An Alternative Natural Deduction for the Intuitionistic Propositional Logic

A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.This work is supported by the Ministary of Science and Technology of Serbia, grant number ON174026

Eccentric connectivity index

The eccentric connectivity index $\xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as $\xi^c (G) = \sum_{v \in V (G)} deg (v) \cdot \epsilon (v)$\,, where $deg (v)$ and $\epsilon (v)$ denote the vertex degree and eccentricity of $v$\,, respectively. We survey some mathematical properties of this index and furthermore support the use of eccentric connectivity index as topological structure descriptor. We present the extremal trees and unicyclic graphs with maximum and minimum eccentric connectivity index subject to the certain graph constraints. Sharp lower and asymptotic upper bound for all graphs are given and various connections with other important graph invariants are established. In addition, we present explicit formulae for the values of eccentric connectivity index for several families of composite graphs and designed a linear algorithm for calculating the eccentric connectivity index of trees. Some open problems and related indices for further study are also listed.Comment: 25 pages, 5 figure

Note on PI and Szeged indices

In theoretical chemistry molecular structure descriptors are used for modeling physico-chemical, pharmacological, toxicologic, biological and other properties of chemical compounds. In this paper we study distance-based graph invariants and present some improved and corrected sharp inequalities for PI, vertex PI, Szeged and edge Szeged topological indices, involving the number of vertices and edges, the diameter, the number of triangles and the Zagreb indices. In addition, we give a complete characterization of the extremal graphs.Comment: 10 pages, 3 figure

Cosmic Microwave and Infrared Backgrounds cross-correlation for ISW detection

We investigate the cross-correlation between the cosmic infrared and microwave backgrounds (CIB & CMB) anisotropies through the integrated Sachs-Wolfe effect. We first describe the CIB anisotropies using a linearly biased power spectrum, then derive the theoretical angular power spectrum of the CMB-CIB cross-correlation for different instruments and frequencies. We discuss the detectability of the ISW signal by performing a signal-to-noise (SNR) analysis with our predicted spectra. The significances obtained range from 6{\sigma} to 7{\sigma} in an ideal case, depending on the frequency ; in realistic cases which account for the presence of noise including astrophysical contaminants, the results span the range 2-5{\sigma}, depending strongly on the major contribution to the noise term.Comment: 4 pages, 1 table. Contribution to the proceedings of the International Conference on Gravitation and Cosmology, Goa, India, December, 201