Branes, fermions, and superspace dualities

We use the superspace formulation of supergravity in eleven and ten dimensions to compute fermion couplings on the M2-brane and on Dp-branes. In this formulation fermionic couplings arise naturally from the θ-expansion of the superfields from which the brane actions are constructed. The techniques we use and develop can in principle be applied to determine the fermionic couplings to general background fields up to arbitrary order. Starting with the superspace formulation of 11-dimensional supergravity, we use a geometric technique known as the ‘normal coordinate’ method to obtain the θ-expansion of the M2-brane action. We then present a method which allows us to translate the knowledge of fermionic couplings on the M2-brane to knowledge of such couplings on the D2-brane, and then to any Dp-brane. This method is based on superspace generalizations of both the compactification taking 11-dimensional supergravity to type IIA supergravity and the T-duality rules connecting the type IIA and type IIB supergravities.

Algorithm based on normal coordinate vectors with 16 segments for the data fusion from hand-written Arabic text implemented with MATLAB

Hand-written text recognition is useful for interpreting records in different fields such as healthcare, surgery and police in which professionals may avoid technical equipment and prefer writing notes on paper. In order to perform data fusion from different data sources, handwriting automatic recognition involves barriers such as different ways of writing letters and deformation due to many reasons. This work presents a novel handwriting recognition approach based on the application of coordinate vectors to find similarities in different kinds of deformations. In particular, it has been implemented using 16 segments in order to distinguish all the particularities in matching the new text considering a dataset with a machine-learning approach. The implementation of this approach with MATLAB shows promising results with accuracy of 92.8% for with ensemble and bagged trees, after analyzing 22 possible combinations of machine learning and processing techniques.

Structural Effects of meso-Halogenation on Porphyrins: meso-Xn-ABCD Macrocycles

The use of halogens in the crystal engineering of porphyrin scaffolds has been a topic of strong interest over the past decades. Previously, this was focused on the introduction of a variety of halogens on the meso-phenyl groups of the porphyrin. However, investigations into the effects of direct halogenation of porphyrins at the meso-position on their crystalline architectures have not been conducted to date. Herein we have characterized a series of direct meso-halogenated porphyrins using single crystal X-ray crystallography. This is accompanied by a detailed conformational analysis of all deposited meso-halogenated porphyrins in the CCDC. In this study we have used the Hirshfeld fingerprint plots together with normal-coordinate structural decomposition and determined crystal structures to elucidate the conformation, present intermolecular interactions, and compare respective contacts within the crystalline architectures. Additionally, we have used density functional theory calculations to determine the structure of several halogenated porphyrins. This contrasts conformational analysis with existing X-ray structures and gives a method to characterize samples that are difficult to crystallize.

Адгезия между жестким индентором и упругим полупространством для несжимаемых градиентных сред с высоким показателем градиентности

Contact problem of cylindrical indenter and graded media with account of adhesion forces between two contacted bodies is considered. Analytical solution of the problem for the case of graded media with power-law dependence of elastic modulus on normal coordinate have been found. The case of uncompressible media with Poisson ratio 1/2 was considered in details. It is shown, that in this case the behavior of system can be qualitatively different from the case of homogeneous media. Influence of roughness of the surface is considered. Surface roughness is presented as axially symmetric “waviness”. The contact of parabolic indenter and a gradient media was considered. Differences from the case of a cylinder is shown.