6,300 research outputs found
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 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 \,, where and
denote the vertex degree and eccentricity of \,, 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
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