Asymptotic approach of generalized orthogonal functional expansions to Wiener kernels

1991 ◽  
Vol 19 (4) ◽  
pp. 383-399 ◽  
Author(s):  
Jonathan D. Victor
Keyword(s):  
Asymptotic Approach ◽  
Wiener Kernels ◽  
Functional Expansions ◽  
Generalized Orthogonal

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Crustacean zooplankton species richness: single- and multiple-year estimates

1998 ◽  
Vol 55 (7) ◽  
pp. 1573-1582 ◽  
Author(s):  
Shelley E Arnott ◽  
John J Magnuson ◽  
Norman D Yan
Keyword(s):  
Spatial Scales ◽  
Species Pool ◽  
Crustacean Zooplankton ◽  
Zooplankton Species ◽  
Asymptotic Approach ◽  
Sampling Programme ◽  
Temporal And Spatial ◽  
Shield Lakes ◽  
The Relationship ◽  
Temporal Extent

Richness estimates are dependent on the spatial and temporal extent of the sampling programme and the method used to predict richness. We assessed crustacean zooplankton richness in eight Canadian Shield lakes at different temporal and spatial scales using three methods of estimation: cumulative, asymptotic, and Chao's index. Percent species detected increased with the number of spatial, intraannual, or interannual samples taken. Single samples detected 50% of the annual species pool and 33% of the total estimated species pool. This suggests that previous estimates of zooplankton richness, based on single samples in individual lakes, are too low. Our richness estimates for individual lakes approach the total number of zooplankton found in some regions of Canada, suggesting that each lake has most taxa at some time, the majority being very rare. Single-year richness estimates provided poor predictions of multiple-year richness. The relationship between richness and environmental variables was dependent on the method of estimation and the number of samples used. We conclude that richness should be treated as an "index" rather than an absolute and sampling efforts should be standardized. We recommend an asymptotic approach to estimate zooplankton richness because the number of samples taken influenced it less.

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