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A heterogeneous and magnetically recyclable Ni–chitosan nanocatalyst was synthesized and thoroughly characterized by powder Fourier-transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD) analysis, scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), energy-dispersive X-ray (EDX) spectroscopy, etc. It was effectively utilized in the eco-friendly synthesis of new C5–C6-unsubstituted 1,4-DHPs under ultrasonic irradiation. The important focus of the methodology was to develop an environmentally friendly protocol with a short reaction time and a simple reaction procedure. The other advantages of this protocol are a wide substrate scope, a very good product yield, the use of an eco-friendly solvent and a recyclable nanocatalyst, as well as reaction at room temperature.

The Lotka-Volterra model of competition has been studied by numerical simulations using the Runge-Kutta-Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The transient behaviours associated with reaching the stable fixed point are studied systematically. It is observed that the time of reaching the stable fixed point in any one of the basins of attraction, depends strongly on the initial distance from the separatrix. As the initial point approached the separatrix, this time was found to diverge logarithmically. The divergence of the time, required to reach the stable fixed point, indicates the critical slowing down near the critical point in equilibrium phase transition. A metastable behaviour was also observed near the saddle fixed point before reaching the stable fixed point.

Flat, non-dispersive bands and topological phase transition in multiple Su-Schrieffer-Heeger (SSH) chains, cross-linked via periodically arranged nodal points are explored within a tight binding framework. We give analytic prescription, based on a real space decimation scheme, that extracts the energy eigenvalues corresponding to the flat bands along with their degeneracy. The topological phase transition is confirmed through the existence of quantized Zak phase for all the Bloch bands, and the edge states that are protected by chiral symmetry, consistent with the bulk-boundary correspondence. In addition to the edge states, the entangled systems are shown to give rise to clusters of localized eigenstates in the bulk of the system, in contrast to a purely one dimensional SSH system.

In modern sciences and technologies, images gain much broader scopes due to the ever growing importance of scientific visualization (of often large-scale complex scientific/experimental data) like microarray data in genetic research, or real-time multi-asset portfolio trading in finance etc. In this paper, a proposal has been presented to implement a Graphical User Interface (GUI) consisting of various MATLAB functions related to image processing and using the same to create a basic image processing editor having different features like, viewing the red, green and blue components of a color image separately, color detection and various other features like noise addition and removal, edge detection, cropping, resizing, rotation, histogram adjust, brightness control that is used in a basic image editor along with object detection and tracking. This has been further extended to provide reliable and a more natural technique for the user to navigate a robot in the natural environment using gestures based on color tracking. Additionally, Voice control technique has been employed to navigate the robot in various directions in the Cartesian plane employing normal Speech recognition techniques available in Microsoft Visual Basic.