Search

The aim of this paper is to introduce the notion of linguistic interval-valued q-rung orthopair fuzzy set (LIVq-ROFS) as a generalization of linguistic q-rung orthopair fuzzy set. We develop some basic operations, score and accuracy functions to compare the LIVq-ROF values (LIVq-ROFVs). Based on the proposed operations a series of aggregation techniques to aggregate the LIVq-ROFVs and some of their desirable properties are discussed in detail. Moreover, a TOPSIS method is developed to solve a multi-criteria decision making (MCDM) problem under LIVq-ROFS setting. Furthermore, a MCDM approach is proposed based on the developed operators and TOPSIS method, then a practical decision making example is given in order to explain the proposed method. To illustrate to effectiveness and application of the proposed method a comparative study is also conducted.

The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

The phenomena like gravitational waves, Hawking radiation, and growth of black holes not only change the curvature of spacetime continuously but also affect the thermodynamical properties of the sources over time. The present study explores the effect of time in the thermodynamical properties of the corresponding spacetime. We define a general time conformal factor e𝜖ζ(t) in the Schwarzschild black hole spacetime, where 𝜖 is a small parameter that brings perturbation in the said spacetime. This technique re-defines the energy content of spacetime. Moreover, the effect of time is explored in the thermodynamical properties of the perturbed Schwarzschild black hole. We calculate the event horizon of the spacetime as a function of t. Then we study the effect of time in the surface gravity, pressure, volume, and Hawking temperature of the perturbed Schwarzschild black hole and analyze them graphically.

The field of point particle dynamics is correlated with the study of particle dynamics around the black hole and one can initiate the study of a more complex motion of extended/celestial bodies. In this article, we consider the study of the dynamics of the neutral/charged particles around the quantum corrected-Schwarzschild black hole and Schwarzschild black hole. We investigate Noether symmetries and their conservation laws corresponding to the quantum corrected-Schwarzschild spacetime. We also study the effect of angular momentum, quantum parameters and magnetic field on the dynamics of neutral and charged particles around the quantum corrected-Schwarzschild black hole and Schwarzschild black hole.

In this article, we study the dynamics of neutral as well as charged particle in the presence of magnetic field around Reissner-Nordstrom black hole surrounded by quintessence by taking into account Noether symmetries and conservation laws in the corresponding spacetime. Using these conservation laws, we explore the effect of angular momentum, quintessence parameter, and magnetic field graphically on the dynamics of neutral/charged particles in the context of the effective potential, effective force, and escape velocity. Additionally, we investigate the orbit stability of the said spacetime with the help of the Lyapunov exponent.

The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon like Hawking radiation, the collapse of black holes and neutron stars. It has been found that during these phenomena, energy of source (black hole and neutron stars) decreases. In this paper, we explore this loss in energy of the source by introducing a time conformal factor in the corresponding spacetime in order to get a nonstatic metric without violating its symmetry structure. This technique gives us information about the loss of momentum and energy of the source. We also consider some novel nonstatic classes of the plane-symmetric spacetime containing 10 Noether symmetries and 7 isometries.

In this paper, we explore the dynamics of neutral and charged particles in presence/absence of magnetic field around the quantum corrected-Schwarzschild black hole as well as the time conformal quantum corrected-Schwarzschild black hole. We investigate the conditions under which the particles move towards or away from the vicinity of black hole when they collide with other particles. We study the effective potential and effective force in presence/absence of magnetic field graphically. Recently many researchers took interest in point particle dynamics and one can initiate the study of a more complex motion of extended celestial bodies. A major area of interest among these important fields, is the particle motions (neutral and charged) around black hole and naked singularities. In this work we want to show that the quantum corrected-Schwarzschild black hole admits the time conformal factor e ϵ g ( t ) without violating the symmetry structure of the black hole, where ϵ is a small parameter that causes perturbation in the proposed spacetime and g ( t ) is a function of time t . The inception of time conformal factor, re-scales all the conservation laws that hold in the given spacetime. This type of study is important because it tells about the formation of gravitational waves and Hawking radiation. The study of thermal stability, horizons and energy conditions corresponding to the time conformal quantum corrected Schwarzschild spacetime is also explored. Furthermore, we analyze and compare the dynamics of charged and neutral particle around time conformal quantum corrected-Schwarzschild black hole with the time conformal Schwarzschild black hole. The effective force and effective potential with magnetic field and angular momentum are given graphically. The stability of the proposed spacetime is also discussed with the help of Lyapunov exponent.

In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

The study of particle dynamics in the vicinity of a black hole environed by dark energy and magnetic field has attracted researchers for their importance in astrophysics and cosmology. In this paper, we study the dynamics of neutral and charged particles in the vicinity of de Sitter–Schwarzschild black hole (DS–Sch-BH) surrounded by quintessence. The effect of the DS part is explored by virtue of effective potential, effective force, and escape velocity of the particle (neutral and charged) moving around DS–Sch-BH. Finally, a comparative study is also investigated.

The phenomena-like Hawking radiation, the collapse of black holes, and neutron stars decrease the curvature of spacetime continuously with the passage of time. The time conformal factor adds some curvature to nonstatic spacetime. In this article, some novel classes of nonstatic plane-symmetric spacetimes are explored by introducing a time conformal factor in the exact plane-symmetric spacetimes in such a way that their symmetric structure remains conserved. This technique re-scales the energy contents of the corresponding spacetimes, which comes with a re-scaled part in each spacetime. The invariant quantities corresponding to the Noether symmetries are also calculated.

In this article, we explore the effect of the cosmological constant ( Λ ) on the dynamics of neutral as well as charged particles in vicinity of the time conformal Schwarzschild black hole. The general time conformal term e ϵ f ( t ) is introduced in the AdS-Schwarzschild spacetime, where f(t) is an arbitrary function of time t and ϵ is a small parameter which causes perturbation in the spacetime. The corresponding Lagrangian is used in the Noether symmetry equation which gives a system of 19 partial differential equations (PDEs). The solution of the 19 PDEs give us the require time conformal AdS-Schwarzschild spacetime along with approximate Noether symmetries and conservation laws. The dynamics of neutral and charged particles are discuss over the fabric of time conformal Ads–Schwarzschild spacetime.

This research provides second-order approximate Noether symmetries of geodetic Lagrangian of time-conformal plane symmetric spacetime. A time-conformal factor is of the form e ϵ f ( t ) which perturbs the plane symmetric static spacetime, where ϵ is small a positive parameter that produces perturbation in the spacetime. By considering the perturbation up to second-order in ϵ in plane symmetric spacetime, we find the second order approximate Noether symmetries for the corresponding Lagrangian. Using Noether theorem, the corresponding second order approximate conservation laws are investigated for plane symmetric gravitational waves like spacetimes. This technique tells about the energy content of the gravitational waves.

Quantitative ultrasound (QUS) measures of bone predict fracture risk in older white women. South Asian women have low bone mineral density (BMD), perhaps related to smaller body size or vitamin D insufficiency, but it is unknown whether this is accompanied by lower QUS.The study compared QUS, BMD and vitamin D status between South Asian and white European women.Participants were 47 postmenopausal women (23 white European, 24 South Asian) aged 55-65 years. BMD was measured at the calcaneus and radius by dual X-ray absorptiometry. The QUS measurements were broadband ultrasound attenuation (BUA) at the calcaneus and speed of sound (SOS) at the calcaneus, radius and tibia. Serum 25-hydroxy vitamin D was determined in late summer.South Asian women had significantly lower serum 25-hydroxyvitamin D than white Europeans (13.0 +/- 5.1 versus 30.3 +/- 7.1 ng mL(-1); p0.001). Calcaneal BMD and BUA were 14% and 10% lower (p = 0.016 and 0.045), respectively, in South Asian women. Radial BMD, and SOS at all sites, did not differ significantly between groups.In this study, postmenopausal South Asian women living in the UK had a high prevalence of vitamin D insufficiency and lower calcaneal BMD than white European women, consistent with previous findings. Differences were detected in calcaneal BUA but not SOS. Further research is needed to evaluate fracture risk and its detection in South Asian women.