scholarly journals Internality, transfer, and infinitesimal modeling of infinite processes†

Author(s):  
Emanuele Bottazzi ◽  
Mikhail G Katz

ABSTRACT A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson’s transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields (surreals, Levi-Civita field, Laurent series) may have advantages over hyperreals in probabilistic modeling. We show that probabilities developed over such fields are less expressive than hyperreal probabilities.

2018 ◽  
Vol 2 ◽  
pp. 9-16
Author(s):  
A. Al-Ammouri ◽  
◽  
H.A. Al-Ammori ◽  
A.E. Klochan ◽  
A.M. Al-Akhmad ◽  
...  

2014 ◽  
Vol 51 (4) ◽  
pp. 454-465
Author(s):  
Lu-Ming Shen ◽  
Huiping Jing

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q ((X^{ - 1} ))$$ \end{document} denote the formal field of all formal Laurent series x = Σ n=ν∞anX−n in an indeterminate X, with coefficients an lying in a given finite field \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}. For any \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} with deg β > 1, it is known that for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} (with respect to the Haar measure), x is β-normal. In this paper, we show the inverse direction, i.e., for any x, for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document}, x is β-normal.


2020 ◽  
Vol 25 (2) ◽  
pp. 125-132
Author(s):  
Bal Bahadur Tamang ◽  
Ajay Singh

This article attempts to describe the continued fraction expansion of ÖD viewed as a Laurent series x-1. As the behavior of the continued fraction expansion of ÖD is related to the solvability of the polynomial Pell’s equation p2-Dq2=1  where D=f2+2g  is monic quadratic polynomial with deg g<deg f  and the solutions p, q  must be integer polynomials. It gives a non-trivial solution if and only if the continued fraction expansion of ÖD  is periodic.


2019 ◽  
pp. 87-93
Author(s):  
Ivan Blahun ◽  
Halyna Leshchuk ◽  
Mariya Kyfor

Considering the important role of tourism in the socio-economic development of regions, the need for information and modeling of ways to increase demand for tourism services and tourism development is being updated. The article uses methods of analytical, logical, comparative analysis and systematic approach to study trends in demand for tourist services in Ukraine. Econometric modeling analyzes the demand for tourism services by the level of income and expenditures of the population in 2018. Trends in demand for tourism services in 2018 in terms of income and expenditure of the population with the use of the Tornquist econometric model have been analyzed. It is proposed to use the decile groups of the population for analyzing income and expenditure by the level of income, total income per capita, the level of household expenditure relative to income, the percentage of tourism expenditure by households, the expenditure on tourism and the elasticity of tourism demand. Average values of the population’s expenditures on tourism were established, which helped to determine the elasticity of effective demand for each decile group. The more than one unit of elasticity of effective tourism demand for each decile group indicated that tourism services for domestic households belong to the group of luxury goods and services. It should be noted that in the following decile income groups of households there is a decrease in elasticity. It means that when income tends to increase indefinitely, elasticity coefficients fall, and this indicates a stabilization of costs of this type. In this case, the percentage of households in each decile group that recorded the costs of organized tourism in their budgets and the value of the probability of household participation in this form of recreation was determined based on an estimated probability model. An analysis of the values of income elasticity indicators in each income decile group has shown that increasing household incomes contribute to increased demand for tourism services and an increase in the share of expenditures for these purposes in household budgets.


Crop Science ◽  
1992 ◽  
Vol 32 (3) ◽  
pp. 704-712 ◽  
Author(s):  
Scott M. Lesch ◽  
Catherine M. Grieve ◽  
Eugene V. Maas ◽  
Leland E. Francois

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