It is shown that a squared Laguerre-Gaussian (LG) vortex beam Fourier-invariant and retains its structure at the focus of spherical lens. In Fresnel diffraction zone, such transformed into superposition conventional LG beams, number which equal to rings in beam. If there only one ring, then structurally stable. A more general beam, “product” two also considered. Such will be if beams same. The ...

This paper investigates static wormhole solutions through Noether symmetry approach in the context of energy–momentum squared gravity. newly developed proposal resolves singularity big bang and yields feasible cosmological results early times. We consider particular model this theory to establish generators corresponding conserved quantities. For constant variable red-shift functions, we examin...

Let $$G = K_{n_1,n_2,\cdots ,n_t}$$ be a complete t-partite graph on $$n=\sum _{i=1}^t n_i$$ vertices. The distance between vertices i and j in G, denoted by $$d_{ij}$$ is defined to the length of shortest path j. squared matrix $$\Delta (G)$$ G $$n\times n$$ with $$(i,j)^{th}$$ entry equal 0 if $$i j$$ $$d_{ij}^2$$ \ne . We define energy $$E_{\Delta }(G)$$ sum absolute values its eigenvalues. ...