An attempt has been made to explore the geometric effects of f(R) action on the galactic dynamics under the weak field approximation. The rotational velocity is calculated beyond the Einstein’s geometric theory of gravity. It is inspired by the cosmological geometric relation obtained in the power-law f(R) gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein–Hilbert gravity action (taking R as $$f(R)\propto R^{1+\delta }$$f(R)∝R1+δ) at the galactic scales for the explanation of the flatness paradox associated with the clustered galactic dark matter. We obtain the contribution of a dynamical f(R) cosmological background geometry on accelerating the test mass. Furthermore, the integrated effective acceleration of the test mass due to a massive spherically symmetric source in f(R) background is calculated via the study of geodesics for the suitable spacetime metric and an equation for the effective rotational velocity has been developed. We test the viability of the proposed model by tracing the motion of a test mass far from the disk of galactic matter for smaller $$\delta $$δ. The possible galactic rotational velocity curves in f(R) background are discussed for the formula obtained with $$\delta<< 1$$δ<<1. We also obtain constraints on $$\delta $$δ$$O(10^{-6})$$O(10-6) confirmed by observations.

This paper examines the effect of the quality of economic institutions on health outcomes for the E.U. countries from 2000 to 2018. Using data from the World Bank and the Fraser Institute, the paper uses fixed effects and random effects models to investigate the relationship between institutional quality and health. The results suggest that an improvement in the quality of economic institutions has a favourable effect on health. Specifically, the results highlight that an efficient legal system, a stable macroeconomic environment, and fewer regulations improve health outcomes in the E.U. countries. The paper also finds that higher per capita income, increase in education, and faster urbanization enhance health outcomes.

We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law f(R) gravity theory of the type $$f(R)\propto R^{1+\delta }$$ f ( R ) ∝ R 1 + δ with $$\delta<<1$$ δ < < 1 for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + f(R) background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in f(R) frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (because of Noether symmetry in f(R) theories) appearing in the effective f(R) rotational velocity profile of a typical galaxy with the model parameter $$\delta \approx O(10^{-6})$$ δ ≈ O ( 10 - 6 ) constrained in previous work. For instance, we work with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore their galactic features by analysing the lensing angle profiles in f(R) background. We also contrast the magnitudes of f(R) lensing angle profiles and the relevant parameters of such galaxies with the generalised pseudo-isothermal galaxy halo model and find consistency.

We explore the shifted $$f(R) (\propto R^{1+\delta })$$ f ( R ) ( ∝ R 1 + δ ) model with $${\delta }$$ δ as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and non-null) along with their conformal analog are investigated. For null geodesics, we discuss the light deflection angle, whereas, for non-null geodesics under the weak field limit, we investigate the perihelion advance of the Mercury orbit in f(R) Schwarzschild background, respectively. The extent of an additional force, appearing for non-null geodesics, depends on $$\delta $$ δ . Such phenomenological investigations allow us to strictly constrain $$\delta $$ δ to be approximately $${\mathcal {O}}(10^{-6})$$ O ( 10 - 6 ) with a difference of unity in orders at galactic and planetary scales and seem to provide a unique f(R) at local scales. Our results suggest that the present form of the model is suitable for the alternative explanation of dark matter-like effects at local scales.

Purpose The purpose of this paper is to design a efficient layout of Multistage interconnection network which has cost effective solution with high reliability and fault-tolerence capability. For parallel computation, various multistage interconnection networks (MINs) have been discussed hitherto in the literature, however, these networks always required further improvement in reliability and fault-tolerance capability. The fault-tolerance capability of the network can be achieved by increasing the number of disjoint paths as a result the reliability of the interconnection networks is also improved. Design/methodology/approach This proposed design is a modification of gamma interconnection network (GIN) and three disjoint path gamma interconnection network (3-DGIN). It has a total seven number of paths for all tag values which is uniform out of these seven paths, three paths are disjoint paths which increase the fault tolerance capability by two faults. Due to the presence of more paths than the GIN and 3-DGIN, this proposed design is more reliable. Findings In this study, a new design layout of a MIN has been proposed which provides three disjoint paths and uniformity in terms of an equal number of paths for all source-destination (S-D) pairs. The new layout contains fewer nodes as compared to GIN and 3-DGIN. This design provides a symmetrical structure, low cost, better terminal reliability and provides an equal number of paths for all tag values (|S-D|) when compared with existing MINs of this class. Originality/value A new design layout of MINs has been purposed and its two terminal reliability is calculated with the help of the reliability block diagram technique.