A functional form for the lower Lipschitz condition for the stable subordinator

1988 ◽  
Vol 77 (4) ◽  
pp. 515-520
Author(s):  
Joop Mijnheer
Keyword(s):  
Lipschitz Condition ◽  
Functional Form ◽  
Stable Subordinator

Terminal-Year Investment In Finite-Horizon Planninq Models (Notes & Comments)

1970 ◽  
Vol 10 (2) ◽  
pp. 272-280
Author(s):  
Richard C. Porter
Keyword(s):  
Functional Form ◽  
Finite Horizon ◽  
Planning Models ◽  
Highly Sensitive ◽  
Output Ratio ◽  
Horizon Planning

A common problem of finite-horizon planning models is that there is no logical determinant of investment in the final year (s). Where post-horizon production is not valued by a model, later-year investment, whose sole function is creation of capacity for post-horizon output, looks as incongruous as last rites for an atheist. A number of artificial devices have been developed to handle this difficulty1, but one predominates: to assume that terminal-year investment is a function of terminal-year output. The purpose of this note is to show: 1) how varied and arbitrary are the assumed functions (Section I); 2) that the terminal-year variables and the apparent feasibility of the resulting Plan are highly sensitive to the choice of function (Section II); and 3) that the arbitrariness of functional form is inevitable in the sense that generally acceptable criteria do not much restrict the choice (Section III). Throughout this note, we shall neglect four complexities that are not essential to the problem at hand. One, the marginal capital-output ratio (

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

scholarly journals Minkowski box from Yangian bootstrap

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luke Corcoran ◽  
Florian Loebbert ◽  
Julian Miczajka ◽  
Matthias Staudacher
Keyword(s):  
Minkowski Space ◽  
Wigner Function ◽  
Functional Form ◽  
A Priori ◽  
Alternative Methods ◽  
Feynman Integrals ◽  
The One

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

scholarly journals Multi-objective parametrization of interatomic potentials for large deformation pathways and fracture of two-dimensional materials

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Xu Zhang ◽  
Hoang Nguyen ◽  
Jeffrey T. Paci ◽  
Subramanian K. R. S. Sankaranarayanan ◽  
Jose L. Mendoza-Cortes ◽  
...  
Keyword(s):  
Large Deformation ◽  
Functional Form ◽  
Principal Component ◽  
Interatomic Potentials ◽  
Two Dimensional ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Two Dimensional Materials ◽  
Definition Of

AbstractThis investigation presents a generally applicable framework for parameterizing interatomic potentials to accurately capture large deformation pathways. It incorporates a multi-objective genetic algorithm, training and screening property sets, and correlation and principal component analyses. The framework enables iterative definition of properties in the training and screening sets, guided by correlation relationships between properties, aiming to achieve optimal parametrizations for properties of interest. Specifically, the performance of increasingly complex potentials, Buckingham, Stillinger-Weber, Tersoff, and modified reactive empirical bond-order potentials are compared. Using MoSe2 as a case study, we demonstrate good reproducibility of training/screening properties and superior transferability. For MoSe2, the best performance is achieved using the Tersoff potential, which is ascribed to its apparent higher flexibility embedded in its functional form. These results should facilitate the selection and parametrization of interatomic potentials for exploring mechanical and phononic properties of a large library of two-dimensional and bulk materials.

scholarly journals Functional Form Model Specification: An Application to Hedonic Pricing

1995 ◽  
Vol 24 (2) ◽  
pp. 166-173 ◽  
Author(s):  
Jeff E. Brown ◽  
Don E. Ethridge
Keyword(s):  
Functional Form ◽  
Hedonic Pricing ◽  
Hedonic Model ◽  
Model Specification ◽  
Estimation Accuracy ◽  
Hedonic Price ◽  
Partial Regression ◽  
Cotton Price ◽  
Residuals Analysis ◽  
Form Model

A combination of conceptual analysis and empirical analysis—partial regression and residuals analysis—was used to derive an appropriate functional form hedonic price model. These procedures are illustrated in the derivation of a functional form hedonic model for an automated, econometric daily cotton price reporting system for the Texas-Oklahoma cotton market. Following conceptualization to deduce the general shapes of relationships, the appropriate specific functional form was found by testing particular attribute transformations identified from partial regression analysis. Minimizing structural errors across attribute levels and estimation accuracy were used in determining when an appropriate functional form for both implicit and explicit prices was found.

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