Abstract-A half-range orthogonality theorem concerning the established elementary solutions of the two-group neutron transport equation for isotropic scattering and plane geometry is proved. The orthogonality relations are based on a Chandrasekhar-type H-matrix, and all necessary normalization integrals are evaluated so that the desired expansion coefficients may be expressed concisely in terms...

Annotated translation of Parastrophic-orthogonal quasigroups, Acad. Nauk Moldav. SSR, Inst. Mat.s Vychisl. Tsentrom, Kishinev, 1983, prepared by A.D.Keedwell and P.Syrbu based on the original Russian and on an earlier English translation supplied to the rst author by Belousov himself. The notion of orthogonality plays an important role in the theory of Latin squares, and consequently also in th...

Wireless digital communication networks are rapidly expanding resulting in a demand for reliable and high spectral efficiency systems. Multi-Carrier Code Division Multiple Access (MC-CDMA) has emerged recently as a promising candidate for the next generation broad-band mobile networks. Also it was found recently that Radon-discrete wavelet transform (DWT) based Orthogonal Frequency Division Mul...

Abstract. The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partially discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain i...

Orthogonality plays a fundamental role in various mathematical theorems and in physics. The orthogonal eigenfunctions that represent the intrinsic motions of various physical systems can also be regarded as transverse wave modes in a straight waveguide. Because of their orthogonality, these modes propagate independently, without mutual interference. When the wall separation fluctuates, the form...

We provide a few natural applications of the analytic newvectors, initiated in \cite{JN} arXiv:1911.01880, to some questions automorphic forms for $\mathrm{PGL}_n(\mathbb{Z})$ with $n\ge 2$, archimedean conductor aspect. prove an orthogonality result Fourier coefficients, density estimate non-tempered forms, equidistribution Satake parameters respect Sato--Tate measure, and second moment centra...