Société de Calcul Mathématique SA /
Mathematical Modelling Company, Corp.
Tools for decision help, since 1995
Dear Colleagues,
You might be interested in these books for your Library, for your Department, or simply for yourselves. All are in English.
1) Archimedes' Modern Works, by Bernard Beauzamy
This book is devoted to Archimedes' modern works: direct consequences of his ideas, leading to progresses in presently unexplored, or poorly explored, domains of science.
This, at first sight, may look quite strange, because Archimedes died more than 2 200 years ago, and most people think that everything he did, no matter how clever he was, has been long ago incorporated by modern science, and that he belongs to the past. Certainly, he is considered as one of the greatest geniuses of all times, but people think that his heritage must be simply of historical value.
But this is not true at all, as this book clearly demonstrates. Two main ideas, namely the "Archimedes Maps" and "the Method", lead to completely new approaches of present problems, with far more powerful tools than the ones which were produced otherwise.
For a complete description, please see : https://scmsa.eu/livres/SCM_AMW_order.htm
2) Simple Random Walks in the Plane, by Bernard Beauzamy
Random Walks in the Plane appear very naturally, when two players flip a coin. The player who wins receives one Euro from the other, and the total gain of each player is a "random walk", given by a sequence of independent variables with same law. Conceptually speaking, this is very simple. But such an experiment, if repeated twice, does not lead to the same results, to the same fortune, which contradicts the assumption of "repeatability" which is usually required for any experiment in Physics.
When we study the behavior of the gains, we find that (despite what most people think), they do not tend to an equilibrium; on the contrary, Nature proceeds by large oscillations.
In this book, we introduce completely new methods for the study of these sums: they are "energy based", which means that, instead of probabilistic statements, we use tools derived from classical analysis, operator theory, special functions and trigonometry. They prove much more efficient and provide sharp quantitative results.
Please see : https://www.scmsa.eu/livres/SCM_SRW_order.htm
3) Probabilistic Information Transfer, by Olga Zeydina and Bernard Beauzamy
In real life situations, one rarely has desirably detailed information. It is sometimes incomplete, sometimes corrupted, or with missing or erroneous data. Conversely, some pieces of information do exist. Therefore, there is a natural wish: to try to use the existing information in order to reconstruct some missing items. However, this should be done with two constraints:
First, one should not add any artificial information, such as model assumptions (for instance, that some growth is linear, or that some law is gaussian) ;
Second, the result should be of probabilistic nature: we do not want a precise value for the reconstruction, but a probability law, which allows estimation of the uncertainties.
This is precisely the topic of this book. We show how to "propagate" the information, from a place where it exists to a place where we want to use it; this propagation deteriorates with the distance, somewhat as a gravitational field decreases with the distance.
Please see: https://scmsa.eu/livres/SCM_PIT_order.htm
All volumes: 50 €, including shipping and handling. One can pay using Paypal, or placing an order through any bookstore.
A general presentation of our activities can be found here :
https://scmsa.eu/fiches/SCM_General_Presentation.pdf
With best regards,
Prof. Bernard Beauzamy
Chairman and CEO, Société de Calcul Mathématique SA
111 Faubourg Saint Honoré, 75008 Paris -France
tel +33 1 42 89 10 89, con...@scmsa.com
www.scmsa.eu
