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Title:

An application of the Tsuji characteristic

Publisher:

Faculty of Science, The University of Tokyo

Year of Publication:

1991

Document Type:

Departmental Bulletin Paper

Language:

eng

Subjects:

410

410 Minimize

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Title:

ON THE ZEROS OF LINEAR DIFFERENTIAL POLYNOMIALS WITH SMALL RATIONAL COEFFICIENTS

Description:

We prove the following: suppose that J{z) is transcendental and meromorphic of finite order in the plane, and that the linear differential polynomial F(z) is defined by and is non-constant, where ak_j(z),.,ao(z) are rational functions vanishing at infinity. Then implies that N(r,l/(fFF')) = N(r,f) = O(logr). A corresponding result is proved for ...

We prove the following: suppose that J{z) is transcendental and meromorphic of finite order in the plane, and that the linear differential polynomial F(z) is defined by and is non-constant, where ak_j(z),.,ao(z) are rational functions vanishing at infinity. Then implies that N(r,l/(fFF')) = N(r,f) = O(logr). A corresponding result is proved for the case where F =f ' + af, where a is a constant. The problem is related to results of Frank and Hellerstein and others. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-12-04

Source:

http://jlms.oxfordjournals.org/cgi/reprint/s2-36/3/445.pdf

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Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Non-real zeros of linear differential polynomials

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Let f be a real entire function with finitely many non-real zeros, not of the form f = Ph with P a polynomial and h in the Laguerre-Pólya class. Lower bounds are given for the number of non-real zeros of f ′ ′ + ωf, where ω is a positive real constant.

Let f be a real entire function with finitely many non-real zeros, not of the form f = Ph with P a polynomial and h in the Laguerre-Pólya class. Lower bounds are given for the number of non-real zeros of f ′ ′ + ωf, where ω is a positive real constant. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-11

Source:

http://arxiv.org/pdf/0707.3339v1.pdf

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Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

EQUILIBRIUM POINTS OF LOGARITHMIC POTENTIALS ON CONVEX DOMAINS

Description:

Abstract. Let D be a convex domain in C. Let ak> 0 be summable constants and let zk ∈ D. If the zk converge sufficiently rapidly to η ∈ ∂D from within an appropriate Stolz angle then the function ∑∞ k=1 ak/(z − zk) has infinitely many zeros in D. An example shows that the hypotheses on the zk are not redundant, and that two recently advanced con...

Abstract. Let D be a convex domain in C. Let ak> 0 be summable constants and let zk ∈ D. If the zk converge sufficiently rapidly to η ∈ ∂D from within an appropriate Stolz angle then the function ∑∞ k=1 ak/(z − zk) has infinitely many zeros in D. An example shows that the hypotheses on the zk are not redundant, and that two recently advanced conjectures are false. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-05

Source:

http://arxiv.org/pdf/math/0601729v1.pdf

http://arxiv.org/pdf/math/0601729v1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

critical points ; potentials ; zeros of meromorphic functions

critical points ; potentials ; zeros of meromorphic functions Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

NON-REAL ZEROS OF DERIVATIVES OF REAL MEROMORPHIC FUNCTIONS

Description:

The main result of the paper determines all real meromorphic functions f of finite order in the plane such that f ′ has finitely many zeros while f and f (k) , for some k ≥ 2, have finitely many non-real zeros.

The main result of the paper determines all real meromorphic functions f of finite order in the plane such that f ′ has finitely many zeros while f and f (k) , for some k ≥ 2, have finitely many non-real zeros. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-11

Source:

http://arxiv.org/pdf/0903.2328v1.pdf

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text

Language:

en

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Title:

The Inference of Structure in Images using Multi-local Quadrature Filters.

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Two techniques are presented for corner detection. First, a band of filters are applied with equal radial spatial frequency, but different orientation preferences locally in the image domain. From the energy response, a linear Fourier transform is taken to give confidence measures of both "cornerness " and "edgeness. Second, we consider a multi-...

Two techniques are presented for corner detection. First, a band of filters are applied with equal radial spatial frequency, but different orientation preferences locally in the image domain. From the energy response, a linear Fourier transform is taken to give confidence measures of both "cornerness " and "edgeness. Second, we consider a multi-local spatial separation of filters that lie on a constant radius from a point of interest. This second stage of processing allows a wider classification of image structure. As a result, we infer the presence of line end points, "L", "T", "Y " and "X " junctions using epistemic probabilities. The results are indicative of a relationship between Fourier and Spatial domain models of filtering. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-20

Source:

http://www.bmva.org/bmvc/1991/bmvc-91-015.pdf

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Document Type:

text

Language:

en

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Title:

Postgraduate notes on complex analysis

Description:

These notes originated from a set of lectures on basic results in Nevanlinna theory and their application to ordinary differential equations in the complex domain, given at the Christian-Albrechts-Universität zu Kiel in December 1998. Over the years additional topics have been added, such as some elements of potential theory which are of use in ...

These notes originated from a set of lectures on basic results in Nevanlinna theory and their application to ordinary differential equations in the complex domain, given at the Christian-Albrechts-Universität zu Kiel in December 1998. Over the years additional topics have been added, such as some elements of potential theory which are of use in value distribution theory, including the important technique of harmonic measure. Analytic continuation and singularities of the inverse function are also discussed, and the various themes are brought together in the Denjoy-Carleman-Ahlfors theorem and a recent theorem of Bergweiler and Eremenko concerning asymptotic values of entire and meromorphic functions. The aim has been to develop in a single set of notes some of the key concepts and methods of function theory, in a form suitable for a postgraduate student starting out in the area. The notes have drawn on many sources, and these are indicated in the course of the development. I would like to thank several people for drawing my attention to numerous obscurities and typos in earlier versions of these notes. These include my PhD students James Hinchliffe, Guy Kendall, Eleanor Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-11

Source:

http://www.maths.nottingham.ac.uk/personal/jkl/pg1.pdf

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Document Type:

text

Language:

en

Subjects:

ii

ii Minimize

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Title:

Real Entire Functions of Infinite Order and a Conjecture of Wiman

Author:

Description:

We prove that if f is a real entire function of infinite order, then ff ## has infinitely many non-real zeros. In conjunction with the result of Sheil-Small for functions of finite order this implies that if f is a real entire function such that ff ## has only real zeros, then f is in the Laguerre-Polya class, the closure of the set of real poly...

We prove that if f is a real entire function of infinite order, then ff ## has infinitely many non-real zeros. In conjunction with the result of Sheil-Small for functions of finite order this implies that if f is a real entire function such that ff ## has only real zeros, then f is in the Laguerre-Polya class, the closure of the set of real polynomials with real zeros. This result completes a long line of development originating from a conjecture of Wiman of 1911. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-18

Source:

http://www.math.purdue.edu/~eremenko/./dvi/bel999.ps

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Document Type:

text

Language:

en

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Title:

BAKER DOMAINS FOR NEWTON’S METHOD

Author:

Description:

Abstract. We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady. 1. Introduction and

Abstract. We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady. 1. Introduction and Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-06

Source:

http://arxiv.org/pdf/math/0601496v1.pdf

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Document Type:

text

Language:

en

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Title:

Real entire functions with real zeros and a conjecture of Wiman

Author:

Description:

An entire function is called real if it maps the real line into itself. The main result of this paper is Theorem 1.1 For every real entire function of infinite order with only real

An entire function is called real if it maps the real line into itself. The main result of this paper is Theorem 1.1 For every real entire function of infinite order with only real Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-21

Source:

http://www.math.purdue.edu/~eremenko/dvi/bel4.pdf

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Document Type:

text

Language:

en

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