In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

If we fix a spanning subgraph H of a graph G, we can define a chromatic number of H with respect to G and we show that it coincides with the chromatic number of a double covering of G with co-support H. We also find a few estimations for the chromatic numbers of H with respect to G.

A nonabelian finite flavor group G ⊂ SO(3) can have double covering G ′ ⊂ SU(2) such that G 6⊂ G ′ . This situation is not contradictory, but quite natural, and we give explicit examples such as G = Dn, G ′ = Q2n and G = T,G ′ = T ′ . This observation can be crucial in particle theory model building. [email protected] [email protected] [email protected]

We give a new geometric obstruction to the iterated Bing double of a knot being a slice link: for n > 1 the (n + 1)st iterated Bing double of a knot is rationally slice if and only if the nth iterated Bing double of the knot is rationally slice. The main technique of the proof is a covering link construction simplifying a given link. We prove certain similar geometric obstructions for n ≤ 1 as ...

‎an  oriented perfect path double cover (oppdc) of a‎ ‎graph $g$ is a collection of directed paths in the symmetric‎ ‎orientation $g_s$ of‎ ‎$g$ such that‎ ‎each arc‎ ‎of $g_s$ lies in exactly one of the paths and each‎ ‎vertex of $g$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎maxov{'a} and ne{v{s}}et{v{r}}il (discrete‎ ‎math‎. ‎276 (2004) 287-294) conjectured that ...

Rough set theory provides a systematic way for rule extraction, attribute reduction and knowledge classification in information systems. Some measurements are important in rough sets. For example, information entropy, knowledge dependency are useful in attribute reduction algorithms. This paper proposes the concepts of the lower and upper covering numbers to establish measurements in covering-b...

We report on low-temperature measurements in a fully tunable carbon nanotube double quantum dot. A new fabrication technique has been used for the top-gates in order to avoid covering the whole nanotube with an oxide layer as in previous experiments. The top-gates allow us to form single dots and control the coupling between them, and we observe 4-fold shell filling. We perform inelastic transp...

We report on a commercially reproducible silicon wafer with a high-reflectance buried distributed Bragg reflector (DBR). The substrate consists of a two-period DBR fabricated using a double silicon-on-insulator (SOI) process. The buried DBR provides a 90% reflecting surface. We have fabricated resonant cavity-enhanced Si photodetectors with 40% quantum efficiency at 860 nm and a full-width at h...