We prove that for any definable subset $X\subset \mathbb {R}^{n}$ in a polynomially bounded o-minimal structure, with ${\rm dim}(X) \lt n$, there is finite set of regular projections (in the sense Mostowski). also give weak version this theor

the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.