Fisher information for optimal planning of X-ray diffraction experiments

Fisher information is a powerful mathematical tool suitable for quantification of data `informativity' and optimization of the experimental setup and measurement conditions. Here, it is applied to X-ray diffraction and an informational approach to choosing the optimal measurement configuration is proposed. The core idea is maximization of the information which can be extracted from the measured data set by the selected analysis technique, over the sets of accessible reflections and measurement geometries. The developed approach is applied to high-resolution X-ray diffraction measurements and microstructure analysis of multilayer samples, and its efficiency and consistency are demonstrated with the results of more straightforward Monte Carlo simulations.

A random signal generator by using analog electronics

The describing function theory is a powerful mathematical tool to predict oscillations in non-linear dynamical systems. This theory is here invoked to design a random signal generator and realized by using analog electronic elements. Then, and according to experimental results, histograms of the resultant signal are shown along with the generated signal in the time domain. Finally, the proposed electronic circuit is simple and cheap to construct.

Denoising of MST RADAR Signal usingCWT and Overlapping Group Shrinkage

Existing algorithmsare generally denouncing the existence of clusters with large amplitude coefficients. The L1 norm as well as other distinct models of sparsity does not attract a cluster tendency (group sparsity). In the light of a minimisation of convex cost work fusing the blended norm, this work introduces the technique "overlapping group shrinking." The groups are completely overlapping in order to abstain from blocking relics. A basic minimization calculation, in light of progressive replacement, is inferred. A straightforward strategy for setting the regularization boundary, in view of constricting the noise to a predefined level, is portrayed in detail by combining OGS with one of the most powerful mathematical tool wavelet transforms. In fact, the CWT coefficients are processed by OGS to produce a noise-free signal. The CWT coefficients are also processed.The proposed approach is represented on MST RADAR signals, the denoised signals delivered by CWT combined with OGS are liberated from noise.

Denoising of MST RADAR Signal usingCWT and Overlapping Group Shrinkage

Existing algorithmsare generally denouncing the existence of clusters with large amplitude coefficients. The L1 norm as well as other distinct models of sparsity does not attract a cluster tendency (group sparsity). In the light of a minimisation of convex cost work fusing the blended norm, this work introduces the technique "overlapping group shrinking." The groups are completely overlapping in order to abstain from blocking relics. A basic minimization calculation, in light of progressive replacement, is inferred. A straightforward strategy for setting the regularization boundary, in view of constricting the noise to a predefined level, is portrayed in detail by combining OGS with one of the most powerful mathematical tool wavelet transforms. In fact, the CWT coefficients are processed by OGS to produce a noise-free signal. The CWT coefficients are also processed.The proposed approach is represented on MST RADAR signals, the denoised signals delivered by CWT combined with OGS are liberated from noise.

Influence of Noise Channel in Quantum One Time Password Authentication

This paper presents an overview of quantum errors and noise channels, their mathematical modeling and its implementation in quantum one time password (QOTP) based user authentication. Quantum noise plays a pivotal role in understanding quantum information theory which is important to build up quantum communication theory. The Kraus operators provide a powerful mathematical tool in understanding and modeling various quantum channels. Use of QOTP provides an impressive method of carrying out user authentication involving quantum operations based on user biometrics. However, the efficiency of this method can be better envisaged by incorporating noise models during qubit transmission.

New solitary Solution for the Kudryashov-Sinelshchikov (KS) equation by Modern Extension of the Hyperbolic Method

In the present paper, we apply the modern extension of the hyperbolic tanh function method of nonlinear partial differential equations (NLPDEs) of Kudryashov - Sinelshchikov (KS) equation for obtaining exact and solitary traveling wave solutions. Through our solutions, we gain various functions, such as, hyperbolic, trigonometric and rational functions. Additionally, we support our results by comparisons with other methods and painting 3D graphics of the exact solutions. It is shown that our method provides a powerful mathematical tool to find exact solutions for many other nonlinear equations in applied mathematics http://dx.doi.org/10.25130/tjps.25.2020.039

A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin–Huxley models

Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin–Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

Symmetry reduction a promising method for heat conduction equations

Though there are many approximate methods, e. g., the variational iteration method and the homotopy perturbation, for non-linear heat conduction equations, exact solutions are needed in optimizing the heat problems. Here we show that the Lie symmetry and the similarity reduction provide a powerful mathematical tool to searching for the needed exact solutions. Lie algorithm is used to obtain the symmetry of the heat conduction equations and wave equations, then the studied equations are reduced by the similarity reduction method.

Approximate analytic solutions of multi-dimensional fractional heat-like models with variable coefficients

In this work, the fractional power series method is applied to solve the 2-D and 3-D fractional heat-like models with variable coefficients. The fractional derivatives are described in the Liouville-Caputo sense. The analytical approximate solutions and exact solutions for the 2-D and 3-D fractional heat-like models with variable coefficients are obtained. It is shown that the proposed method provides a very effective, convenient and powerful mathematical tool for solving fractional differential equations in mathematical physics.

Applications of modified mathematical method on some nonlinear water wave dynamical models

The extended simple equation method is applied to construct solitary wave solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony (KP-BBM), Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM), Breaking soliton (BS) and (2 + 1) Maccari system waves system of equations. These models have prevalent usage in modern science. This technique can also be functional to solve different kinds of nonlinear evolution problems in contemporary areas of research. It is an effective and powerful mathematical tool in finding solitary wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics.