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Factorization of Hankel operators, range inclusion of Toeplitz and Hankel operators on the vector-valued Hardy space
No full textUsing Douglas theorem on factorization and range inclusion of bounded linear operators, we give the factorization of Hankel operators, range inclusion of Hankel and Toeplitz operators defined on vector-valued Hardy spaces
Fano resonances in tilted Weyl semimetals in an oscillating quantum well
No full textConsidering the low-energy model of tilted Weyl semimetal, we study the electronic transmission through a periodically driven quantum well, oriented in the transverse direction with respect to the tilt. We adopt the formalism of Floquet scattering theory and investigate the emergence of Fano resonances as an outcome of matching between the Floquet sidebands and quasi-bound states. The Fano resonance energy changes linearly with the tilt strength suggesting the fact that tilt-mediated part of quasi-bound states energies depends on the above factor. Given a value of momentum parallel (perpendicular) to the tilt, we find that the energy gap between two Fano resonances, appearing for two adjacent values of transverse (collinear) momentum with respect to the tilt direction, is insensitive (sensitive) to the change in the tilt strength. Such a coupled (decoupled) behavior of tilt strength and the collinear (transverse) momentum can be understood from the tilt-mediated and normal parts of the quasi-bound state energies inside the potential well. We vary the other tilt parameters and chirality of the Weyl points to conclusively verify the exact form of the tilt-mediated part of the quasi-bound state energy that is the same as the tilt term in the static dispersion. The tilt orientation can significantly alter the transport in terms of evolution of Fano resoance energy with tilt momentum. We analytically find the explicit form of the bound state energy that further supports all our numerical findings. Our work paves the way to probe the tilt-mediated part of quasi-bound state energy to understand the complex interplay between the tilt and Fano resonance
Fast 3D Volumetric Image Reconstruction from 2D MRI Slices by Parallel Processing
No full textMagnetic Resonance Imaging (MRI) is a technology for non-invasive imaging of anatomical features in detail. It can help in functional analysis of organs of a specimen but it is very costly. In this work, methods for (1) virtual three-dimensional (3D) reconstruction from a single sequence of two-dimensional (2D) slices of MR images of a human spine and brain taken at a certain gap along a single axis, and (2) generation of missing inter-slice data are proposed. Our approach helps in preserving the edges, shape, and size, as well as the internal tissue structures of the object being captured. The sequence of original 2D slices along a single axis is divided into smaller equal sub-parts which are then reconstructed using edge-preserved kriging interpolation to predict the missing slice information. In order to speed up the process of interpolation, we have used parallel processing by carrying out the initial interpolation on parallel cores. From the 3D matrix thus formed, shearlet transform is applied to estimate the edges considering the 2D blocks along the Z axis, and to minimize the blurring effect using a proposed mean-median logic. Finally, for visualization, the sub-matrices are merged into a final 3D matrix. Next, the newly formed 3D matrix is split up into voxels, and the marching cubes method is applied to get the approximate 3D image for viewing. To the best of our knowledge it is a first of its kind approach based on kriging interpolation and parallel processing for 3D reconstruction from 2D slices, and approximately 98.89% accuracy is achieved with respect to similarity metrics for image comparison. The time required for reconstruction has also been reduced by approximately 70% with parallel processing even for a large input data set compared to that with single core processing
Gender peer effects in high schools: Evidence from India
No full textThis paper presents evidence of gender peer effects in high schools in India using new administrative data. Identification of gender peer effects is achieved by exploiting variation induced by idiosyncratic changes in gender composition across cohorts within schools, in addition to controlling for past scores. The proportion of female classmates in a student\u27s cohort has a sizeable positive effect on the test scores of both male and female students. We find that peer effects vary non-linearly with the proportion of female students. Finally, we provide suggestive evidence on plausible mechanisms. We show that achievement spillovers are not the main driver of positive gender peer effects. Using a supplemental dataset, we show that a greater proportion of female students leads to an improved classroom environment in the context of Indian schools
Global synchronization on time-varying higher-order structures
No full textSynchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real-world applications, the latter are not static but do evolve in time, in this work we thus discuss the impact of the time-varying nature of higher-order structures in the emergence of global synchronization. To achieve this goal, we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart-Landau nonlinear oscillator and the Lorenz chaotic oscillator
Impact of bottom explosions on wave formation in the presence of an inertial surface and wave current in a viscous fluid
No full textThis study examines the impact of a bottom explosion on wave generation in an inertial surface, considering the roles of fluid viscosity, wave current, and the nature of a slippery porous sea bottom. The Fourier and Laplace transform techniques are employed to calculate the surface elevation in terms of an infinite integral. Further, the infinite integral is evaluated asymptotically using the stationary-phase approach for larger time and distance values. The influence of viscosity, inertial surface, current, and slip parameters on wave generation is analyzed for different times and distances. The study reveals that the presence of an inertial surface lessens the amplitude of free surface elevation. Further, the free surface elevation\u27s amplitude reduces as the current speed and liquid viscosity approach closer to a small value. In the case of a slippery porous bottom, as the slip parameter increases, the free surface elevation\u27s amplitude decreases
Impact of Predator-Driven Allee and Spatiotemporal Effect on a Simple Predator-Prey Model
No full textIn this research paper, we consider a Leslie-Gower Reaction-Diffusion (RD) model with a predator-driven Allee term in the prey population. We derive conditions for the existence of nontrivial solutions, uniform boundedness, local stability at co-existing equilibrium points, and Hopf bifurcation criteria from the temporal system. We identify sufficient conditions for Turing instability with no-flux boundary condition for the spatial system. Our investigation delves into the analysis of diffusion-induced Turing instability, incorporating stability conditions for the constant steady-state in the spatial model. We also investigate the conditions for the existence and nonexistence of nonconstant steady states in the diffusion-induced model. During numerical simulations, we observe that the predator-driven Allee term is essential for the model to generate Turing structures. Our findings reveal intriguing properties within the RD system, demonstrating its ability to produce patterns within the Turing domain. The simulation confirms that cold-hot spots and stripes-like patterns (a mixture of spots and strips) arises for different strengths of the predation parameter and Allee parameter. In contrast, we observe that for the above threshold value of the Allee parameter, the above-mentioned patterns may disappear from the system. Interestingly, we also observe that the stationary system produces patterns for both large and small amplitudes of perturbation in the vicinity of the Turing boundary. Our research may contribute valuable insights into the Allee effect and enhance our understanding of predator-prey interactions in naturalistic environments
Innovation and governance
No full textInnovation is a key driver of long-term economic growth and has significantly improved living standards. Corporate innovation efforts are at the forefront of this process. We propose a two-period career concern model to better understand the factors that influence a corporation’s decision to undertake risky innovation. In this model, a corporation’s manager is influenced by the company’s corporate governance structure and the level of competition in the product market. Our research shows that strong corporate governance positively impacts a manager’s decision to innovate due to career concerns. However, we also found that firms in industries with low competition benefit more from good governance than those in highly competitive industries. This conclusion is supported by our analysis of a panel data set from the 1990s, which contains information on time-varying patent citations in the US
INVARIANT SUBSPACES OF CONTRACTIONS WITH CONSTANT CHARACTERISTIC FUNCTION
No full textWe describe all the invariant subspaces of a completely nonunitary contraction Tc with nonzero scalar constant characteristic function c, where |c| \u3c 1. Moreover, we show that Tc and restriction to its invariant subspaces are essentially normal. Using this description of Tc-invariant subspaces, we then identify the hyperinvariant subspaces