Free Objects in the Category of Geometries

The categories of lattice-valued maps, equalities, free objects, and $mathcal C$-reticulation

In this paper, we study the concept of $mathcal C$-reticulation for the category $mathcal C$ whose objects are lattice-valued maps. The relation between the free objects in $mathcal C$ and the $mathcal C$-reticulation of rings and modules is discussed. Also, a method to construct $mathcal C$-reticulation is presented, in the case where $mathcal C$ is equational. Some relations between the conce...

A Novel Toolbox for Generating Realistic Biological Cell Geometries for Electromagnetic Microdosimetry

Researchers in bioelectromagnetics often require realistic tissue, cellular and sub-cellular geometry models for their simulations. However, biological shapes are often extremely irregular, while conventional geometrical modeling tools on the market cannot meet the demand for fast and efficient construction of irregular geometries. We have designed a free, user-friendly tool in MATLAB that comb...

ON Q-BITOPOLOGICAL SPACES

We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski ob...

Category of Polygroup Objects

Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit

 The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...