scholarly journals Decomposable Extensions of Difference Fields

2010 ◽  
Vol 53 (3) ◽  
pp. 489-501 ◽  
Author(s):  
Seiji Nishioka
Keyword(s):  
Difference Fields

scholarly journals Automated Proofs for Some Stirling Number Identities

10.37236/726 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Manuel Kauers ◽  
Carsten Schneider
Keyword(s):  
Stirling Number ◽  
Eulerian Numbers ◽  
Difference Fields

We present computer-generated proofs for some summation identities for ($q$-)Stirling and ($q$-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number identities with a recurrence solver for difference fields.

scholarly journals Pseudofinite difference fields

2019 ◽  
Vol 19 (02) ◽  
pp. 1950011
Author(s):  
Tingxiang Zou
Keyword(s):  
Finite Fields ◽  
Transcendence Degree ◽  
Order Property ◽  
Frobenius Automorphism ◽  
Difference Fields ◽  
Definable Sets ◽  
Partial Connection

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we establish a partial connection between coarse dimension and transformal transcendence degree in these difference fields.

scholarly journals Seasonal Variation and Spatial Patterns of the Atmospheric Component of the Pacific Decadal Oscillation

2013 ◽  
Vol 26 (5) ◽  
pp. 1575-1594 ◽  
Author(s):  
Catrin M. Mills ◽  
John E. Walsh
Keyword(s):  
United States ◽  
North America ◽  
Air Temperature ◽  
Pacific Decadal Oscillation ◽  
Southern Oscillation ◽  
Grid Point ◽  
Southeastern United States ◽  
Surface Air Temperature ◽  
The Pacific ◽  
Difference Fields

Abstract The Pacific decadal oscillation (PDO) is an El Niño–Southern Oscillation (ENSO)-like climate oscillation that varies on multidecadal and higher-frequency scales, with a sea surface temperature (SST) dipole in the Pacific. This study addresses the seasonality, vertical structure, and across-variable relationships of the local North Pacific and downstream North American atmospheric signal of the PDO. The PDO-based composite difference fields of 500-mb geopotential height, surface air temperature, sea level pressure, and precipitation vary not only across seasons, but also from one calendar month to another within a season, although month-to-month continuity is apparent. The most significant signals occur in western North America and in the southeastern United States, where a positive PDO is associated with negative heights, consistent with underlying temperatures in the winter. In summer, a negative precipitation signal in the southeastern United States associated with a positive PDO phase is consistent with a ridge over the region. When an annual harmonic is fit to the 12 monthly surface air temperature differences at each grid point, the PDO temperature signal peaks in winter in most of North America, while a peak in summer occurs in the southeastern United States. Approximately 25% of the variance of the PDO index is accounted for by ENSO. Atmospheric composite differences based on a residual (ENSO linearly removed) PDO index have many similarities to those of the full PDO signal.

scholarly journals Pseudofinite difference fields and counting dimensions

2020 ◽  
Vol 21 (01) ◽  
pp. 2050022
Author(s):  
Tingxiang Zou
Keyword(s):  
Finite Fields ◽  
Transcendence Degree ◽  
Order Property ◽  
Frobenius Automorphism ◽  
Difference Fields ◽  
Definable Sets

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we also discuss the possible connection between coarse dimension and transformal transcendence degree in these difference fields.

scholarly journals Model theory of difference fields

1999 ◽  
Vol 351 (8) ◽  
pp. 2997-3071 ◽  
Author(s):  
Zoé Chatzidakis ◽  
Ehud Hrushovski
Keyword(s):  
Model Theory ◽  
Difference Fields
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