These notes are based on research conducted at the University of Chicago. They represent a more self-contained version of a chapter from my dissertation [C1]. [Note added in 2006: Some of these ideas more recently appeared in [C2], [C3], and [C4].] The main result of [C1] established a normal form for a generic complex tangent of a real m-submanifold in a complex n-manifold, in the case m < n. ...

In this paper we discuss conversion methods from the conjunctive normal form (CNF) to the algebraic normal form (ANF) of a Boolean function. Whereas the reverse conversion has been studied before, the CNF to ANF conversion has been achieved predominantly via a standard method which tends to produce many polynomials of high degree. Based on a block-building mechanism, we design a new blockwise a...

Abstract We present a new method for the stable reconstruction of class binary images from small number measurements. The we consider are characteristic functions algebraic domains, that is, domains defined as zero loci bivariate polynomials, and assume to know only finite set uniform samples each image. solution such problem can be up in terms linear equations associated image moments. However...

Disjoint AND-decomposition of a boolean formula means its representation as a conjunction of two (or several) formulas having disjoint sets of variables. We show that deciding AND-decomposability is intractable in general for boolean formulas given in CNF or DNF and prove tractability of computing AND-decompositions of boolean formulas given in positive DNF, Full DNF, and ANF. The results follo...

We propose a new semantics for rewrite systems ba.~ed on interpreting rewrite rules as in­ equatioIlB between terms in an ordered algebra. In part.icular, we show thai the algebra. of normal forms in a terminating system is a uniqnely minimal covering of the term algebra. In the non-terminating ca..~e, the existence of this minimal covering is established in the comple­ tion of an ordered algeb...

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...