Algebraic transformations of a complex variable realized by linkages

Algebraic Solving of Complex Interval Linear Systems by Limiting ‎Factors‎

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...

Planar Linkages and Algebraic Sets

An abstract linkage is a one dimensional simplicial complex L with a positive number `(vw) assigned to each edge vw. A planar realization of an abstract linkage (L, `) is a mapping φ from the vertices of L to C so that |φ(v) − φ(w)| = `(vw) for all edges vw. We will investigate the topology of the space of planar realizations of linkages. You may think of an abstract linkage as an ideal mechani...

Scalable Numerical Queries by Algebraic Inequality Transformations

To enable historical analyses of logged data streams by SQL queries, the Stream Log Analysis System (SLAS) bulk loads data streams derived from sensor readings into a relational database system. SQL queries over such log data often involve numerical conditions containing inequalities, e.g. to find suspected deviations from normal behavior based on some function over measured sensor values. Howe...

Algebraic Transformations Ofpolynomial Equations

Linear Algebraic Transformations of theBidomain

In this paper we give a mathematical framework for the treatment of the bidomain equations used to model propagation in cardiac tissue. We show how previous work ts into this framework and discuss the implications of various linear transformations of the equations on the numerical methods of solution.