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In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of super-position and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel performs well for spin squeezing generation and generates permanent spin squeezing in the superposition of GHZ and W states.

In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new families of Schroder-type methods for multiple roots with cubic convergence. Proposed families are derived from modified Newton's method for multiple roots and one-parameter family of Schroder's method. Numerical examples are also provided to show that these new methods are competitive to other known methods for multiple roots. (Contains 2 tables.)

In modern industries, basalt and glass are the most commonly used fibers for the fabrication of various engineering components. Present work is focused on the fabrication of hybrid fiber reinforced plastic (FRP) composites, comprises of basalt and glass fibers. The aim of the work is to fabricate a composite justifying the current requirement of the era followed by the identification of the capabilities of fabricated composite by investigating its mechanical properties. Further, the machining of the fabricated composite has also been explored in order to limit the common problems in machining like fiber pull-out and delamination. From the results, it has been perceived that the fabricated composite can be machined flawlessly using laser beam machine subjected to the selection of input parameters. The proposed methodology seems helpful for researchers in fabricating the FRP composite and in identifying the range of input parameters suitable for machining. [ABSTRACT FROM AUTHOR]

This paper reveals the future prospects of quantum algorithms in high energy physics (HEP). Particle identification, knowing their properties and characteristics is a challenging problem in experimental HEP. The key technique to solve these problems is pattern recognition, which is an important application of machine learning and unconditionally used for HEP problems. To execute pattern recognition task for track and vertex reconstruction, the particle physics community vastly use statistical machine learning methods. These methods vary from detector-to-detector geometry and magnetic field used in the experiment. Here, in this paper, we deliver the future possibilities for the lucid application of quantum computation and quantum machine learning in HEP, rather than focusing on deep mathematical structures of techniques arising in this domain. [ABSTRACT FROM AUTHOR]

Quasi‐optimal error estimates are derived for the continuous‐time orthogonal spline collocation (OSC) method and also two discrete‐time OSC methods for approximating the solution of 1D parabolic singularly perturbed reaction–diffusion problems. OSC with C1 splines of degree r ≥ 3 on a Shishkin mesh is employed for the spatial discretization while the Crank–Nicolson method and the BDF2 scheme are considered for the time‐stepping. The results of numerical experiments validate the theoretical analysis and also exhibit additional quasi‐optimal results, in particular, superconvergence phenomena. [ABSTRACT FROM AUTHOR]

In this article, we study numerical approximation for a class of singularly perturbed parabolic (SPP) convection‐diffusion turning point problems. The considered SPP problem exhibits a parabolic boundary layer in the neighborhood of one of the sides of the domain. Some a priori bounds are given on the exact solution and its derivatives, which are necessary for the error analysis. A numerical scheme comprising of implicit finite difference method for time discretization on a uniform mesh and a hybrid scheme for spatial discretization on a generalized Shishkin mesh is proposed. Then Richardson extrapolation method is applied to increase the order of convergence in time direction. The resulting scheme has second‐order convergence up to a logarithmic factor in space and second‐order convergence in time. Numerical experiments are conducted to demonstrate the theoretical results and the comparative study is done with the existing schemes in literature to show better accuracy of the proposed schemes. [ABSTRACT FROM AUTHOR]

An orthogonal spline collocation method (OSCM) with C¹ splines of degree r ≤ 3 is analyzed for the numerical solution of singularly perturbed reaction diffusion problems in one dimension. The method is applied on a Shishkin mesh and quasi-optimal error estimates in weighted Hm norms for m = 1; 2 and in a discrete L²-norm are derived. These estimates are valid uniformly with respect to the perturbation parameter. The results of numerical experiments are presented for C¹ cubic splines (r = 3) and C¹ quintic splines (r = 5) to demonstrate the efficacy of the OSCM and confirm our theoretical findings. Further, quasi-optimal a priori estimates in L², L∞ and W1;∞-norms are observed in numerical computations. Finally, superconvergence of order 2r - 2 at the mesh points is observed in the approximate solution and also in its first derivative when r = 5. [ABSTRACT FROM AUTHOR]