Based on a proven exact method to solve the forward kinematics problem , this article investigates the forward kinematics problem formulation specifically applied to planar parallel manipulators. This first part focuses on the position-based equation systems. The majority of planar tripods can modeled by the 3-RPR parallel manipulator. This manipulator is a tripod constituted by a fixed base an...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

cozero maps are generalized forms of cozero elements. two particular cases of cozero maps, slim and regular cozero maps, are significant. in this paper we present methods to construct slim and regular cozero maps from a given  cozero map. the construction of the slim and the regular cozero map from a cozero map are called slimming and regularization of the cozero map, respectively. also, we pro...

the operations in the set of fuzzy numbers are usually obtained bythe zadeh extension principle. but these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. in fact the zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

Gröbner bases constitute an important tool for solving algebraic systems of equations, and their computation is often the hard part of the resolution. This thesis is devoted to the complexity analysis of Gröbner basis computations for overdetermined algebraic systems (the number m of equations is greater than the number n of variables). In the generic (”random”) case, tools exist to analyze the...

By building on a method introduced by Kashiwara (Invent. Math. 38 (1976/77), 33–53) and refined Lichtin (Ark. Mat. 27 (1989), 283–304), we give upper bounds for the roots of certain $b$-functions associated to regular function $f$ in terms log resolution singularities. As applications, recover with more elementary methods result Budur Saito (J. Algebraic Geom. 14 (2005), 269–282) describing mul...

The field of proof complexity aims at characterizing which statements have short proofs in a given formal proof system. This thesis is a contribution to proof complexity broadly construed as the field that studies the sizes of structured or symbolic proofs. Our focus will be on the development and complexity-theoretic study of new frameworks, mainly of an algebraic nature, for providing, among ...

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra to geometr...