24,168 research outputs found
Quantum Field Theory: Where We Are
We comment on the present status, the concepts and their limitations, and the
successes and open problems of the various approaches to a relativistic quantum
theory of elementary particles, with a hindsight to questions concerning
quantum gravity and string theory.Comment: To appear in: An Assessment of Current Paradigms in the Physics of
Fundamental Phenomena, to be published by Springer Verlag (2006
Teaching linear algebra at university
Linear algebra represents, with calculus, the two main mathematical subjects
taught in science universities. However this teaching has always been
difficult. In the last two decades, it became an active area for research works
in mathematics education in several countries. Our goal is to give a synthetic
overview of the main results of these works focusing on the most recent
developments. The main issues we will address concern: the epistemological
specificity of linear algebra and the interaction with research in history of
mathematics; the cognitive flexibility at stake in learning linear algebra;
three principles for the teaching of linear algebra as postulated by G. Harel;
the relation between geometry and linear algebra; an original teaching design
experimented by M. Rogalsk
Requirements modelling and formal analysis using graph operations
The increasing complexity of enterprise systems requires a more advanced
analysis of the representation of services expected than is currently possible.
Consequently, the specification stage, which could be facilitated by formal
verification, becomes very important to the system life-cycle. This paper presents
a formal modelling approach, which may be used in order to better represent
the reality of the system and to verify the awaited or existing system’s properties,
taking into account the environmental characteristics. For that, we firstly propose
a formalization process based upon properties specification, and secondly we
use Conceptual Graphs operations to develop reasoning mechanisms of verifying
requirements statements. The graphic visualization of these reasoning enables us
to correctly capture the system specifications by making it easier to determine if
desired properties hold. It is applied to the field of Enterprise modelling
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
Doing and Showing
The persisting gap between the formal and the informal mathematics is due to
an inadequate notion of mathematical theory behind the current formalization
techniques. I mean the (informal) notion of axiomatic theory according to which
a mathematical theory consists of a set of axioms and further theorems deduced
from these axioms according to certain rules of logical inference. Thus the
usual notion of axiomatic method is inadequate and needs a replacement.Comment: 54 pages, 2 figure
Points. Lack thereof
I will discuss some aspects of the concept of "point" in quantum gravity,
using mainly the tool of noncommutative geometry. I will argue that at Planck's
distances the very concept of point may lose its meaning. I will then show how,
using the spectral action and a high momenta expansion, the connections between
points, as probed by boson propagators, vanish. This discussion follows closely
[1] (Kurkov-Lizzi-Vassilevich Phys. Lett. B 731 (2014) 311, [arXiv:1312.2235
[hep-th]].Comment: Proceedings of the XXII Krakow Methodological Conference: Emergence
of the Classical, Copernicus Centre, 11-12 October 2018. Mostly based on
arXiv:1312.2235. V2 corrects several typo
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