###
*Using* *Matrix* *Analysis* to *Achieve* *Traction*, *Coherence*, *Progression* and *Closure* in *Problem-Solution* *Oriented* *Research*

, 2011

"... Abstract In this contribution we propose the use of two types of matrices as conceptual scaffolding at the beginning of a problem-solution oriented research project when solutions to problems under investigation are finite while ignorance about them is more or less infinite. The first type of matri ..."

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Abstract In this contribution we propose the

*use*of two types of matrices as conceptual scaffolding at the beginning of a*problem-solution**oriented**research*project when*solutions*to*problems*under investigation are finite while ignorance about them is more or less infinite. The first type### INSTITUT DE ROB `OTICA I INFORM `ATICA INDUSTRIAL- PREPRINT 1 A Branch-and-Prune Solver for Distance Constraints

"... Abstract — Given some geometric elements such as points and lines in , subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such as the position ..."

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as the position

*analysis*of serial and parallel manipulators) and CAD/CAM (such as the interactive placement of objects) can be formulated in this way. The strategy herein proposed consists in looking for some of the a priori unknown distances, whose derivation permits solving the*problem*rather trivially### Downloaded from

"... The kinematic analyses, of manipulators and other robotic devices composed of mechanical links, usually depend on the solution of sets of nonlinear equations. There are a variety of both numerical and algebraic techniques available to solve such systems of equations and to give bounds on the number ..."

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of such systems are reviewed, and the three most

*useful**solution*techniques are summarized. The*solution*techniques are polynomial continuation, Gröbner bases, and elimination. We then discuss the results that have been obtained with these techniques in the*solution*of two basic*problems*, namely, the inverse### Akademisk avhandling för teknisk doktorsexamen vid

, 1994

"... mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group ..."

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mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.

### Volume I: Computer Science and Software Engineering

, 2013

"... Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations in Sc ..."

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Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations in Sciences and

### 05 SIMULTANEOUS CLASSICAL-QUANTUM CAPACITIES OF QUANTUM MULTIPLE ACCESS CHANNELS

, 2005

"... ar ..."

### ALGEBRAIC ALGORITHMS1

, 2012

"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up- ..."

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This is a preliminary version of a Chapter on Algebraic Algorithms in the up-