An interferometric model is proposed to estimate the phase differences in lossless, strongly coupled biconical fiber couplers. This approximate method is simpler than the traditional s-parameter network theory-based analysis technique and minimizes the number of unknowns. The phase difference between the transmitted and coupled light fields is directly related to the field interaction and can b...

The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using semi-analytical approach. They based on partitions of the computational domain by polygonal/polyhedral subregions, where shape functions approximate local Dirichlet problems with piecewise polynomial trace data. Using this operator adaptation approach, and imposing starlike scali...

The paper reviews the history of B-spline methods for atomic structure calculations bound states. It highlights various aspects variational method, particularly with regard to orthogonality requirements, iterative self-consistent eigenvalue problem, and related sphf, dbsr-hf, spmchf programs. B-splines facilitate mapping solutions from one grid another. following describes a two-stage approach ...

Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality enc...

In this paper, we study the broadcasting performance of urban Vehicle-to-everything (V2X) communications at road intersections. such environments, dense buildings obstruct radio channel between vehicles in adjacent segments and Non-Line-Of-Sight (NLOS) signal propagation reduces received power level. Therefore, messages that originate from roads traveling a non-parallel direction usually have w...

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856–869] is an iterative method for approximately solving linear systems , with initial guess residual . employs the Arnoldi process to generate Krylov basis vectors (the columns ). It well known that this can be viewed as a factorization matrix at each iteration. Despite loss orthogonality, unit roundoff conditi...