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

Removal Efficiency of Textile Dyes from Aqueous Solutions Using Calcined Waste of Eggshells as Eco-friendly Adsorbent: Kinetic and Thermodynamic Studies

This research investigates the removal of textile dyes (Rhodamine B and Alizarin Red S) from aqueous solution by a low-cost adsorbent prepared from eggshell waste. Batch adsorption experiments were conducted in order to determine the effect of different parameters such as pH, dye concentration, contact time, adsorbent dosage, particle size, and temperature. The best correlation was found by Langmuir model, and the maximum adsorption capacity was 175.58 mg g–1 for Rhodamine B and 156.56 mg g–1 for Alizarin Red S. Thermodynamic studies showed that the adsorption of Rhodamine B and Alizarin Red S were feasible, spontaneous, and exothermic in nature. Regeneration study conducted to test the reusability (five cycles) and comparison of adsorption capacities of Rhodamine B and Alizarin Red S showed that calcined eggshell adsorbent could potentially be used for the removal of dyes from aqueous solutions. This work is licensed under a Creative Commons Attribution 4.0 International License

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

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