Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces

We study the local convergence analysis of a fifth order method and its multi-step version in Banach spaces. The hypotheses used are based on the first Fréchet-derivative only. The new approach provides a computable radius of convergence, error bounds on the distances involved, and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives, which may not exist or may be very expensive or impossible to compute. Numerical examples are provided to validate the theoretical results. Convergence domains of the methods are also checked through complex geometry shown by drawing basins of attraction. The boundaries of the basins show fractal-like shapes through which the basins are symmetric.

A STUDY ON INTERNET DEPENDENCY, SOCIAL ISOLATION AND PERSONALITY USING MAHALANOBIS DISTANCE

With the advent of the globalised 21st century, hominids have metamorphosed to the credence and dependence on the internet. From education to shopping, there is a cumbersome dependence on this media. Yet, this rapid chrysalis of the Internet is unfortunate enough on the other side, since it bears a large impact on the human personality, coercing people to isolate from the social world. The present study accords with comparison among different psychological aspects of postgraduate level students with the help of Mahalanobis Distance. Different variables viz. Internet Dependency, Social Isolation and five different factors of Personality are considered for this study. Different groups like science and arts, male and female are formed for this study. Seven dependent variables like Internet Dependency, Social Isolation, Extraversion, Agreeableness, Conscientiousness, Neuroticism and Openness are taken as a branch for two dichotomous independent variables sex (male and female) and stream (arts and science) and Mahalanobis Distances are measured. It can be wrapped up on this note with a conclusion that there are no significant differences in dynamical nature between male and female students and arts and science students. KEYWORDS: Internet Dependency, Social Isolation, PG Level Students and Mahalanobis Distance.

Dynamical tadpoles and Weak Gravity Constraints

Non-supersymmetric string models are plagued with tadpoles for dynamical fields, which signal uncanceled forces sourced by the vacuum. We argue that in certain cases, uncanceled dynamical tadpoles can lead to inconsistencies with quantum gravity, via violation of swampland constraints. We describe an explicit realization in a supersymmetric toroidal Z2 × Z2 orientifold with D7-branes, where the dynamical tadpole generated by displacement of the D7-branes off its minimum leads to violation of the axion Weak Gravity Conjecture. In these examples, cancellation of dynamical tadpoles provides consistency conditions for the configuration, of dynamical nature (as opposed to the topological conditions of topological tadpoles, such as RR tadpole cancellation in compact spaces). We show that this approach provides a re-derivation of the Z-minimization criterion for AdS vacua giving the gravitational dual of a-maximization in 4d $$ \mathcal{N} $$ N = 1 toric quiver SCFTs.

Structural plasticity of the selectivity filter in a nonselective ion channel

The sodium potassium ion channel (NaK) is a nonselective ion channel that conducts both sodium and potassium across the cellular membrane. A new crystallographic structure of NaK reveals conformational differences in the residues that make up the selectivity filter between the four subunits that form the ion channel and the inner helix of the ion channel. The crystallographic structure also identifies a side-entry, ion-conduction pathway for Na+ permeation that is unique to NaK. NMR studies and molecular dynamics simulations confirmed the dynamical nature of the top part of the selectivity filter and the inner helix in NaK as also observed in the crystal structure. Taken together, these results indicate that the structural plasticity of the selectivity filter combined with the dynamics of the inner helix of NaK are vital for the efficient conduction of different ions through the non-selective ion channel of NaK.

Charney Problem with a Generic Stratosphere

This paper reports a comprehensive instability analysis of a 3D Charney-like model with an observationally compatible generic stratosphere. It is found that the values of a single non-dimensional parameter (detailed definition in text), in conjunction with representative values of four other non-dimensional parameters, would dictate the existence of multiple branches of unstable modes as a function of the zonal wavenumber. Prototype Charney mode, Green mode, and two additional structurally distinct modes (Charney+ Mode and Tropopause Mode) are identified. The latter result from the additional strong influence of the tropopause. The dynamical nature of all modes is delineated in terms of their meridional fluxes of heat and potential-vorticity. The three-dimensional structure of the ageostrophic velocity field in each mode is presented to identify its potential of inducing frontogenesis. Optimal-mode analyses are also performed to ascertain how a disturbance with a predisposed structure would explosively develop towards each type of normal mode. In view of the pivotal role of Γ in baroclinic instability and for historical reason, we name it the Charney Number. It is most instructive to think of Γ as a ratio of the meridional gradient of PV associated with the basic flow in the troposphere, , to that associated with the earth’s rotation, β.

Dissecting the role of glutamine in seeding peptide aggregation

ABSTRACTPoly glutamine and glutamine-rich peptides play a central role in a plethora of pathological aggregation events. However, biophysical characterization of soluble oligomers —the most toxic species involved in these processes— remains elusive due to their structural heterogeneity and dynamical nature. Here, we exploit the high spatio-temporal resolution of simulations as a computational microscope to characterize the aggregation propensity and morphology of a series of polyglutamine and glutamine-rich peptides. Comparative analysis of ab-initio aggregation pinpointed a double role for glutamines. In the first phase, glutamines mediate seeding by pairing monomeric peptides, which serve as primers for higher-order nucleation. According to the glutamine content, these low molecular-weight oligomers may then proceed to create larger aggregates. Once within the aggregates, buried glutamines continue to play a role in their maturation by optimizing solvent-protected hydrogen bonds networks.TOC / Abstract Figure

Constraints on the electron-to-proton mass ratio variation at the epoch of reionization

ABSTRACT Far-infrared fine-structure transitions of [C i] and [C ii] and rotational transitions of CO are used to probe hypothetical variations of the electron-to-proton mass ratio μ = me/mp at the epoch of reionization (z > 6). A constraint on Δμ/μ = (μobs − μlab)/μlab = (0.7 ± 1.2) × 10−5 (1σ) obtained at $\bar{z} = 6.31$ is the most stringent up-to-date limit on the variation of μ at such high redshift. For all available estimates of Δμ/μ ranging between z = 0 and z ∼ 1100, the epoch of recombination, a regression curve Δμ/μ = kμ(1 + z)p, with kμ = (1.6 ± 0.3) × 10−8 and p = 2.00 ± 0.03, is deduced. If confirmed, this would imply a dynamical nature of dark matter/dark energy.

Vibration Analysis and Control of Locomotive System

Vibration is an undesirable phenomenon of ground vehicles like locomotives and vibration control of vehicle suspension system is an active subject of research. The main aim of the present work is to modeling and analysis of locomotive system. The simplified equations for dynamical locomotive are firstly established. Then the dynamical nature of the locomotive without control is investigated, and also active control suspension and passive control suspension are compare and discussed. The obtained simulation shows that suspension of the locomotive with feedback control could decrease the locomotive vibration. According to the above control strategy along with angular acceleration it also reduces the possibility of vibration of the locomotive body, to improves the stability of vehicle operation.

Dissipative collapse of a Karmarkar star

In this paper, we employ the Karmarkar condition to model a spherically symmetric radiating star undergoing dissipative gravitational collapse within the framework of classical general relativity. The collapse ensues from an initial static core satisfying the Karmarkar condition in isotropic coordinates and proceeds nonadiabatically by emitting energy in the form of a radial heat flux to the exterior Vaidya spacetime. We show that the dynamical nature of the collapse is sensitive to the initial static configuration that inherently links the embedding to the final remnant. Our model considered several physical tests on how an initially static stellar structure onset to a radiative collapse.

Complex Dynamic Behavior of a Discrete Prey–Predator–Scavenger Model with Fractional Order

This present work, we discuss the complex dynamical nature of the three species prey–predator system in presence of scavenger with fractional order. A discretization process is applied to obtain its discrete version and the impact of the scavenger on the ecosystem is discussed. Firstly, existence and local stability of the equilibria state of the model are addressed. The presences of Flip bifurcation and Neimark-Sacker bifurcation around boundary and coexistence equilibrium states are studied by using bifurcation theory. The trajectories and phase plane diagrams are plotted for biologically meaningful sets of parameter values. Numerical simulations for the effect of step size and fractional order parameters of the system are performed, on the first part to demonstrate the analytical results and on the second part revealing new motivating the dynamics behaviors of the scavenger model including period-doubling cascades (flip), periods—2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24 and 32 orbits, invariant cycles, a chaotic attractors, and the rich dynamic behaviors of the discretized model is exhibited.