Algebraic Geometry Realization of Quantum Hall Soliton

Using Iqbal-Netzike-Vafa dictionary giving the correspondence between the H$_{2}$ homology of del Pezzo surfaces and p-branes, we develop a new way to approach system of brane bounds in M-theory on $\mathbb{S}^{1}$. We first review the structure of ten dimensional quantum Hall soliton (QHS) from the view of M-theory on $\mathbb{S}^{1}$. Then, we show how the D0 dissolution in D2-brane is realized in M-theory language and derive the p-brane constraint eqs used to define appropriately QHS. Finally, we build an algebraic geometry realization of the QHS in type IIA superstring and show how to get its type IIB dual. Others aspects are also discussed. Keywords: Branes Physics, Algebraic Geometry, Homology of Curves in Del Pezzo surfaces, Quantum Hall Solitons.Comment: 19 pages, 12 figure

Classification of N=2 supersymmetric CFT_{4}s: Indefinite Series

Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s. Since the geometric engineering of these CFT$_{4}$s involve type II strings on K3 fibered CY3 singularities, we conjecture the existence of three kinds of singular complex surfaces containing, in addition to the two standard classes, a third indefinite set. To illustrate this hypothesis, we give explicit examples of K3 surfaces with H$_{3}^{4}$ and E$_{10}$ hyperbolic singularities. We also derive a hierarchy of indefinite complex algebraic geometries based on affine $A_{r}$ and T$$ algebras going beyond the hyperbolic subset. Such hierarchical surfaces have a remarkable signature that is manifested by the presence of poles.Comment: 12 pages, 2 figure

Thermal-Mechanical Coupled Manufacturing Simulation in Heterogeneous Materials

This work is aimed to investigate on thermal and thermo-mechanical behaviour of 6061 Aluminium alloy. The main target of the present investigation is to apply a numerical procedure to assess the thermo-mechanical damage. Finite element analyses of the notched tensile specimens at high temperature have been carried out using ABAQUS Software. The objective was to study the combined effects of thermal and mechanical loads on the strength and ductility of the material. The performance of the proposed model is in general good and it is believed that the presented results and experimental–numerical calibration procedure can be used in practical finite-element simulation

Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case

Using Katz, Klemm and Vafa geometric engineering method of $\mathcal{N}=2$ supersymmetric QFT$_{4}$s and results on the classification of generalized Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of $\mathcal{N}=2$ CFT$_{4}$s based on \textit{indefinite} singularities. We show that the vanishing condition for the general expression of holomorphic beta function of $\mathcal{N}=2$ quiver gauge QFT$_{4}$s coincides exactly with the fundamental classification theorem of KM algebras. Explicit solutions are derived for mirror geometries of CY threefolds with \textit{% hyperbolic} singularities.Comment: 23 pages, 4 figures, minor change

On F-theory Quiver Models and Kac-Moody Algebras

We discuss quiver gauge models with bi-fundamental and fundamental matter obtained from F-theory compactified on ALE spaces over a four dimensional base space. We focus on the base geometry which consists of intersecting F0=CP1xCP1 Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds of Kac-Moody (KM) algebras: ordinary, i.e finite dimensional, affine and indefinite, in particular hyperbolic. We interpret the equations defining these three classes of generalized Lie algebras as the anomaly cancelation condition of the corresponding N =1 F-theory quivers in four dimensions. We analyze in some detail hyperbolic geometries obtained from the affine A base geometry by adding a node, and we find that it can be used to incorporate fundamental fields to a product of SU-type gauge groups and fields.Comment: 13 pages; new equations added in section 3, one reference added and typos correcte

Molecular Characterization and Study of Genetic Relationships among local Cultivars of the Moroccan fig (Ficus carica L.) using Microsatellite and ISSR Markers

Molecular characterization of Moroccan local fig (Ficus carica L.) germplasm was performed on the cultivars present in a collection of the National School of Agriculture of Meknes. A total of 22 fig samples were analysed using 7 ISSR primers and 9 loci S.S.R. A total of 54 I.S.S.R. polymorphic bands with an average of 8 per primers and 42 S.S.R. alleles with means 5 alleles per locus were revealed by these analyses. The ISSR markers allowed distinguishing 22 molecular profiles and S.S.R. loci differentiated between 21 different profiles. Pairwise Comparing, 87% of cultivars pairs were differentiated by 7 to 24 alleles and 89% by 9 to 29 ISSR bands. The statistical analysis and genetic distances have shown a wide molecular diversity in the collection, where the average observed heterozygosity was 0.42. The average similarity between cultivars is 70% using SSR markers and 71.6 for ISSR markers. The same SSR profile was obtained for Nabout1 and Nabout2 with 0 allele difference. Small differences of 1 to 6 alleles were obtained among cultivars which have the same names, which presumably corresponds to somaclonal variations obtained through intense vegetative propagation over long periods, while the differences over 7 alleles suggests the problems of homonyms

On ADE Quiver Models and F-Theory Compactification

Based on mirror symmetry, we discuss geometric engineering of N=1 ADE quiver models from F-theory compactifications on elliptic K3 surfaces fibered over certain four-dimensional base spaces. The latter are constructed as intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the construction of Calabi-Yau threefolds used in geometric engineering in type II superstring theory. Matter is incorporated by considering D7-branes wrapping these 4-cycles. Using a geometric procedure referred to as folding, we discuss how the corresponding physics can be converted into a scenario with D5-branes wrapping 2-cycles of ALE spaces.Comment: 21 pages, Latex, minor change