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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:

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

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-11

Source:

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

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

Document Type:

text

Language:

en

Rights:

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:

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

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Description:

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

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-20

Source:

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

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

Document Type:

text

Language:

en

Rights:

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

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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

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

Document Type:

text

Language:

en

Rights:

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

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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

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-11

Source:

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

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

Document Type:

text

Language:

en

Subjects:

ii

ii Minimize

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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

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-11

Source:

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

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

Document Type:

text

Language:

en

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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

Contributors:

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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Title:

Functional Neuroimaging of Memory: Implications for Cognitive Aging

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Our understanding of the ways in which changes in specific neural systems mediate adult age differences in memory is rapidly increasing, due in no small part to the advent of functional neuroimaging techniques. This article reviews age-related changes in memory performance obtained with behavioral measures, describes models of the neural mechani...

Our understanding of the ways in which changes in specific neural systems mediate adult age differences in memory is rapidly increasing, due in no small part to the advent of functional neuroimaging techniques. This article reviews age-related changes in memory performance obtained with behavioral measures, describes models of the neural mechanisms of memory, and derives predictions from these models regarding age-related changes in brain activation patterns. The neuroimaging findings obtained to date support models emphasizing the role of prefrontal cortex in age-related changes in memory functioning, especially for episodic memory retrieval. In general, neural activation associated with episodic memory encoding is regionally similar for younger and older adults but relatively lower in magnitude for older adults. During retrieval, activation that is restricted to the right prefrontal cortex for younger adults is more likely to be bilateral for older adults. Prefrontal activation exhibits an age-related increase when working memory tasks require simple storage and an age-related decrease when working memory requires higher-level executive processes. Although the evidence is limited, behavioral performance and activation patterns appear to be similar among younger and older adults on tests of semantic (context-independent) and implicit memory. We conclude that several methodological issues, such as defining the relation between brain structure and function, and determining the relationship between performance and activation, are particularly important for understanding age-related changes. Future directions for aging research include further investigation of the relation between encoding and retrieval and the identification of both spared and impaired n. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-18

Source:

http://www.geri.duke.edu/cogpsych/pdf/Langley_Madden.pdf

http://www.geri.duke.edu/cogpsych/pdf/Langley_Madden.pdf Minimize

Document Type:

text

Language:

en

Subjects:

KEY WORDS PET ; fMRI ; brain function ; activation ; learning ; information processing

KEY WORDS PET ; fMRI ; brain function ; activation ; learning ; information processing Minimize

DDC:

150 Psychology *(computed)*

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Title:

Correlates of comorbid anxiety and externalizing disorders in childhood obsessive compulsive disorder

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The present study examines the influence of diagnostic comorbidity on the demographic, psychiatric, and functional status of youth with a primary diagnosis of obsessive compulsive disorder (OCD). Two hundred and fifteen children (ages 5–17) referred to a university-based OCD specialty clinic were compared based on DSM-IV diagnostic profile: OCD ...

The present study examines the influence of diagnostic comorbidity on the demographic, psychiatric, and functional status of youth with a primary diagnosis of obsessive compulsive disorder (OCD). Two hundred and fifteen children (ages 5–17) referred to a university-based OCD specialty clinic were compared based on DSM-IV diagnostic profile: OCD without comorbid anxiety or externalizing disorder, OCD plus anxiety disorder, and OCD plus externalizing disorder. No age or gender differences were found across groups. Higher OCD severity was found for the OCD + ANX group, while the OCD + EXT group reported greater functional impairment than the other two groups. Lower family cohesion was reported by the OCD + EXT group compared to the OCD group and the OCD + ANX group reported higher family conflict compared to the OCD + EXT group. The OCD + ANX group had significantly lower rates of tic disorders while rates of depressive disorders did not differ among the three groups. The presence of comorbid anxiety and externalizing psychopathology are associated with greater symptom severity and functional and family impairment and underscores the importance of a better understanding of the relationship of OCD characteristics and associated disorders. Results and clinical implications are further discussed. Minimize

Publisher:

Springer-Verlag

Year of Publication:

2010-08-01

Source:

European Child & Adolescent Psychiatry, 2010-08-01, Volume 19, pp 637-645

European Child & Adolescent Psychiatry, 2010-08-01, Volume 19, pp 637-645 Minimize

Document Type:

Original Contribution

Language:

En

Subjects:

Child ; Adolescent ; OCD ; Comorbidity ; Anxiety ; Externalizing

Child ; Adolescent ; OCD ; Comorbidity ; Anxiety ; Externalizing Minimize

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Title:

Real entire functions of infinite order and a conjecture of Wiman

Author:

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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-Pólya class, the closure of the set of real polynomi...

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-Pólya 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

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-25

Source:

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

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

Document Type:

text

Language:

en

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