Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions

Michael Fundator

doi:doi:10.11648/j.acm.20180703.13

| Peer-Reviewed

Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions

Michael Fundator

Published in Applied and Computational Mathematics (Volume 7, Issue 3)

Received: 9 November 2017 Accepted: 8 February 2018 Published: 5 July 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean prime ideal theorem and Stone duality and can be indexed by an index set considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability through consideration of extension of the classical Stone duality to the category of Boolean spaces, locally compact Hausdorff spaces. The introduction of probabilistical prediction philosophically based on Erdős–Rényi LLN for the prediction through Descartes’ cycles, Gauss methods of trigonometric interpolation and least squares to reduce error in determination of the orbits of planetary bodies, and Farey series continued by sampling on the Sierpinski gasket.

Published in	Applied and Computational Mathematics (Volume 7, Issue 3)
DOI	10.11648/j.acm.20180703.13
Page(s)	89-93
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Multidimensional Time Model, Law of Large Numbers, Geometrical Predictions

References

[1]	M. Fundator Applications of Multidimensional Time Model for Probability Cumulative Function for Parameter and Risk Reduction. In JSM Proceedings Health Policy Statistics Section Alexandria, VA: American Statistical Association. 433-441.
[2]	M. Fundator. Multidimensional Time Model for Probability Cumulative Function. In JSM Proceedings Health Policy Statistics Section. 4029-4039.
[3]	M. Fundator. Testing Statistical Hypothesis in Light of Mathematical Aspects in Analysis of Probability doi:10.20944/preprints201607.0069.v1.
[4]	M. Fundator Application of Multidimensional time model for probability Cumulative Function to Brownian motion on fractals in chemical reactions (44th Middle Atlantic Regional Meeting, June/9-12/16, Riverdale, NY) Academia Journal of Scientific Research (ISSN 2315-7712) DOI: 10.15413/ajsr.2016.0167 In preparation for publication.
[5]	Michael Fundator Application of Multidimensional time model for probability Cumulative Function to Brownian motion on fractals in chemical reactions (Northeast Regional Meeting, Binghamton, NY, October/5-8/16). Academia Journal of Scientific Research (ISSN 2315-7712) DOI: 10.15413/ajsr.2016.0168 In preparation for publication.
[6]	Michael Fundator Applications of Multidimensional Time Model for Probability Cumulative Function for design and analysis of stepped wedge randomized trials. Academia Journal of Scientific Research (ISSN 2315-7712) DOI: 10.15413/ajsr.2016.0169 In preparation for publication.
[7]	Michael Fundator Multidimensional Time Model for Probability Cumulative Function and Connections Between Deterministic Computations and Probabilities Journal of Mathematics and System Science 7 (2017) 101-109 doi: 10.17265/2159-5291/2017.04.001.
[8]	A. De Moivre, “The Doctrine of Chances”, 2nd ed. (London, England: H. Woodfall, 1738).
[9]	Pierre Simon, Marquis De Laplace “Analytical theory of Probability”.
[10]	Pierre Simon, Marquis De Laplace “Philosophical essay on Probability”.
[11]	Peirce, Charles S. (c. 1909 MS), Collected Papers.
[12]	P. Erdos “On the strong Law of Large Numbers”.
[13]	Josef Steinebach “On a necessary condition for the Erdos-Renyi law of large numbers” Proceedings of the American Mathematical Society Volume 68, Number 1, January/78.
[14]	P. Erdös and A. Rényi, On a new law of large numbers, J. Anal. Math. 23 (1970), 103–111.
[15]	Sandor Csorgo Erdos-Renyi Laws The Annals of Statistics Vol. 7, No. 4 (Jul., 1979), pp. 772-787.
[16]	L. Dumbgen, P. D. Conte-Zerial On low-dimensional projections of high-dimensional distributions.
[17]	H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 7, 4, 284-304 (1940).
[18]	Seneta E. A Tricentenary history of the Law of Large Numbers. Bernoulli 19 (4), 2013, 1088–1121.
[19]	W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1 (Wiley, New York, 1966).
[20]	H S M Coxeter An Absolute Property of Four Mutually Tangent Circles www.math.yorku.ca/dcoxeter/chap1/b%20-%20An%20Absolute%20Property.pdf.
[21]	Pedoe, Daniel. "On a Theorem in Geometry." Amer. Math. Monthly 74.6 (1967): 627-640.

Cite This Article

Plain Text BibTeX RIS

APA Style

Michael Fundator. (2018). Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions. Applied and Computational Mathematics, 7(3), 89-93. https://doi.org/10.11648/j.acm.20180703.13

Copy | Download

ACS Style

Michael Fundator. Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions. Appl. Comput. Math. 2018, 7(3), 89-93. doi: 10.11648/j.acm.20180703.13

Copy | Download

AMA Style

Michael Fundator. Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions. Appl Comput Math. 2018;7(3):89-93. doi: 10.11648/j.acm.20180703.13

Copy | Download

@article{10.11648/j.acm.20180703.13,
  author = {Michael Fundator},
  title = {Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {3},
  pages = {89-93},
  doi = {10.11648/j.acm.20180703.13},
  url = {https://doi.org/10.11648/j.acm.20180703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180703.13},
  abstract = {Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean prime ideal theorem and Stone duality and can be indexed by an index set considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability through consideration of extension of the classical Stone duality to the category of Boolean spaces, locally compact Hausdorff spaces. The introduction of probabilistical prediction philosophically based on Erdős–Rényi LLN for the prediction through Descartes’ cycles, Gauss methods of trigonometric interpolation and least squares to reduce error in determination of the orbits of planetary bodies, and Farey series continued by sampling on the Sierpinski gasket.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions
AU  - Michael Fundator
Y1  - 2018/07/05
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180703.13
DO  - 10.11648/j.acm.20180703.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 89
EP  - 93
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180703.13
AB  - Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean prime ideal theorem and Stone duality and can be indexed by an index set considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability through consideration of extension of the classical Stone duality to the category of Boolean spaces, locally compact Hausdorff spaces. The introduction of probabilistical prediction philosophically based on Erdős–Rényi LLN for the prediction through Descartes’ cycles, Gauss methods of trigonometric interpolation and least squares to reduce error in determination of the orbits of planetary bodies, and Farey series continued by sampling on the Sierpinski gasket.
VL  - 7
IS  - 3
ER  -

Copy | Download

Author Information

Michael Fundator

Division of Behavioral and Social Sciences and Education, National Academies of Sciences, Engineering, Medicine, Washington, USA

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Michael Fundator. (2018). Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions. Applied and Computational Mathematics, 7(3), 89-93. https://doi.org/10.11648/j.acm.20180703.13

Copy | Download

ACS Style

Michael Fundator. Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions. Appl. Comput. Math. 2018, 7(3), 89-93. doi: 10.11648/j.acm.20180703.13

Copy | Download

AMA Style

Michael Fundator. Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions. Appl Comput Math. 2018;7(3):89-93. doi: 10.11648/j.acm.20180703.13

Copy | Download

@article{10.11648/j.acm.20180703.13,
  author = {Michael Fundator},
  title = {Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {3},
  pages = {89-93},
  doi = {10.11648/j.acm.20180703.13},
  url = {https://doi.org/10.11648/j.acm.20180703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180703.13},
  abstract = {Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean prime ideal theorem and Stone duality and can be indexed by an index set considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability through consideration of extension of the classical Stone duality to the category of Boolean spaces, locally compact Hausdorff spaces. The introduction of probabilistical prediction philosophically based on Erdős–Rényi LLN for the prediction through Descartes’ cycles, Gauss methods of trigonometric interpolation and least squares to reduce error in determination of the orbits of planetary bodies, and Farey series continued by sampling on the Sierpinski gasket.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions
AU  - Michael Fundator
Y1  - 2018/07/05
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180703.13
DO  - 10.11648/j.acm.20180703.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 89
EP  - 93
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180703.13
AB  - Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model through application of Boolean prime ideal theorem and Stone duality and can be indexed by an index set considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability through consideration of extension of the classical Stone duality to the category of Boolean spaces, locally compact Hausdorff spaces. The introduction of probabilistical prediction philosophically based on Erdős–Rényi LLN for the prediction through Descartes’ cycles, Gauss methods of trigonometric interpolation and least squares to reduce error in determination of the orbits of planetary bodies, and Farey series continued by sampling on the Sierpinski gasket.
VL  - 7
IS  - 3
ER  -

Copy | Download