IUMA: Mathematics, Graphics and Computing

Affiliated Research areas

• Mathematics
• Scientific computing and data processing
• Products and Processes Engineering

Scientific Areas

• Not available

Keywords

• Lidar
• Proofs without words
• Sequences
• Bisection
• Engineering
• Simplices
• point clouds
• Proofs
• Fibonacci
• Algorithm
• Combinatorics
• Meshes
• Refinement
• Applied Mathematics
• Meshes

Summary

- Generalized fibonacci successions: Generalized Fibonacci sequences. Generalized Fibonacci integer sequences and related issues. Generalized k-Fibonacci integer sequences are studied. These sequences generalizing among others, the classic Fibonacci sequence and the Pell sequence were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers have been deduced. Other related issues are k-Lucas sequences, matrix methods, spirals and metallic numbers, combinatorial aspects, etc.
- Words without words: Math proofs of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
- Bissection -based sympons partitions: Study of the mathematical properties of partitions of simplices and meshes. Partition based on the bisection of simplices.
- Point clouds, lidar: algoritmos y aplicaciones: Geometric structures based on point clouds, meshes, with geospatial and urban applications, and representation of objects.
- Mesh generation and refinement algorithms: Mesh generation and refinement algorithms. Development and application of refinement and derefinement algorithms. The mesh generation algorithms and refinements are geometric techniques to discretize geometrical domains in any dimensions. Research activities in this line focus on the design, development and validation of new geometrical partitions and their implementation through refinement and coarsening algorithms. Furthermore, using mathematical methods we address the characterization and new properties of these algorithms and partitions as for example, convergence, quality, finiteness, non-degeneracy etc.