The Riddle of Gravitation

There is no doubt that both the special and general theories of relativity capture the imagination. The anti-intuitive properties of the special theory of relativity and its deep philosophical implications, the bizzare and dazzling predictions of the general theory of relativity: the curvature of spacetime, the exotic characteristics of black holes, the bewildering prospects of gravitational waves, the discovery of astronomical objects as quasers and pulsers, the expansion and the (possible) recontraction of the universe..., are all breathtaking phenomena. In this paper, we give a philosophical non-technical treatment of both the special and the general theory of relativity together with an exposition of some of the latest physical theories. We then give an outline of an axiomatic approach to relativity theories due to Andreka and Nemeti that throws light on the logical structure of both theories. This is followed by an exposition of some of the bewildering results established by Andreka and Nemeti concerning the foundations of mathematics using the notion of relativistic computers. We next give a survey on the meaning and philosophical implications of the the quantum theory and end the paper by an imaginary debate between Einstein and Neils Bohr reflecting both Einstein's and Bohr's philosophical views on the quantum world. The paper is written in a somewhat untraditional manner; there are too many footnotes. In order not to burden the reader with all the details, we have collected the more advanced material the footnotes. We think that this makes the paper easier to read and simpler to follow. The paper in full is adressed more to experts.Comment: 40 pages, LaTeX-fil

New SU(1, 1) Position-Dependent Effective Mass Coherent States for the Generalized Shifted Harmonic Oscillator

A new SU(1, 1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM system and construct a new set of operators which close the su(1, 1) Lie algebra, being the PDEM CS of the basis for its unitary irreducible representation. The residual potential is associated to the SHO. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut-Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. We show that the probability density of dynamical evolution in the PDEM CS oscillates back and forth as time goes by and behaves as classical wave packet.Comment: 13 page

Un système à base de connaissances pour une communication parlée personne-système multilingue

La tâche de reconnaissance automatique de la parole (RAP), qui est au coeur de la communication parlée Personne-Système, peut être vue comme une gestion de l’information issue de la microstructure acoustique du signal vocal pour la transformer en une information représentée par la macrostructure phonétique implicite. La correspondance avec le moins d’erreurs possible de ces deux structures nécessite une intégration de connaissances a priori sur la macrostructure phonétique dans des systèmes dédiés à la gestion de l’information acoustico-phonétique. Dans cet article, nous abordons des aspects liés tant à la gestion de l’information phonétique véhiculée par le signal vocal qu’à la topologie de systèmes experts capables de conduire des processus de reconnaissance phonémique multilingue. La démarche que nous proposons consiste à enrichir la base de connaissances de ces experts par des indices représentatifs de la majorité des langues humaines afin de rehausser les performances d’identification des macro-classes et des traits phonétiques divers. Les résultats obtenus sur des corpus de logatomes et de phrases en langues française et arabe montrent qu’il est possible d’orienter la conception des systèmes vers une unification du processus de reconnaissance pour l’adapter à une identification phonémique multilingue.Automatic Speech Recognition (ASR) is at the heart of Man-Machine speech communication. It can be seen as a management of the information emanating from the speech acoustical microstructure. This process aims to transform this information in such a way that it can be represented by the phonetic implicit macrostructure. The effective matching between the two structures requires the integration into expert systems, of an a priori knowledge about the phonetic macrostructures. These expert systems are dedicated to the management of acoustic-phonetic information. This paper investigates aspects linked either to the management of phonetic information contained in the speech signal, or to the topology of expert systems that are capable of conducting a multilingual phonemic recognition process. The proposed method consists of feeding the knowledge base of these expert systems with indicative parameters representing the major human languages in order to enhance the identification performance of phonetic macro-classes and features. The results of experiments carried out on corpora composed of both French and Arabic utterances show that it is possible to conceive systems based on the concept of unified recognition processes dedicated to multilingual phonetic identification

On (n,m)(n,m)-AA-normal and (n,m)(n,m)-AA-quasinormal semi-Hilbertian space operators

summary:The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let ${\mathcal H}$ be a Hilbert space and let $A$ be a positive bounded operator on ${\mathcal H}$. The semi-inner product $\langle h\mid k\rangle _A:=\langle Ah\mid k\rangle$, $h,k \in {\mathcal H}$, induces a semi-norm $\|{\cdot }\|_A$. This makes ${\mathcal H}$ into a semi-Hilbertian space. An operator $T\in {\mathcal B}_A({\mathcal H})$ is said to be $(n,m)$-$A$-normal if $[T^n,(T^{\sharp _A})^m]:=T^n(T^{\sharp _A})^m-(T^{\sharp _A})^mT^n=0$ for some positive integers $n$ and $m$