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A cosmic no-hair theorem for all initially contracting, spatially homogeneous, orthogonal Bianchi Cosmologies is derived - which shows that all such Universes asymptote to a spatially flat, isotropic Universe with the inclusion of a shear viscous stress. This establishes a new mechanism of isotropisation in a contracting Universe, which does not take recourse to an ekpyrosis-like mechanism using an effective ultra-stiff equation of state fluid, that is, one in which the pressure is much greater than the energy density., 9 pages

A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous solution of Einstein's equations and it can represent the space-averaged Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe with non-singular bounces which are quasi-isotropic. A fluid with a non-linear equation of state allows non-singular bounces. Using negative anisotropic stresses successfully isotropises this Universe and mitigates the well known Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster, going through an infinite series of different cycles separated by bounces, with a sizable fraction of cycles isotropic enough to be well approximated by a standard Friedmann-Lema\^itre-Robertson-Walker model from the radiation era onward., Comment: 5 pages, 4 figures

Signature-based authentication of human is still very popular approach. Manual checking is not always accurate and it depends on expertise. The need is an automated and accurate system for signature classification. The signatures do not necessarily comprise of well-formed letters. It can be a random combination of curves and lines. The written signature may be of variable sized, inclined in arbitrary angle or misplaced. This makes the classification task more challenging. This paper proposes an automated approach of handwritten signature classification addressing those problems. The binarized version of the input image is pre-processed in various ways to compensate translation, rotation and noise removal. The four features, which does not vary due to scaling, are selected from the pre-processed image for the classification using k-NN classifier. Overall system accuracy of the proposed approach is 92% on a dataset of 100 images.

This article calculates the magnitude of wage differentials across industries in the organized manufacturing sector of India and identifies the major determinants of wage differentiation among the industries. Using data from Annual Survey of Industries in India for the period from 2000–2001 to 2015–2016, this study shows that mean wage is less in labour-intensive industries compared to the capital-intensive industries. The results of panel regression of annual average wage on various industry-specific factors show that productivity of labour is the most important factor in wage determination, and productivity largely depends on capital–labour ratio. The other significant factors in this regard are farm size, amount of profit and proportion of casual and female workers in total employment. Important policy implication of this study is that regulatory wage fixation and wage bargaining outcomes are not as significant as productivity differentials in explaining wage gaps across industries.

We consider the robustness of small-field inflation in the presence of scalar field inhomogeneities. Previous numerical work has shown that if the scalar potential is flat only over a narrow interval, such as in commonly considered inflection-point models, even small-amplitude inhomogeneities present at the would-be onset of inflation at $\tau = \tau_i$ can disrupt the accelerated expansion. In this paper, we parametrise and evolve the inhomogeneities from an earlier time $\tau_{IC}$ at which the initial data were imprinted, and show that for a broad range of inflationary and pre-inflationary models, inflection-point inflation withstands initial inhomogeneities. We consider three classes of perturbative pre-inflationary solutions (corresponding to energetic domination by the scalar field kinetic term, a relativistic fluid, and isotropic negative curvature), and two classes of exact solutions to Einstein's equations with large inhomogeneities (corresponding to a stiff fluid with cylindrical symmetry, and anisotropic negative curvature). We derive a stability condition that depends on the Hubble scales $H(\tau_ i)$ and $H(\tau_{IC})$, and a few properties of the pre-inflationary cosmology. For initial data imprinted at the Planck scale, the absence of an inhomogeneous initial data problem for inflection-point inflation leads to a novel, lower limit on the tensor-to-scalar ratio., Comment: 31 pages, 4 figures. Changes in v2: minor clarifications, some calculations moved to an appendix. This is an author-created, un-copyedited version of an article published in JCAP. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

We study a model of a cyclic, spatially homogeneous, anisotropic mixmaster universe of Bianchi type IX 'mixmaster' universe, containing the a radiation field with non-comoving ('tilted' with respect to the tetrad frame of reference) velocities and vorticity. We employ a combination of numerical and approximate analytic methods to investigate the consequences of the second law of thermodynamics on the evolution. We model a smooth cycle-to-cycle evolution of the mixmaster universe, bouncing at a finite minimum, by the device of adding a comoving 'ghost' field with negative energy density. In the absence of a cosmological constant, an increase in entropy, injected at the start of each cycle, causes an increase in the volume maxima, increasing approach to flatness, falling velocities and vorticities, and growing anisotropy at the expansion maxima of successive cycles. We find that the velocities oscillate rapidly as they evolve and change logarithmically in time relative to the expansion volume. When the conservation of momentum and angular momentum constraints are imposed, the spatial components of these velocities fall to smaller values when the entropy density increases, and vice versa. Isotropisation is found to occur when a positive cosmological constant is added because the sequence of oscillations ends and the dynamics expand forever, evolving towards a quasi de Sitter asymptote with constant velocity amplitudes. The case of a single cycle of evolution with a negative cosmological constant added is also studied., J. D. B. is supported by the Science and Technology Facilities Council (STFC) of the United Kingdom. C. G. is supported by the Jawaharlal Nehru Memorial Trust Cambridge International Scholarship.

We investigate the behaviour of bouncing Bianchi type IX `Mixmaster' universes in general relativity. This generalises all previous studies of the cyclic behaviour of closed spatially homogeneous universes with and without entropy increase. We determine the behaviour of models containing radiation by analytic and numerical integration and show that increase of radiation entropy leads to increasing cycle size and duration. We introduce a null energy condition violating ghost field to create a smooth, non-singular bounce of finite size at the end of each cycle and compute the evolution through many cycles with and without entropy increase injected at the start of each cycle. In the presence of increasing entropy we find that the cycles grow larger and longer and the dynamics approach flatness, as in the isotropic case. However, successive cycles become increasingly anisotropic at the expansion maxima which is dominated by the general-relativistic effects of anisotropic 3-curvature. However, it becomes positive after expansion drives the dynamics close enough to isotropy for the curvature to become positive and for gravitational collapse to ensue. In the presence of a positive cosmological constant, radiation and a ghost field we show that, for a very wide range of cosmological constant values, the growing oscillations always cease and the dynamics subsequently approach those of the isotropic de Sitter universe at late times. This model is not included in the scope of earlier cosmic no-hair theorems because the 3-curvature can be positive. In the case of negative cosmological constant, radiation and an ultra-stiff field (to create non-singular bounces) we show that a sequence of chaotic oscillations also occurs, with sensitive dependence on initial conditions. In all cases, we follow the oscillatory evolution of the scale factors, the shear, and the 3-curvature from cycle to cycle., 19 pages, 27 figures

What happens to the most general closed oscillating universes in general relativity? We sketch the development of interest in cyclic universes from the early work of Friedmann and Tolman to modern variations introduced by the presence of a cosmological constant. Then we show what happens in the cyclic evolution of the most general closed anisotropic universes provided by the Mixmaster universe. We show that in the presence of entropy increase its cycles grow in size and age, increasingly approaching flatness. But these cycles also grow increasingly anisotropic at their expansion maxima. If there is a positive cosmological constant, or dark energy, present then these oscillations always end and the last cycle evolves from an anisotropic inflexion point towards a de Sitter future of everlasting expansion., Awarded Honorable Mention in the 2017 Gravity Research Foundation Essay competition; 4 pages, 6 figures

The rapid development of information and communication technologies(ICTs) and the move towards more knowledge-intensive, interdependent and internationalized societies create new challenges and opportunities for the design and delivery of educationICT is transforming the global economy and creating new networks that cross cultures as well as minimize distances opening up new horizons for progress and exchange of creativity and intercultural dialogue. The emergence of the Internet and rapid diffusion of digital platforms such as the World-Wide-Web, mobile telephony and broadband networks has had and will increasingly have radical effect on the transformation of education and training in all sectors demonstrating how pervasive ICT has become with various implications on economic growth at macro and national levels However growing digital divide in terms of access, applicability and affordability is actually leading to greater inequalities in development of not only developed and developing nations but among developing nations with spatial heterogeneity with particular reference to SAARC member nations.. Nevertheless the growing digital divide is actually leading to greater inequalities in development giving rise to paradoxical situations where those who have the greatest need of them- disadvantaged groups, rural communities, illiterate populations or even entire countries- do not have access to the tools which would enable them to become full-fledged members of the knowledge society. This is particularly true for the developing nations of South Asia particularly SAARC members which are characterised by huge pool of human capital with sharp differences at disaggregated levels (such as between the rural and urban population, skilled and unskilled workers.

It is possible to associate temperatures with the non-extremal horizons of a large class of spherically symmetric spacetimes using periodicity in the Euclidean sector and this procedure works for the de Sitter spacetime as well. But, unlike e.g., the black hole spacetimes, the de Sitter spacetime also allows a description in Friedmann coordinates. This raises the question of whether the thermality of the de Sitter horizon can be obtained, working entirely in the Friedmann coordinates, without reference to the static coordinates or using the symmetries of de Sitter spacetime. We discuss several aspects of this issue for de Sitter and approximately de Sitter spacetimes, in the Friedmann coordinates (with a time-dependent background and the associated ambiguities in defining the vacuum states). The different choices for the vacuum states, behaviour of the mode functions and the detector response are studied in both (1+1) and (1+3) dimensions. We compare and contrast the differences brought about by the different choices. In the last part of the paper, we also describe a general procedure for studying quantum field theory in spacetimes which are approximately de Sitter and, as an example, derive the corrections to thermal spectrum due to the presence of pressure-free matter., Comment: 26 pages

Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a fluctuating thermodynamic description of self propelled particles using simple models of velocity dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation dissipation relation, characterizing the linear response at non-equilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot model of self propelled particles., 8 pages, version accepted in Phys. Rev. E

Using the Newman–Janis method to construct the axion–dilaton coupled charged rotating black holes, we show that the energy extraction from such black holes via the Penrose process takes place from the axion/Kalb–Ramond field energy responsible for rendering the angular momentum to the black hole. Determining the explicit form for the Kalb–Ramond field strength, which is argued to be equivalent to spacetime torsion, we demonstrate that at the end of the energy extraction process, the spacetime becomes torsion free with a spherically symmetric non-rotating black hole remnant. In this context, applications to physical phenomena, such as the emission of neutral particles in astrophysical jets, are also discussed. It is seen that the infalling matter gains energy from the rotation of the black hole, or equivalently from the axion field, and that it is ejected as a highly collimated astrophysical jet.