We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented, while maintaining its non-reduced structure. This yields a more subtle invariant, called the schemic Grothendieck ring, in which we can formulate a form of integration resembling Kontsevich’s motivic integration via arc schemes. In view of i...

We propose a great circle arc detector in a scene represented by an equirectangular image, i.e. a spherical image of the 360 longitude and 180 latitude field of view. Since the straight lines appears curved in equirectangular images, the standard line detection algorithm cannot be used directly in this context. We extend the LSD method (Gioi et al., 2010) to deal with the equirectangular images...

This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that reali...

We deal with different algorithmic questions regarding properly arc-colored s-t trails, paths and circuits in arc-colored digraphs. Given an arc-colored digraph D with c ≥ 2 colors, we show that the problem of determining the maximum number of arc disjoint properly arc-colored s-t trails can be solved in polynomial time. Surprisingly, we prove that the determination of a properly arc-colored s-...

Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The longest arc-preserving common subsequence problem has been introduced in [1], [2] as a framework for studying the similarity of arc-annotated sequences. In this paper, we consider arc-annotated sequences with various arc structures. Mathematics Subject Classification: 68Q15

In this sequel to the paper ‘Arc-transitive abelian regular covers of cubic graphs’, all arc-transitive abelian regular covers of the Heawood graph are found. These covers include graphs that are 1-arc-regular, and others that are 4-arc-regular (like the Heawood graph). Remarkably, also some of these covers are 2-arc-regular.

The present paper describes the arc-length continuation method; a mathematical technique that can solve a wide variety of chemical engineering problems. Several case studies involving distillation, reaction engineering, and thermodynamics are treated with the help of this method. The approach is powerful enough to elucidate situations when several turning points occur. Finally, the authors conc...

Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinal...