The k-zero-divisor hypergraph

Haouaoui, Amor; Benhissi, Ali

doi:10.1007/s11587-011-0117-x

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…SEiVI images of the machined ECAE copper bar obtained at the center and outer radius locations under ^=1 m/s, doc =0.05 mm, and /=0.15 mm/rev 90 deg die, giving a total true strain of 4.6 [5]. Grain sizes were refined from 75 fim to 300 nm, and the resultant NS/UFG copper exhibited a yield stress of 350 MPa and an ultimate tensile stress of 450 MPa, as compared with coarse-grained commercially pure OFHC copper with a yield stress of 51 MPa and an ultimate tensile stress of 256 MPa.…”

Section: Fig 2 Experimental Preparation: (A) Machining Setup Schematmentioning

confidence: 99%

“…Only the outside and inside locations were scanned for the unmachined ECAE bar since the bar is considered to be relatively homogeneous throughout its cross-section [5]. XRD analysis was not conducted for the coarse-grained copper samples because of the difficulty to obtain accurate XRD measurements for coarse grains (>1 /tm).…”

Section: Microstructure Characterized Using Xrdmentioning

confidence: 99%

“…Depending on different operating conditions, SPD-processed materials contain more homogeneous and reasonably equiaxed microstructures, making them 25-100% stronger than materials produced through conventional techniques (cold rolling, drawing, etc.) [2,5]. Such SPD-processed materials are favored for their high strength, wear resistance, ductility, and high strain rate superplasticity [1] and are finding their applications in lightweight engineering and medical industry.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, commercially pure (99.99%) oxygen-free high conductivity (OFHC) ECAE processed NS/UFG copper [5] has been tested for its microstructure stability in dry turning. The paper first introduces the machining setup and experiment design, then the NS/UFG copper grain size and dislocation density are examined to study the potential microstructure evolution using XRD and/or electron microscopy.…”

Section: Introductionmentioning

confidence: 99%

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Study of Machining-Induced Microstructure Variations of Nanostructured/Ultrafine-Grained Copper Using XRD

Huang

Morehead

2011

Journal of Engineering Materials and Technology

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Various methods for the production of bulk nanostructured (NS)/ultrafine-grained (UFG) materials have been developed, including equal channel angular extrusion (ECAE), a form of severe plastic deformation. Using an ECAE NS/UFG copper bar as an example, this study has investigated machining-induced workpiece microstrueture variation using X-ray diffraetion. It has been found that (I) under gentle cutting conditions, there was a 10% increase in the median grain size compared with unmachined ECAE NS/UFG copper bars. Increases in the arithmetic-, area-, and volume-weighted grain sizes were fourui to be 10%, 8%, and 8%, respectively, and (2) an average 27% drop in the dislocation density was observed between the machined and unmachined ECAE copper bars. The dislocation density was shown to have the most reduction (-39%) at the outer radius of the machined ECAE bar where more heat and/or higher pressure were experienced.

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Section: Fig 2 Experimental Preparation: (A) Machining Setup Schematmentioning

confidence: 99%

Section: Microstructure Characterized Using Xrdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Study of Machining-Induced Microstructure Variations of Nanostructured/Ultrafine-Grained Copper Using XRD

Huang

Morehead

2011

Journal of Engineering Materials and Technology

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“…So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. Some papers in this context can be seen in [6] and [7].…”

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confidence: 99%

On characterization of finite modules by hypergraphs

Hamzekolaee

Norouzi

2022

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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With a finite R-module M we associate a hypergraph 𝒞𝒥ℋ R (M) having the set V of vertices being the set of all nontrivial submodules of M. Moreover, a subset Ei of V with at least two elements is a hyperedge if for K, L in Ei there is K ∩ L ≠ = 0 and Ei is maximal with respect to this property. We investigate some general properties of 𝒞𝒥ℋ R (M), providing condition under which 𝒞𝒥ℋ R (M) is connected, and find its diameter. Besides, we study the form of the hypergraph 𝒞𝒥ℋ R (M) when M is semisimple, uniform module and it is a direct sum of its each two nontrivial submodules. Moreover, we characterize finite modules with three nontrivial submodules according to their co-intersection hypergraphs. Finally, we present some illustrative examples for 𝒞𝒥ℋ R (M).

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