Nevanlinna Theory of Several Variables

In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F. Gross in [2].) The thrust of Steinmetz’ central results on factorization is that if g(z) is entire and f(z) is meromorphic in C such that the composite fog satisfies an algebraic differential equation, then so do f(z) and, degenerate cases aside, g(z). In addition, the more one knows about the equation for fog (e.g. degree, weight, autonomy), the more one can conclude about the equations for f and g.In this note we generalize Steinmetz’ work to show the following:a) Steinmetz’ two basic results, Satz 1 and Korollar 1 of [4] can be seen as one-variable specializations of a single two variable result, andb) the function g(z) can itself be allowed to be a function of several variables.

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Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-97-01874-6 ◽

1997 ◽

Vol 349 (12) ◽

pp. 5043-5071 ◽

Cited By ~ 8

Author(s):

William Cherry ◽

Zhuan Ye

Keyword(s):

Inverse Problem ◽

Nevanlinna Theory ◽

Several Variables

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THE TUMURA–CLUNIE THEOREM IN SEVERAL COMPLEX VARIABLES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972714000446 ◽

2014 ◽

Vol 90 (3) ◽

pp. 444-456 ◽

Cited By ~ 4

Author(s):

PEI-CHU HU ◽

CHUNG-CHUN YANG

Keyword(s):

Meromorphic Function ◽

Complex Variable ◽

Nevanlinna Theory ◽

Meromorphic Functions ◽

Complex Variables ◽

Several Complex Variables ◽

Several Variables

AbstractIt is a well-known result that if a nonconstant meromorphic function $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f$ on $\mathbb{C}$ and its $l$th derivative $f^{(l)}$ have no zeros for some $l\geq 2$, then $f$ is of the form $f(z)=\exp (Az+B)$ or $f(z)=(Az+B)^{-n}$ for some constants $A$, $B$. We extend this result to meromorphic functions of several variables, by first extending the classic Tumura–Clunie theorem for meromorphic functions of one complex variable to that of meromorphic functions of several complex variables using Nevanlinna theory.

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Theq-Difference Theorems for Meromorphic Functions of Several Variables

Abstract and Applied Analysis ◽

10.1155/2014/736021 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Zhi-Tao Wen

Keyword(s):

Meromorphic Function ◽

Nevanlinna Theory ◽

Meromorphic Functions ◽

Logarithmic Derivative ◽

Zero Order ◽

Logarithmic Density ◽

Several Variables

We investigateq-shift analogue of the lemma on logarithmic derivative of several variables. Letfbe a meromorphic function inℂnof zero order such thatf(0)≠0,∞, and letq∈ℂn\{0}. Then we havem(r,f(qz)/f(z))=o(T(r,f))on a set of logarithmic density 1. Theq-shift analogue of the first and the second main theorems of Nevanlinna theory of several variables and their applications is also shown.

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Topographische Orientierung bei Patienten mit erworbener Hirnschädigung

Zeitschrift für Neuropsychologie ◽

10.1024//1016-264x.10.2.77 ◽

1999 ◽

Vol 10 (2) ◽

pp. 77-86

Author(s):

Martina Kindsmüller ◽

Andrea Kaindl ◽

Uwe Schuri ◽

Alf Zimmer

Keyword(s):

Brain Damage ◽

Cognitive Deficits ◽

Hospital Setting ◽

Hospital Staff ◽

Reading Test ◽

Map Reading ◽

Several Variables ◽

Topographical Orientation ◽

The One ◽

Behavioral Memory

Topographical Orientation in Patients with Acquired Brain Damage Abstract: A study was conducted to investigate the abilities of topographical orientation in patients with acquired brain damage. The first study investigates the correlation between wayfinding in a hospital setting and various sensory and cognitive deficits as well as the predictability of navigating performance by specific tests, self-rating of orientation ability and rating by staff. The investigation included 35 neuropsychological patients as well as 9 control subjects. Several variables predicted the wayfinding performance reasonably well: memory tests like the one introduced by Muramoto and a subtest of the Rivermead Behavioral Memory Test, the Map Reading Test and the rating by hospital staff. Patients with hemianopia experienced significant difficulty in the task.

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Pengaruh Lintas Budaya Pada Pemasaran Internasional Dengan Pendekatan Perilaku Konsumen

Jurnal Riset Manajemen Sekolah Tinggi Ilmu Ekonomi Widya Wiwaha Program Magister Manajemen ◽

10.32477/jrm.v1i2.28 ◽

2017 ◽

Vol 1 (2) ◽

pp. 168-176

Author(s):

Endy Gunanto ◽

Yenni Kurnia Gusti

Keyword(s):

Consumer Behavior ◽

Marketing Strategy ◽

Consumer Culture ◽

International Organization ◽

Future Research ◽

Special Issue ◽

Cross Culture ◽

Several Variables ◽

Cultural Orientations ◽

The Impact

In this article we present a conceptual of the effect of cross culture on consumer behavior incorporating the impact of globalization. This conceptual idea shows that culture inûuences various domains of consumer behavior directly as well as through international organization to implement marketing strategy. The conceptual identify several factors such as norm and value in the community, several variables and also depicts the impact of other environmental factors and marketing strategy elements on consumer behavior. We also identify categories of consumer culture orientation resulting from globalization. Highlights of each of the several other articles included in this special issue in Asia region. We conclude with the contributions of the articles in terms of the consumer cultural orientations and identify directions for future research.

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Courting the Youth Vote in 2008: The Obama Effect

Vanderbilt Undergraduate Research Journal ◽

10.15695/vurj.v5i0.2814 ◽

2009 ◽

Vol 5 ◽

Author(s):

Lindsey C Bohl

Keyword(s):

Presidential Elections ◽

Voter Registration ◽

The Internet ◽

The Past ◽

Several Variables ◽

High Turnout ◽

Short And Long Term ◽

Use Of The Internet ◽

Youth Vote

This paper examines a few of the numerous factors that may have led to increased youth turnout in 2008 Election. First, theories of voter behavior and turnout are related to courting the youth vote. Several variables that are perceived to affect youth turnout such as party polarization, perceived candidate difference, voter registration, effective campaigning and mobilization, and use of the Internet, are examined. Over the past 40 years, presidential elections have failed to engage the majority of young citizens (ages 18-29) to the point that they became inclined to participate. This trend began to reverse starting in 2000 Election and the youth turnout reached its peak in 2008. While both short and long-term factors played a significant role in recent elections, high turnout among youth voters in 2008 can be largely attributed to the Obama candidacy and campaign, which mobilized young citizens in unprecedented ways.

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Frontiers in Complex Dynamics

10.23943/princeton/9780691159294.001.0001 ◽

2014 ◽

Author(s):

Araceli Bonifant ◽

Misha Lyubich ◽

Scott Sutherland

Keyword(s):

Historical Perspective ◽

Complex Dynamics ◽

Short Paper ◽

Combinatorial Group Theory ◽

Entropy Theory ◽

Holomorphic Dynamics ◽

Eightieth Birthday ◽

Several Variables ◽

Fields Medal ◽

Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

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