Traditional binary component models do not support the application-speci c customization of components at integration-time . This problem cannot be solved by introducing new component languages, because it is rooted in the properties of executable, binary code and not in the implementation language of the component. In this paper we suggest using \open components" instead of binary component mo...

The equation of motion a microparticle in various force fields is the Schr¨odinger wave equation.Many questions quantum mechanics, particular thermal radiation electromagneticwaves, lead to problem separability singular differential operators. One such operator isthe above Schr?dinger operator. In this paper, named studied by methods offunctional analysis. Found sufficient conditions for existe...

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

This paper concerns the Schrr odinger operator ?+V (x) in R d ; d 3, with periodic potential V. Under the assumption V 2 L d=2 loc (R d), it is shown that the spectrum of ?+V (x) is absolutely continuous. The condition on the potential V is optimal in the context of L p spaces.

The one-dimensional Schrr odinger equation is considered when the potential and its rst moment are absolutely integrable. The transmission coeecient vanishes at zero energy in the generic case, and it never vanishes in the exceptional case. It is shown that any nontrivial exceptional potential can always be fragmented into two generic potentials. Furthermore, any nontrivial potential, generic o...