A mathematical model for free-form solid modelling was presented in previous published works. The key aspects of this model are the decomposition of the volume occupied by the solid into non-disjoint cells, and the representation of the solid as an algebraic sum of these cells. Here we apply this scheme to represent CSG solids built by combining free-form solids in boolean operations. As a proo...

This paper suggests a closed-form solution of particular case of an algebraic Riccati equation and its application example to optimal and smooth motion planning for a given linear quadratic performance index. Actually, the algebraic Riccati equation can be changed into Moser-Veselov equation by deriving both symmetric and skew-symmetric conditions from an algebraic Riccati equation itself. Also...

Complex sfotware systems typically involve features like time, concurrency and probability, and probabilistic computations are playing an increasing role. However it is currently challenging to formalize languages incorporating all those features. Recently the language PTSC has been proposed to integrate probability and time with shared-variable concurrency [56, 59], where the operational seman...

This article introduces the concept of isosingular sets, which are irreducible algebraic subsets of the set of solutions to a system of polynomial equations that share a common singularity structure. The definition of these sets depends on deflation, a procedure that uses differentiation to regularize solutions. A weak form of deflation has proven useful in regularizing algebraic sets, making t...

Probabilistic inference in many real-world problems requires graphical models with deterministic algebraic constraints between random variables (e.g., Newtonian mechanics, Pascal’s law, Ohm’s law) that are known to be problematic for many inference methods such as Monte Carlo sampling. Fortunately, when such constraints are invertible, the model can be collapsed and the constraints eliminated t...

We study the electromagnetic form factors of the nucleon in a collective model of baryons. In an algebraic approach to hadron structure, we derive closed expressions for both elastic and transition form factors, and consequently for the helicity amplitudes that can be measured in electroand photoproduction.

Several new algorithms are proposed that in effect transform DAEs (Differential Algebraic Equations) to a special index one form that can be simulated with standard DAE integrators. The transformation to this form is performed without solving linear and/or nonlinear equation systems, the sparsity of the equations is kept, and array equations remain array equations or differentiated versions of ...

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserve the shapeinvariance property presented by primary system. q-deformed generalizations of Morse, Scarf, and ...