The Generalized Poisson–Nernst–Planck System with Nonlinear Interface Conditions

2018 ◽  
pp. 101-106 ◽  
Author(s):  
Anna V. Zubkova
Keyword(s):  
Interface Conditions ◽  
Generalized Poisson ◽  
Nonlinear Interface

Analytic Elements from Separation of Variables

2020 ◽  
pp. 165-226
Author(s):  
David R. Steward
Keyword(s):  
Separation Of Variables ◽  
Three Dimensional ◽  
Interface Conditions ◽  
Helmholtz Equations ◽  
Oblate Spheroids ◽  
Complex Functions ◽  
Analytic Elements ◽  
Nonlinear Interface ◽  
Modified Helmholtz Equations ◽  
Finite Domains

Separation of variables provides influence functions for analytic elements, which extend the solutions available with complex functions to problems involving the Helmholtz and modified Helmholtz equations. Methods are introduced for one-dimensional problems that provide the background vector field for many problems, and these solutions are extended to finite domains with interconnected rectangle elements in Section 4.3. Circular elements are developed in Section 4.4 using series of Bessel and Fourier functions to model wave propagation around and through collections of elements, and vadose zone solutions are extended to solve the nonlinear interface conditions occurring along circles. Methods are extended to three-dimensional problems for spheres (Section 4.5), and prolate and oblate spheroids in Section 4.6.

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

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