A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations… (More)
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial differential equations with Dirichlet/Neumann boundary conditions. The construction is checked by evaluating several known… (More)
Super-matrix KdV and super-generalized non-linear Schrödinger equations are shown to arise from a symmetry reduction of ordinary self-dual Yang-Mills equations with supergauge groups.
Next generation implantable medical devices will have the potential to provide more precise and effective therapies through adaptive closed-loop controllers that combine sensing and stimulation across larger numbers of electrode channels. A major challenge in the design of such devices is balancing increased functionality and channel counts with the… (More)
Metamaterials, materials that are constructed with arrays of small elements have significant potential to provide material properties that are useful for electromagnetic applications but are not found in nature. Slight changes to a repeated unit cell can be used to tune the effective bulk material properties of a metamaterial, replacing the need to discover… (More)
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
This paper summarizes developments aimed at providing cheap manufacturable 5 GHz data radio front-ends for the newly created U-NII and HIPERLAN bands. The result is a set of reconfigurable modules for radio architecture experimentation and a small form factor 5 GHz radio for WLAN and link applications which is economical and manufacturable in volume. 1.… (More)