Non Trivial Extension of the (1+2)-Poincar\'e Algebra and Conformal Invariance on the Boundary of AdS3AdS_3

Using recent results on string on $AdS_{3}\times N^d$, where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de Traubenberg and Slupinsky, refs [1] and [29]. We show by explicit computation that this new extension is a special kind of fractional supersymmetric algebra which may be derived from the deformation of the conformal structure living on the boundary of $AdS_3$. The two so(1,2) Lorentz modules of spin $\pm{1\over k}$ used in building of the generalisation of the (1+2) Poincar\'e algebra are re-interpreted in our analysis as highest weight representations of the left and right Virasoro symmetries on the boundary of $AdS_3$. We also complete known results on 2d-fractional supersymmetry by using spectral flow of affine Kac-Moody and superconformal symmetries. Finally we make preliminary comments on the trick of introducing Fth-roots of g-modules to generalise the so(1,2) result to higher rank lie algebras g.Comment: Latex, 31 page

Trisomie 21 et prise en charge orthodontique

Les signes cliniques liés à la trisomie 21 mettent en évidence un retard cognitif associé à des modifications morphologiques de la sphère cervico-bucco-faciale, des bases osseuses mais aussi de la denture. Les troubles fonctionnels associés compliquent le tableau clinique qui s'aggrave au cours de la croissance de l'enfant entraînant une dysmorphose importante. L'enfant porteur de trisomie 21 est, par conséquent, un patient orthodontique, du fait de sa dysmorphose primaire. Nous proposons une réflexion sur la prise en charge orthodontique du patient porteur de trisomie 21 en envisageant les possibilités thérapeutiques et leurs limites en fonction des différents facteurs généraux et locaux liés à l'aberration chromosomique

On Non Commutative Calabi-Yau Hypersurfaces

Using the algebraic geometry method of Berenstein et al (hep-th/0005087), we reconsider the derivation of the non commutative quintic algebra ${\mathcal{A}}_{nc}(5)$ and derive new representations by choosing different sets of Calabi-Yau charges ${C_{i}^{a}}$. Next we extend these results to higher $d$ complex dimension non commutative Calabi-Yau hypersurface algebras ${\mathcal{A}}_{nc}(d+2)$. We derive and solve the set of constraint eqs carrying the non commutative structure in terms of Calabi-Yau charges and discrete torsion. Finally we construct the representations of ${\mathcal{A}}_{nc}(d+2)$ preserving manifestly the Calabi-Yau condition $\sum_{i}C_{i}^{a}=0$ and give comments on the non commutative subalgebras.Comment: 16 pages, Latex. One more subsection on fractional branes, one reference and minor changes are added. To appear in Phy. Let.

Salinité et pollution par les nitrates des eaux souterraines de la plaine des Triffa

Les eaux souterraines de la plaine des Triffa (Basse Moulouya) deviennent de plus en plus polluées. Les résultats analytiques montrent que la plupart des puits sont chargés en sels et en nitrates, donc impropres à la consommation humaine et peuvent avoir un effet négatif sur les cultures maraîchères de la région. Dans la zone étudiée, des teneurs de 2,32 à 174,70 mg/l de NO3-, de 134 à 3614 mg/l de Cl- et de 103 à 1518 mg/l de Na+ ne sont pas exceptionnelles. Elles dépassent largement les normes fixées par l’OMS et la CEE (50 mg/l pour les NO3 -, de 250 mg/l pour Cl- et de 175 mg/l pour Na+). L’intensification de l’agriculture dans la plaine, notamment dans les périmètres irrigués, l’épandage excessif des engrais, les applications répétées, et à quantités fortes, de fumiers, l’irrigation, les précipitations et la remontée de la nappe dans certaines régions ont engendré une pollution croissante des ressources en eau

Fractional Supersymmetry As a Matrix Model

Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative geometry are overpassed in the parafermionic approach. Moreover we find that fractional supersymmetric algebras are naturally realized as matrix models. The K=3 case is studied in details. Links between 2d $({1\over 3},0)$ and $(({1\over 3}^{2}),0)$ fractional supersymmetries and N=2 U(1) and N=4 su(2) standard supersymmetries respectively are exhibited. Field theoretical models describing the self couplings of the matter multiplets $(0^{2},({1\over 3})^{2},({2\over 3})^{2})$ and $(0^{4},({1\over 3})^{4},({2\over 3})^{4})$ are given.Comment: Latex,no figure,17page

On Non-Commutative Orbifolds of K3 Surfaces

Using the algebraic geometry method of Berenstein and Leigh for the construction of the toroidal orbifold (T^2 x T^2 x T^2) / (Z_2 x Z_2) with discrete torsion and considering local K3 surfaces, we present non-commutative aspects of the orbifolds of product of K3 surfaces. In this way, the ordinary complex deformation of K3 can be identified with the resolution of stringy singularities by non-commutative algebras using crossed products. We give representations and make some comments regarding the fractionation of branes. Illustrating examples are presented.Comment: 23 page

NC Effective Gauge Model for Multilayer FQH States

We develop an effective field model for describing FQH states with rational filling factors that are not of Laughlin type. These kinds of systems, which concern single layer hierarchical states and multilayer ones, were observed experimentally; but have not yet a satisfactory non commutative effective field description like in the case of Susskind model. Using $D$ brane analysis and fiber bundle techniques, we first classify such states in terms of representations characterized, amongst others, by the filling factor of the layers; but also by proper subgroups of the underlying $U(n)$ gauge symmetry. Multilayer states in the lowest Landau level are interpreted in terms of systems of $D2$ branes; but hierarchical ones are realized as Fiber bundles on $D2$ which we construct explicitly. In this picture, Jain and Haldane series are recovered as special cases and have a remarkable interpretation in terms of Fiber bundles with specific intersection matrices. We also derive the general NC commutative effective field and matrix models for FQH states, extending Susskind theory, and give the general expression of the rational filling factors as well as their non abelian gauge symmetries.Comment: 54 pages 11 figures, LaTe

Empirical investigation to explore potential gains from the amalgamation of Phase Changing Materials (PCMs) and wood shavings

The reduction of gained heat, heat peak shifting and the mitigation of air temperature fluctuations are some desirable properties that are sought after in any thermal insulation system. It cannot be overstated that these factors, in addition to others, govern the performance of such systems thus their effect on indoor ambient conditions. The effect of such systems extends also to Heating, Ventilation and Air-conditioning (HVAC) systems that are set up to operate optimally in certain conditions. Where literature shows that PCMs and natural materials such as wood-shavings can provide efficient passive insulation for buildings, it is evident that such approaches utilise methods that are of a degree of intricacy which requires specialist knowledge and complex techniques, such as micro-encapsulation for instance. With technical and economic aspects in mind, an amalgam of PCM and wood-shavings has been created for the purpose of being utilised as a feasible thermal insulation. The amalgamation was performed in the simplest of methods, through submerging the wood shavings in PCM. An experimental procedure was devised to test the thermal performance of the amalgam and compare this to the performance of the same un-amalgamated materials. Comparative analysis revealed that no significant thermal gains would be expected from such amalgamation. However, significant reduction in the total weight of the insulation system would be achieved that, in this case, shown to be up to 20.94%. Thus, further reducing possible strains on structural elements due to the application of insulation on buildings. This can be especially beneficial in vernacular architectural approaches where considerably large amounts and thicknesses of insulations are used. In addition, cost reduction could be attained as wood shavings are significantly cheaper compared to the cost of PCMs