Topological reducibilities for discontinuous functions and their structures

Algorithmic reducibilities of algebraic structures

Using admissibility for a computable model theory for uncountable structures

TOPOLOGICAL OPTIMIZATION OF VIBRATING CONTINUUM STRUCTURES FOR OPTIMAL NATURAL EIGENFREQUENCY

Keeping the eigenfrequencies of a structure away from the external excitation frequencies is one of the main goals in the design of vibrating structures in order to avoid risk of resonance. This paper is devoted to the topological design of freely vibrating continuum structures with the aim of maximizing the fundamental eigenfrequency. Since in the process of topology optimization some areas of...

Effective Reducibilities on Structures and Degrees of Presentability

In this survey paper we consider presentations of structures in admissible sets and some effective reducibilities between structures and their degrees of presentability. Degrees of Σ-definability of structures, as well as degrees of presentability with respect to different effective reducibilities, are natural measures of complexity which are total, i.e. defined for any structure. We also consi...

Cell Decomposition and Dimension Functions in First-order Topological Structures

The notion of a cell and that of a cell decomposition has been a central one in the study of certain first-order theories. A cell is a particular kind of definable set. The notion of a cell was first explicitly considered in [8], in the context of the theory of real closed fields. Collins defined a class of cells in this context, and showed that every definable subset of a real closed field is ...

Topological Approximation and Compression of Functions and Their Wavelet Expansions