boron nitride semiconducting zigzag swcnt, $b_{cb}$$n_{cn}$$c_{1-cb-cn}$, as a potential candidate for making nanoelectronic devices was examined. in contrast to the previous dft calculations, wherein just one boron and nitrogen doping configuration have been considered, here for the average over all possible configurations, density of states (dos) was calculated in terms of boron and nitrogen concentrations. it was shown that semiconducting average gap, $e_{g}$, could be controlled by doping nitrogen and boron. but in contrast to many-body techniques where gap edge in the average dos is sharp, the gap edge is smeared and impurity states appear in the swcnt semiconducting gap. for each boron and nitrogen concentrations, also, exact magnitude of the energy gap, $e_{g}$, was calculated. all bn nanotubes are semiconductor nanostructures regardless of diameter or chirality, in contrast to the carbon nanotubes that have both metallic and semiconducting features. in this case, the electronic properties of defected bnnts for spin-up and spin-down electrons were explored. we have looked into two types of defects, vacancy and substitution of carbon and oxygen by boron or nitrogen. the formation energy calculation reveals that for both vacancies defected zigzag and armchair bnnts, the probability of the nitrogen vacancy case is higher than that of the boron one. also in the carbon doping process of bnnts, the substitution of boron by carbon is more possible with respect to nitrogen by carbon. in the oxygen doping substitution process, substitution of boron by oxygen is less favorable than nitrogen by oxygen. for the higher-probability cases the spin-up and spin-down band structures show different features. for the first and second cases, the spin-up band structure shows a n-type semiconductor, while the spin-down band structure illustrates a wide band gap semiconductor. but for the oxygen-doped bnnts case, the spin-up band structure shows a wide band gap semiconductor, while the spin-down band structure illustrates a n-type semiconductor. all defected bnnts have a 1.0 $mu_{b}$ total magnetic moment. like bnnts, gannts, another wide band gap nanostructures, are of interest. structure and electronic properties of gan nanotubes (gannts) were studied in our work. the optimized structures (bond-lengths and angles between them) of zigzag gannts (n, 0) and armchair gannts (n, n) ($4 < n < 11$) were calculated by full optimization. the difference between nitrogen ring diameter and gallium ring diameter (buckling distance) and semiconducting energy gap in term of diameter for zigzag and armchair gannts have also been calculated. we observed that buckling distance decreases by increasing nanotube diameter. furthermore, we have examined the effects of nitrogen and gallium vacancies on structure and electronic properties of zigzag gannt (5, 0) using spin dependent density functional theory. by calculating the formation energy, we determined that n vacancy in gannt (5, 0) is more favorable than ga vacancy. the nitrogen vacancy in zigzag gannt induces a 1.0 $mu_{b}$ magnetization and makes a polarized structure. we realized that in polarized gannt a flat band near the fermi energy splits to occupied spin up and unoccupied spin down levels. finally, the electronic properties of dwcnts were investigated. the dwcnts were separated into four categories wherein the inner–outer nanotubes are metal–metal, metal–semiconductor, semiconductor–metal and semiconductor–semiconductor single-wall nanotubes. the band structure of dwcnts, the local density of states of the inner and outer nanotubes, and the total density of states were calculated. we obtained that for the metal–metal dwcnts, the inner and outer nanotubes remain metallic for different distances between the walls, while for the metal–semiconductor dwcnts, decreasing the distance between the walls leads to a phase transition in which both nanotubes become metallic. in the case of semiconductor–metal dwcnts, it is found that at some distance the inner wall becomes metallic, while the outer wall becomes a semiconductor, and if the distance is decreased, both walls become metallic. finally, in the semiconductor–semiconductor dwcnts, if the two walls are far from each other, then the whole dwcnt and both walls remain semiconducting. by decreasing the wall distance, first the inner, and then the outer, nanotube becomes metallic.