Suppose G is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids, and show G is integrable if and only if the groupoid C∗-algebra C∗(G) has bounded trace.

In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system (B,L,θ,Iα). For the first groupoid, associate an inverse semigroup to and use tight spectrum T as unit space groupoid Γ(B,L,θ,Iα) that is isomorphic Gtight. The other one defined Renault-Deaconu Γ(∂E,σE) arising topological correspondence E associated with system. We then prove homeomorphi...

The degradable polymers poly(orthoester) (POE), poly(L-lactic acid) (PLA), and the nondegradable polymers polysulfone (PSF), polyethylene (PE), and poly(ether ether ketone) (PEEK) were exposed to cultures of Staphylococcus epidermidis, Pseudomonas aeruginosa, or Escherichia coli. Bacteria washed and resuspended in phosphate buffered saline (PBS) adhered to polymers in amounts nearly twice those...

The tribology properties of TiO2/POE, SiO2/POE and TiO2-SiO2/POE nanolubricants were investigated for an automotive air-conditioning system with electrically-driven compressor (EDC). A two-step preparation method was used in dispersing TiO2 SiO2 nanoparticles into Polyol-ester (POE)-based lubricant at different volume concentrations 0.01 to 0.1%. coefficient friction (COF) wear scar diameter (W...

The aim of this paper is to obtain a group-2-groupoid as 2-groupoid object in the category groups and also special kind an internal group-groupoids. Corresponding group-2-groupoids, we some categorical structures related crossed modules group-groupoids prove equivalences between them. These results enable us 2-dimensional notions

Groupoids graded by the groupoid of bijections between finite sets admit generating functions which encode cardinalities their components. As suggested in work Baez and Dolan, we use analytic continuation such to define a complex-valued cardinality for groupoids whose usual diverges. The complex nature invariant is shown reflect recursion structure refer as ‘nested equivalence’.