Showing posts with label negative Schwarz’ derivative. Show all posts
Showing posts with label negative Schwarz’ derivative. Show all posts

Thursday, 8 June 2023

The Beginning of a New Paradigm: From D. Bernouilli to M. Allais | Chapter 11 | Research and Applications Towards Mathematics and Computer Science Vol. 1

To show the interaction of the human with welcome environment and allowing him express it, therefore mixing the subject with the object and determining what was missing from Quantum theory. In our polynomial the emotional factor Xo exposes in the numerator and leads to an objective appraisal since of a finite standard. Study also revives an approach to extract human preferences established the stimuli-answer procedure long lost. Fifty years ago a new hypothesis, Elementary Catastrophe Theory,(E.C.T.), unfolding a singular Potential in our brain, determined the underlying movement needed to discharge all the desiderata of the so-called school of Psycho-Physics (Weber-Fechner, 1860), pursuing to make numerical sense of the procedure above. The axiomatization of a self-calculation process removes some "a priori" acceptances about human motivation from the clarification of the empirical dossier. This 5th degree symmetric polynomial exhibits a characteristic (Negative Schwarz' Derivative) that goes at a great distance to resolve disputes and remove barriers in the development of Portfolio Theory apart from meeting the bigger landmark tests in the fields of Value and Utility.  Given that theory of randomness has the divergence of Newton's Method as a example, we have brought order to a conceivably chaotic process cause our algorithm guarantees local and global union through the careful collection of initial points. The feasibility of expanding the approach to the complex field is heartened by the verbalization of the Schwarz derivative's invariance to the Mobius transformation.

Author(s) Details:

William M. Saade,
Formerly with the Stanford Research Institute at the Decision Analysis Group-333, Ravenswood Ave, Menlo Park, CA -94025, United States.

Please see the link here: https://stm.bookpi.org/RATMCS-V1/article/view/10720

Tuesday, 8 February 2022

Arrow and Pratt Revisited: The Case for a Polynomial Representation | Chapter 08 | Recent Advances in Mathematical Research and Computer Science Vol. 7

 This work resurrects a long-forgotten method for eliciting human preferences based on the stimuli-response procedure. The so-called Psycho-Physics school (Weber-Fechner, 1860) [1] attempted to mathematically explain the procedure above. A new theory, Elementary Catastrophe Theory (E.C.T.) [2, which unfolded a unique Potential in human brain fifty years ago, offered the underlying dynamics needed to fulfil all the desiderata at the time. This axiomatization of a self-measurement process gives empirical data a reason that is free of any "a priori" assumptions about human aim. This 5th degree symmetric polynomial exhibits a characteristic (Negative Schwarz' Derivative) [3] that goes a long way to solving controversies and removing roadblocks in the progress of Portfolio Theory [4]. It also fits the major landmark criteria in the fields of Value and Utility, such as the Arrow Impossibility result. We reprint a long-overdue addition to Pratt's [5] in the Annex. Finally, Free Energy could displace Entropy as a paradigm in this field [7] with this newly discovered Human Scale (Cardinal) [6, which is based simply on the postulate of Non-Satiation.


Author(S) Details


William M. Saade
Formerly with the Stanford Research Institute at the Decision Analysis Group 333, Ravenswood Ave, Menlo Park, CA 94025, USA.

View Book:- https://stm.bookpi.org/RAMRCS-V7/article/view/5493