Reference [1] introduces a method for the computation of the Floquet matrix, which is a time-history solution of a periodic-coefficient system over one period. Reference [2] generalizes both first order and second order forms to the case for which all coefficients are periodic. Numerical results for rotor flap-lag response show the Sinha method to be much more efficient than conventional time-m...

Abstract This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As matter of fact, the (VFD) that has been used is in Caputo sense. The first step this constructive on construction using shifted Legendre–Laguerre polynomials unknown coefficients. second involves combination collocation method and operatio...

Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of “mixed state” for any nonlinear version of quantum theory are introduced: (i) genuine mixture corresponds to operational “mixing” of different ensembles, and (ii) a mixture described by single density matrix without having a canonical operational possibility to pick out its specific convex decompos...

In this work, the degradation of Basic Red 29 (BR29), an azo dye, was investigated using a high-frequency ultrasonic reactor (300 kHz). The influence of several parameters such as initial substrate concentration (5–200 mg L−1) , pH (3–10.1), ultrasonic power (20–80 W), and nature of the dissolved gas (Ar, air, and N2) on the degradation of BR29 was assessed. Additionally, the impact of natural ...

Algorithms based on kernel methods play a central role in statistical machine learning. At their core are a number of linear algebra operations on matrices of kernel functions which take as arguments the training and testing data. These range from the simple matrix-vector product, to more complex matrix decompositions, and iterative formulations of these. Often the algorithms scale quadraticall...

Immobilization process is to optimize the operational performance of an enzyme for industrial applications. So far different matrices have been described in the literature to improve the performance of the immobilized enzymes. With the advent of nanotechnology, the nanomaterials because of their unique physico-chemical properties constitute novel and interesting matrices for enzyme immobilizati...

The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF (2) is found to fully accommodate the algebra of 15 operators — generalized Pauli matrices — characterizing two-qubit systems. The relevant sub-configuration consists of 15 points each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the lin...

This paper proposes a trajectory planning and tracking approach for cylindrical heat exchanger process that is considered, under some assumptions, as a bilinear system. The proposed technique is based on orthogonal functions and especially the use of operational integration and product matrices. These operational tools allow the conversion of a bilinear differential state equation into an algeb...

Recent structural collapses of bridges and damaging occurred on deck and dampers of suspension bridges, are driving the development of monitoring techniques for the structural integrity assessment of primary lifelines. Structural Health Monitoring combines a variety of methods for observed dynamic systems response detection of different structural systems. Among others techniques, Operational M...