In this study, nearness near-ring, subnearness M-group and ideal are introduced. By considering operations on the set of all near left weak cosets, near-ring cosets homomorphism also presented. Moreover, some properties these structures investigated.

An explicit formula for a type of beams, which in this work are called the ``special'' hyperbolic Bessel-Gaussian (SHBG) has been derived, using method Hankel transform formulated our previous [T. Rado\ifmmode \dot{z}\else \.{z}\fi{}ycki, arXiv:2103.06988]. The fundamental properties these beams analyzed. parameters that define beam shape have identified and related to those Gaussian beam. anal...