In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using operator-theoretical formulation, transfer the to operator in appropriate Hilbert space. It is proved that self-adjoint. We also give asymptotic formulas of eigenvalues problem. Moreover, Green’s function discussed.

For the multicast rearrangeable 3-stage Clos networks where input crossbars do not have fan-out capability, Kirkpatrick, Klawe, and Pippenger gave a sufficient condition and also a necessary condition which differs from the sufficient condition by a factor of 2. In this paper, we first tighten their conditions. Then we propose a new necessary condition based on the affine plane such that the ne...

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying the theorem of implicit function in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for existence of p...

It well known that the Pontryagin maximum principle is a necessary optimality condition for control problems. For linear control problems, it is also a sufficient condition, but for a nonlinear control problems in common form, it is not. We found a class of nonlinear control problems for which the Pontryagin maximum principle is also a sufficient optimality condition. This is a class of problem...