K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

A comprehensive comparison between generalized incidence calculus and Dempster-Shafer theory of evidence.

Dealing with uncertainty problems in intelligent systems has attracted a lot of attention in the AI community. Quite a few techniques have been proposed. Among them, the Dempster-Shafer theory of evidence (DS theory) has been widely appreciated. In DS theory, Dempster's combination rule plays a major role. However, it has been pointed out that the application domains of the rule are rather limited and the application of the theory sometimes gives unexpected results. We have previously explored the problem with Dempster's combination rule and proposed an alternative combination mechanism in generalized incidence calculus. In this paper we give a comprehensive comparison between generalized incidence calculus and the Dempster-Shafer theory of evidence. We first prove that these two theories have the same ability in representing evidence and combining DS-independent evidence. We then show that the new approach can deal with some dependent situations while Dempster's combination rule cannot. Various examples in the paper show the ways of using generalized incidence calculus in expert systems.

Electro-thermal theory of intermodulation distortion in lossy microwave components

An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz.