Wormholes in R2R^2-gravity within the f(R,T)f(R,T) formalism

We propose, as a novelty in the literature, the modelling of wormholes within the particular case of the $f(R,T)$ gravity, namely $f(R,T)=R+\alpha R^{2}+\lambda T$, with $R$ and $T$ being the Ricci scalar and trace of the energy-momentum tensor, respectively, while $\alpha$ and $\lambda$ are constants. Although such a functional form application can be found in the literature, those concern to compact astrophysical objects, such that no wormhole analysis has been done so far. The quadratic geometric and linear material corrections of this theory make the matter content of the wormhole to remarkably be able to obey the energy conditions.Comment: Published versio

f(R,T)=f(R)+λTf(R,T)=f(R)+\lambda T gravity models as alternatives to cosmic acceleration

This article presents cosmological models that arise in a subclass of $f(R,T)=f(R)+f(T)$ gravity models, with different $f(R)$ functions and fixed $T$-dependence. That is, the gravitational lagrangian is considered as $f(R,T)=f(R)+\lambda T$, with constant $\lambda$. Here $R$ and $T$ represent the Ricci scalar and trace of the stress-energy tensor, respectively. The modified gravitational field equations are obtained through the metric formalism for the Friedmann-Lema\^itre-Robertson-Walker metric with signature $(+,-,-,-)$. We work with $f(R)=R+\alpha R^2-\frac{\mu^4}{R}$, $f(R)=R+k\ln(\gamma R)$ and $f(R)=R+me^{[-nR]}$, with $\alpha, \mu, k, \gamma, m$ and $n$ all free parameters, which lead to three different cosmological models for our Universe. For the choice of $\lambda=0$, this reduces to widely discussed $f(R)$ gravity models. This manuscript clearly describes the effects of adding the trace of the energy-momentum tensor in the $f(R)$ lagrangian. The exact solution of the modified field equations are obtained under the hybrid expansion law. Also we present the Om diagnostic analysis for the discussed models.Comment: 11 pages, 20 figures, Accepted version in EPJ

Loyalty Programme Applications in Indian Service Industry

Retaining all customers would not be a good idea for any business. In contrast, allowing the profitable customers to leave would be an even worse idea. Consequently the real solution rests in knowing the value of each customer and then focusing loyalty efforts on those customers. Customers are more likely to be loyal to a group of brands than to a single brand. This is particularly true if the chosen brand is the category leader and costs more. In contrast to the one – brand- for – life mentality of the past, today’s consumers are blatant in their divided loyalties, for their own safety and pleasure. The conceptual framework presented helps to understand the evolving logic of loyalty programs and process of implementing the same. Applications in different service industry for building and sustaining loyalty provide an overview of the status of such programmes.

Wormholes in exponential f(R,T)f(R,T) gravity

Alternative gravity is nowadays an extremely important tool to address some persistent observational issues, such as the dark sector of the universe. They can also be applied to stellar astrophysics, leading to outcomes one step ahead of those obtained through General Relativity. In the present article we test a novel $f(R,T)$ gravity model within the physics and geometry of wormholes. The $f(R,T)$ gravity is a reputed alternative gravity theory in which the Ricci scalar $R$ in the Einstein-Hilbert gravitational lagrangian is replaced by a general function of $R$ and $T$, namely $f(R,T)$, with $T$ representing the trace of the energy-momentum tensor. We propose, for the first time in the literature, an exponential form for the dependence of the theory on $T$. We derive the field equations as well as the non-continuity equation and solve those to wormhole metric and energy-momentum tensor. The importance of applying alternative gravity to wormholes is that through these theories it might be possible to obtain wormhole solutions satisfying the energy conditions, departing from General Relativity well-known outcomes. In this article, we indeed show that it is possible to obtain wormhole solutions satisfying the energy conditions in the exponential $f(R,T)$ gravity. Naturally, there is still a lot to do with this model, as cosmological, galactical and stellar astrophysics applications, and the reader is strongly encouraged to do so, but, anyhow, one can see the present outcomes as a good indicative for the theory.Comment: 6 pages, 3 figures, To appear in European Physical Journal

Learning Equations for Extrapolation and Control

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.Comment: 9 pages, 9 figures, ICML 201

The simplest non-minimal matter-geometry coupling in the f(R,T)f(R,T) cosmology

The $f(R,T)$ gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar $R$ and trace of the energy-momentum tensor $T$. In this way, $f(R,T)$ models are capable of describing a non-minimal coupling between geometry (through terms in $R$) and matter (through terms in $T$). In this article we construct a cosmological model from the simplest non-minimal matter-geometry coupling within the $f(R,T)$ gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter-geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the $f(R,T)$ formalism in order to check its reliability in other fields, rather than cosmology.Comment: 8 pages (two column) 9 figure