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Small EHF satellites can significantly complement the anti-jam service provided by basic EHF MILSATCOM space segments. Mobile/survivable launch vehicles with rapid launch preparations can be utilized to responsively deploy these small satellites into high altitude elliptical or circular orbits. From such orbits, only a few satellites are needed to provide high duty cycle coverage of a critical area. The communications capabilities provided by these EHF payloads can range from low data rate services (75 to 2400 bps per channel) to high data rate links (10 Mbps or more per link) depending on the payload configuration. Through the use of EHF waveform standards, these augmentation/ restoration satellites will be compatible with existing and planned EHF terminals. Advanced technologies permit the development of the highly capable lightweight payloads required for these roles. Some of the key payload technologies include adaptive uplink antennas; high speed low power digital signal processing subsystems; lightweight frequency hopping synthesizers; and efficient solid-state transmitters.

In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not. Ph. D.

Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ℏ → 0 over the infinite time domain -∞ < t < ∞. After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propogation of a semiclassical wavepacket over the time domain -∞ < t < ∞. This result has long been known for dimension n ≥ 3, and we extend it to one and two space dimensions. Next, we present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the three-body problem over the time domain -∞ < t < ∞. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry. Ph. D.

This dissertation is devoted to investigating the time dependent neutron transport equations with reflecting boundary conditions. Two typical geometries --- slab geometry and spherical geometry --- are considered in the setting of L^p including L^1. Some aspects of the spectral properties of the transport operator A and the strongly continuous semigroup T(t) generated by A are studied. It is shown under fairly general assumptions that the accumulation points of { m Pas}(A):=sigma (A) cap { lambda :{ m Re}lambda > -lambda^{ast} }, if they exist, could only appear on the line { m Re}lambda =-lambda^{ast}, where lambda^{ast} is the essential infimum of the total collision frequency. The spectrum of T(t) outside the disk {lambda : |lambda| leq exp (-lambda^{ast} t)} consists of isolated eigenvalues of T(t) with finite algebraic multiplicity, and the accumulation points of sigma (T(t)) igcap{ lambda : |lambda| > exp (-lambda^{ast} t)}, if they exist, could only appear on the circle {lambda :|lambda| =exp (-lambda^{ast} t)}. Consequently, the asymptotic behavior of the time dependent solution is obtained. Ph. D.