in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a g...

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of singleelectron Green’s functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange...

A mapping f from F2m to itself is almost perfect nonlinear (APN) if its directional derivatives in nonzero directions are all 2-to-1. Let Cf be the binary linear code of length 2 − 1, whose parity check matrix has its j-th column [ π f(π) ] , where π is a primitive element in F2m and j = 0, 1, · · · , 2 − 2. For m ≥ 3 and any quadratic APN function f(x) = ∑m−1 i,j=0 ai,jx 2+2 , ai,j ∈ F2m , it ...

This paper presents a simple, yet effective method of enhancing the inherent diversity among packet retransmissions in digital communication systems that employ high-order modulations such as M -PSK and M -QAM through frequency-selective channels. Diversity is enhanced by uniquely redefining the bitto-symbol mapping for each retransmission. Finding the optimal mappings leads to iterative soluti...

the paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. attention goes to the number of limit cycles produced by the period annulus under perturbations. by using the appropriate p...

Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve ...

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic Poisson superpairs over a semi-finitely-filtered polarized Z2-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in t...

We give a complete numerical description of the geometry of the four-point contact interaction of closed bosonic string field theory. Namely, we compute the boundary of the relevant region of the moduli space of the four-punctured spheres, and everywhere in this region we give the local coordinates around each punctures in terms of a Strebel quadratic differential and mapping radii. The numeric...

From a functional viewpoint, a spiking neuron is a device that transforms input spike trains on its various synapses into an output spike train on its axon. We demonstrate in this paper that the function mapping underlying the device can be tractably learned based on input and output spike train data alone. We begin by posing the problem in a classification based framework. We then derive a nov...