Iterative technique for generating numerical on-axis holograms of an object on tilted planes using Rayleigh-Sommerfeld approximation

We present a new iterative technique based on successive field propagation using the Reyleigh-Sommerfeld (RS) approximation, to generate by computer the amplitude on-axis hologram of an object on a tilted plane. The technique was validated doing optical and computational reconstruction of the hologram.

An Iterative Technique to Solve Fuzzy Delay Integro-Differential Equations

In this exploration work, we make an assessment on the get together of nonlinear Volterra fuzzy delay integro-differential conditions, with the help of an iterative technique. The outcome is contrasted with the precise outcome with verify the legitimacy and proficiency of the method to deal with nonlinear Volterra fuzzy delay integro-differential condition. To display the suitable highlights of this proposed system, a numerical worldview is represented.

Approximating Solutions of Matrix Equations via Fixed Point Techniques

The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the setting of a partially ordered Banach space. To estimate solutions to these matrix equations, we use the Krasnosel’skiĭ iterative technique. We also discuss some useful examples to illustrate our results.

Iterative technique for a beam lying on a transversely isotropic foundation

The effect of the foundation heterogeneity on the mechanical behaviour of a beam on Vlasov soils is discussed. According to a refined Vlasov soil model, the static problem of beams lying on transversely isotropic soils can be solved by an iterative method. In this paper, based on the energy variational principle, the differential equations for beams under an axial force on refined Vlasov foundations are derived. The methods for solving the internal forces and deformations of beams lying on refined elastic foundations are given. Additionally, an equation for the attenuation parameters is also established, and the characteristic parameters of the refined model are solved by iterative technique. Numerical results show that the foundation heterogeneity have a influence on the deformations and internal forces of the beam-soil system. Moreover, relatively accurate characteristic parameters can be obtained through the iterative process. The refined Vlasov model has broad application prospects.

Criteria for the Oscillation of Solutions to Linear Second-Order Delay Differential Equation with a Damping Term

The aim of this work is to present new oscillation results for a class of second-order delay differential equations with damping term. The new criterion of oscillation depends on improving the asymptotic properties of the positive solutions of the studied equation by using an iterative technique. Our results extend some of the results recently published in the literature.

Convergence of approximate solutions for singular difference systems with maxima

In this paper, by introducing a new singular fractional difference comparison theorem, the existence of maximal and minimal quasi-solutions are proved for the singular fractional difference system with maxima combined with the method of upper and lower solutions and the monotone iterative technique. Finally, we give an example to show the validity of the established results.

Uniform Ray Description of Physical Optics Scattering by Finite Locally Periodic Metasurfaces

<div><div><div><p>This paper presents a uniform ray description of electromagnetic wave scattering by locally periodic metasurfaces of polygonal shape. The model is derived by asymptotically evaluating the critical-point contributions of a physical optics scattering integral. It is valid for metasurfaces whose bulk scattering coefficients are periodic functions of a phase parameter which, in turn, is a continuous and smooth function of surface coordinates. The scattered field is expressed in terms of reflected, transmitted and diffracted rays that do not generally obey conventional geometrical constraints (i.e., Snell’s law and the Keller cone). An iterative technique is presented to determine the locations of critical points on one or multiple interacting metasurfaces. Numerical results demonstrating the utility and accuracy of the asymptotic physical optics model are also provided.</p></div></div></div>

Uniform Ray Description of Physical Optics Scattering by Finite Locally Periodic Metasurfaces

<div><div><div><p>This paper presents a uniform ray description of electromagnetic wave scattering by locally periodic metasurfaces of polygonal shape. The model is derived by asymptotically evaluating the critical-point contributions of a physical optics scattering integral. It is valid for metasurfaces whose bulk scattering coefficients are periodic functions of a phase parameter which, in turn, is a continuous and smooth function of surface coordinates. The scattered field is expressed in terms of reflected, transmitted and diffracted rays that do not generally obey conventional geometrical constraints (i.e., Snell’s law and the Keller cone). An iterative technique is presented to determine the locations of critical points on one or multiple interacting metasurfaces. Numerical results demonstrating the utility and accuracy of the asymptotic physical optics model are also provided.</p></div></div></div>