Related papers: The structure of multigranular rough sets
We classify $R$-spaces that admit a certain natural $\Gamma$-symmetric structure. We further determine the maximal antipodal sets of these structures.
We study the quantization of systems that contain both ordinary fields with a positive norm and their counterparts obeying different statistics. The systems have novel fermionic symmetries different from the space-time supersymmetry and the…
Antichain based semantics for general rough sets were introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations,…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the…
In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of…
In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…
The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving…
A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices…
We introduce a 2-dimensional lattice model of granular matter. We use a combination of proof and simulation to demonstrate an order/disorder phase transition in the model, to which we associate the granular phenomenon of random close…
Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…
We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
By considering nests on a given space, we explore order-theoretical and topological properties that are closely related to the structure of a nest. In particular, we see how subbases given by two dual nests can be an indicator of how close…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction…