scholarly journals On covariance generating functions and spectral densities of periodically correlated autoregressive processes

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Z. Shishebor ◽  
A. R. Nematollahi ◽  
A. R. Soltani
Keyword(s):  
Finite Order ◽  
Spectral Theory ◽  
Generating Functions ◽  
New Technique ◽  
Autoregressive Processes ◽  
Nonstationary Processes ◽  
Spectral Densities ◽  
Covariance Functions ◽  
Periodically Correlated Processes ◽  
A New Technique

Periodically correlated autoregressive nonstationary processes of finite order are considered. The corresponding Yule-Walker equations are applied to derive the generating functions of the covariance functions, what are called here the periodic covariance generating functions. We also provide closed formulas for the spectral densities by using the periodic covariance generating functions, which is a new technique in the spectral theory of periodically correlated processes.

scholarly journals A generalisation of two partition theorems of Andrews

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Jehanne Dousse
Keyword(s):  
Representation Theory ◽  
Difference Equations ◽  
Generating Functions ◽  
Quantum Algebra ◽  
New Technique ◽  
Schur’S Theorem ◽  
Partition Identity ◽  
Partition Theorems ◽  
International Audience ◽  
A New Technique

International audience In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in the theory of partitions, finding applications in combinatorics, representation theory and quantum algebra. In this paper we generalise both of Andrews’ theorems to overpartitions. The proofs use a new technique which consists in going back and forth from $q$-difference equations on generating functions to recurrence equations on their coefficients. En 1968 et 1969, Andrews a prouvé deux identités de partitions du type Rogers-Ramanujan qui généralisent le célèbre théorème de Schur (1926). Ces deux généralisations sont devenues deux des théorèmes les plus importants de la théorie des partitions, avec des applications en combinatoire, en théorie des représentations et en algèbre quantique. Dans ce papier, nous généralisons les deux théorèmes de Andrews aux surpartitions. Les preuves utilisent une nouvelle technique qui consiste à faire des allers-retours entre équations aux $q$-différences sur les séries génératrices et équations de récurrence sur leurs coefficients.

A new technique for the mapping of oxygen tension on the brain surface

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S543-S543
Author(s):  
Satoshi Kimura ◽  
Keigo Matsumoto ◽  
Yoshio Imahori ◽  
Katsuyoshi Mineura ◽  
Toshiyuki Itoh
Keyword(s):  
Oxygen Tension ◽  
New Technique ◽  
Brain Surface ◽  
A New Technique ◽  
The Brain

A new technique to visualize alveolar dynamics in a rabbit model

2009 ◽  
Vol 56 (S 01) ◽  
Author(s):  
J Bickenbach ◽  
R Rossaint ◽  
R Autschbach ◽  
R Dembinski
Keyword(s):  
Rabbit Model ◽  
New Technique ◽  
A New Technique
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