in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

Nodal-point and Nodal-line structures in the dispersion of electron energy bands are characterized by their high degeneracy certain corners or lines Brillouin zone (BZ). These nodal can also exist itinerant electrons magnetically ordered materials whose symmetry groups anti-unitary called magnetic space groups. In present work, we provide a complete list which host symmetry-protected nodal-poin...

The striking left-right asymmetry of visceral organs is known to depend on left- and right-side-specific cascades of gene expression during early embryogenesis. Now, developmental biologists are characterizing the earliest steps in asymmetry determination that dictate the sidedness of asymmetric gene expression. The proteins and structures involved control fascinating physiological processes, s...

An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...