound \[\left\vert z\right\vert
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Walailak Journal of Science and Technology, 2019 In this note we discuss the Gauss-Lucas theorem (for the zeros of the derivative of a polynomial) and Speiser’s equivalent for the Riemann hypothesis (about the location of zeros of the Riemann zeta-function).
Janyarak TONGSOMPORN, Jörn STEUDING
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Journal of Combinatorial Theory, Series A, 2004 In this article we introduce the flow polynomial of a digraph and use it to study nowhere-zero flows from a commutative algebraic perspective. Using Hilbert's Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals.
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$q$-Eulerian Polynomials and Polynomials with Only Real Zeros [PDF]
The Electronic Journal of Combinatorics, 2008 Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the location and multiplicity of the real zeros of $f$ and $F$, which generalizes and unifies many known results, including the results of Brenti and Brändén about the $q$-Eulerian polynomials.
Ma, Shi-Mei, Wang, Yi
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Convergence of Comonotone Histopolating Splines
Mathematical Modelling and Analysis, 2015 The convergence rate of histopolation on an interval with combined splines of class C1 having linear/linear rational or quadratic polynomial pieces is studied.
Helle Hallik, Peeter Oja
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Zero-one Grothendieck polynomials
Science China MathematicsFink, Mészáros and St.Dizier showed that the Schubert polynomial $\mathfrak{S}_w(x)$ is zero-one if and only if $w$ avoids twelve permutation patterns. In this paper, we prove that the Grothendieck polynomial $\mathfrak{G}_w(x)$ is zero-one, i.e., with coefficients either 0 or $\pm$1, if and only if $w$ avoids six patterns.
Chen, Yiming, Fan, Neil J. Y., Ye, Zelin
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Inequalities for the Polar Derivative of a Polynomial
Abstract and Applied Analysis, 2012 For a polynomial 𝑝(𝑧) of degree 𝑛, we consider an operator 𝐷𝛼 which map a polynomial 𝑝(𝑧) into 𝐷𝛼𝑝(𝑧)∶=(𝛼−𝑧)𝑝′(𝑧)+𝑛𝑝(𝑧) with respect to 𝛼. It was proved by Liman et al. (2010) that if 𝑝(𝑧) has no zeros in |𝑧|
Ahmad Zireh
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Iterated sequences and the geometry of zeros
, 2009 We study the effect on the zeros of generating functions of sequences under certain non-linear transformations. Characterizations of P\'olya--Schur type are given of the transformations that preserve the property of having only real and non-positive ...
Brändén, Petter
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On zeros of paraorthogonal polynomials [PDF]
Proceedings of the American Mathematical Society, 2019 We prove some results concerning the behaviour of zeros of families of paraorthogonal polynomials on the unit circle. We establish an interlacing property of the zeros of some functions related to the paraorthogonal polynomials. Monotonicity with respect to a parameter is also discussed in detail.
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Arthritis Care &Research, Accepted Article.Objectives This study aimed to investigate hand function trajectories over 5 years in primary hand osteoarthritis. Additionally, determinants of baseline and longitudinal hand function were assessed. Methods 538 patients with both baseline and 5‐year study visits were analyzed.
Annemiek V.E.M. Olde Meule +4 more
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