Two families of pro-𝑝 groups that are not absolute Galois groups

Let 𝑝 be a prime. We produce two new families of pro-𝑝 groups which are not realizable as absolute Galois groups of fields. To prove this, we use the 1-smoothness property of absolute Galois pro-𝑝 groups. Moreover, we show in these families, one has several pro-𝑝 groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of the norm residue theorem), or the vanishing of Massey products in Galois cohomology.

New Definition of Atomic Bond Connectivity Index to Overcome Deficiency of Structure Sensitivity and Abruptness in Existing Definition

Topological Index (TI) is a numerical value associated with the molecular graph of the compound. Smoothness property states that a TI is good if its Structure Sensitivity (SS) is as large as possible and its Abruptness (Abr) is small. In 2013, Gutman proved that Atomic Bond Connectivity (ABC) index has small SS and high Abr. In this paper, we defined reverse Atomic Bond Connectivity (ABC) index to overcome this problem. Moreover, we computed reverse ABC index for Silicon Carbides, Bismith Tri-Iodide and Dendrimers.

Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.

Atlas-based Reconstruction of 3D Volumes of Lower Extremity from 2D Calibrated X-ray Images

A new atlas-based 2D-3D reconstruction of 3D volumes of lower extremity from a pair of calibrated X-ray images was presented. The approach combines non-rigid 2D- 2D registration based 3D landmark reconstruction with the B-spline parametrization of TPS transformation, incorporating the smoothness property of B-splines for regularization. Efficacy of the present approach was evaluated on the calibrated X-ray images and CT data. Also, we take the knee joint articulation into consideration. Articulated B-spline parameterization leads to the almost same accuracy as individual B-spline parameterization and has the superiority over the latter when it comes to the prevention from the knee joint penetration.

New SAR Interferogram denoising method via sparse recovery based on L0 norm

The goal of this paper is to estimate a denoised phase image from the observed noisy SAR interferogram. We proposed a linear model to obtain a sparse representation of the interferomteric phase image. The main idea is based on the smoothness property of the phases inside interferometric fringes which leads to get a sparse image when applying the gradient operator twice, along <i>x</i> or <i>y</i> direction, on the interferogram. The new sparse representation of the interferometric phase image allows to transform the denoising problem to an optimization one. So the estimated interferogram is achieved using the approximate message passing algorithm. The proposed approach is validated on different cases of simulated and real interferograms.