An Empirical Study of National Education and Economic Development Based on a Variable Coefficient Model

This paper studies the relationship between the level of national education and economic development in 31 provinces and cities in China from 2012 to 2019. Principal component analysis is used to comprehensively evaluate the level of national education, on the basis of which a variable coefficient model is tested and a constant coefficient model is established for comparison. The results show that: (1) there is a co-integration relationship between the level of national education and economic development, i.e. the two are in equilibrium in the long run. (2) In some provinces and cities in China, economic development is positively correlated with the level of national education, and some provinces and cities are negatively correlated. (3) Economic development has different effects on the level of national education in the east, middle and west. (4) Economic development and national education level are positively correlated in the average sense in China.

An Empirical Study of National Education and Economic Development Based on a Variable Coefficient Model

This paper studies the relationship between the level of national education and economic development in 31 provinces and cities in China from 2012 to 2019. Principal component analysis is used to comprehensively evaluate the level of national education, on the basis of which a variable coefficient model is tested and a constant coefficient model is established for comparison. The results show that: (1) there is a co-integration relationship between the level of national education and economic development, i.e. the two are in equilibrium in the long run. (2) In some provinces and cities in China, economic development is positively correlated with the level of national education, and some provinces and cities are negatively correlated. (3) Economic development has different effects on the level of national education in the east, middle and west. (4) Economic development and national education level are positively correlated in the average sense in China.

On the representation by bivariate ridge functions

UDC 517.5 We consider the problem of representation of a bivariate function by sums of ridge functions. It is shown that if a function of a certain smoothness class is represented by a sum of finitely many arbitrarily behaved ridge functions, then it can also be represented by a sum of ridge functions of the same smoothness class. As an example, this result is applied to a homogeneous constant coefficient partial differential equation.

The Scan-LM to Test Instability in the Constant Coefficient of Spatial Autoregressive Models

This paper presents a test based on the principle of Lagrange Multipliers to identify spatial instability in the constant coefficient of regression models including substantive spatial dependence. The test has been adapted to the Scan methodology. Its main advantage is that it identifies areas with differential behavior without the need to provide information about their location, shape, or size. The study shows the utility of the test, reconsidering the results obtained by Mur et al.(2008) about instability in the distribution of per capita income in European regions.

Understanding change in hydrometeorological extremes with statistical models - the importance of model parametrization

<p>The potential for changes in hydrometeorological extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations, allowing one or more distribution parameters to change as a function of time or some physically-motivated covariate. In most practical extreme value analyses, the main quantity of interest though is the upper quantiles of the distribution, rather than the parameters' values. This study focuses on the changes in quantile estimates under different change-permitting models. First, metrics which measure the impact of changes in parameters on changes in quantiles are introduced. The mathematical structure of these change metrics is investigated for several models based on the Generalised Extreme Value (GEV) distribution. It is shown that for the most commonly used models, the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret. Next, it is posited that commonly used change-permitting GEV models do not preserve a constant coefficient of variation, a property that is typically assumed to hold and that is related to the scaling properties of extremes. To address these shortcomings a new (parsimonious) model is proposed: the model assumes a constant coefficient of variation, allowing the location and scale parameters to change simultaneously. The proposed model results in more interpretable changes in the quantile function. The consequences of the different modelling choices on quantile estimates are exemplified using a dataset of extreme peak river flow measurements.</p>

A Further Investigation on the Application of Critical Pore Size as an Approach for Reservoir Rock Typing

The correct definition of rock types plays a critical role in reservoir characterization, simulation, and field development planning. In this study, we use the critical pore size (linf) as an approach for reservoir rock typing. Two linf relations were separately derived based on two permeability prediction models and then merged together to drive a generalized linf relation. The proposed rock typing methodology includes two main parts: in the first part, we determine an appropriate constant coefficient, and in the second part, we perform reservoir rock typing based on two different scenarios. The first scenario is based on the forming groups of rocks using statistical analysis, and the second scenario is based on the forming groups of rocks with similar capillary pressure curves. This approach was applied to three data sets. In detail, two data sets were used to determine the constant coefficient, and one data set was used to show the applicability of the linf method in comparison with FZI for rock typing.

On the Theory of ψ-Hilfer Nonlocal Cauchy Problem

In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results